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Title: Watch and Clock Escapements
       A Complete Study in Theory and Practice of the Lever, Cylinder and Chronometer Escapements, Together with a Brief Account of the Origin and Evolution of the Escapement in Horology


Author: Anonymous



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WATCH AND CLOCK ESCAPEMENTS

A Complete Study in Theory and Practice of the Lever, Cylinder and
Chronometer Escapements, Together with a Brief Account of the Origin
and Evolution of the Escapement in Horology

Compiled from the well-known Escapement Serials
published in The Keystone

Nearly Two Hundred Original Illustrations







Published by
The Keystone
The Organ of the Jewelry and Optical Trades
19th & Brown Sts., Philadelphia, U.S.A.

1904

All Rights Reserved
Copyright, 1904, By B. Thorpe,
Publisher of the Keystone.




PREFACE


Especially notable among the achievements of The Keystone in the field
of horology were the three serials devoted to the lever, cylinder and
chronometer escapements. So highly valued were these serials when
published that on the completion of each we were importuned to republish
it in book form, but we deemed it advisable to postpone such publication
until the completion of all three, in order that the volume should be a
complete treatise on the several escapements in use in horology. The
recent completion of the third serial gave us the opportunity to
republish in book form, and the present volume is the result. We present
it to the trade and students of horology happy in the knowledge that its
contents have already received their approval. An interesting addition
to the book is the illustrated story of the escapements, from the first
crude conceptions to their present perfection.




  CONTENTS


  CHAPTER I.

  THE DETACHED LEVER ESCAPEMENT      9


  CHAPTER II.

  THE CYLINDER ESCAPEMENT          111


  CHAPTER III.

  THE CHRONOMETER ESCAPEMENT       131


  CHAPTER IV.

  HISTORY OF ESCAPEMENTS           153


  CHAPTER V.

  PUTTING IN A NEW CYLINDER        169


  INDEX                            177






WATCH AND CLOCK ESCAPEMENTS




CHAPTER I.

THE DETACHED LEVER ESCAPEMENT.


In this treatise we do not propose to go into the history of this
escapement and give a long dissertation on its origin and evolution, but
shall confine ourselves strictly to the designing and construction as
employed in our best watches. By designing, we mean giving full
instructions for drawing an escapement of this kind to the best
proportions. The workman will need but few drawing instruments, and a
drawing-board about 15" by 18" will be quite large enough. The necessary
drawing-instruments are a T-square with 15" blade; a scale of inches
divided into decimal parts; two pairs dividers with pen and pencil
points--one pair of these dividers to be 5" and the other 6"; one ruling
pen. Other instruments can be added as the workman finds he needs them.
Those enumerated above, however, will be all that are absolutely
necessary.

[Illustration: Fig. 1]

We shall, in addition, need an arc of degrees, which we can best make
for ourselves. To construct one, we procure a piece of No. 24 brass,
about 5½" long by 1¼" wide. We show such a piece of brass at _A_,
Fig. 1. On this piece of brass we sweep two arcs with a pair of dividers
set at precisely 5", as shown (reduced) at _a a_ and _b b_. On these
arcs we set off the space held in our dividers--that is 5"--as shown at
the short radial lines at each end of the two arcs. Now it is a
well-known fact that the space embraced by our dividers contains exactly
sixty degrees of the arcs _a a_ and _b b_, or one-sixth of the entire
circle; consequently, we divide the arcs _a a_ and _b b_ into sixty
equal parts, to represent degrees, and at one end of these arcs we
halve five spaces so we can get at half degrees.

[Illustration: Fig. 2]

Before we take up the details of drawing an escapement we will say a few
words about "degrees," as this seems to be something difficult to
understand by most pupils in horology when learning to draw parts of
watches to scale. At Fig. 2 we show several short arcs of fifteen
degrees, all having the common center _g_. Most learners seem to have an
idea that a degree must be a specific space, like an inch or a foot. Now
the first thing in learning to draw an escapement is to fix in our minds
the fact that the extent of a degree depends entirely on the radius of
the arc we employ. To aid in this explanation we refer to Fig. 2. Here
the arcs _c_, _d_, _e_ and _f_ are all fifteen degrees, although the
linear extent of the degree on the arc _c_ is twice that of the degree
on the arc _f_. When we speak of a degree in connection with a circle we
mean the one-three-hundred-and-sixtieth part of the periphery of such a
circle. In dividing the arcs _a a_ and _b b_ we first divide them into
six spaces, as shown, and each of these spaces into ten minor spaces, as
is also shown. We halve five of the degree spaces, as shown at _h_. We
should be very careful about making the degree arcs shown at Fig. 1, as
the accuracy of our drawings depends a great deal on the perfection of
the division on the scale _A_. In connection with such a fixed scale of
degrees as is shown at Fig. 1, a pair of small dividers, constantly set
to a degree space, is very convenient.


MAKING A PAIR OF DIVIDERS.

[Illustration: Fig. 3]

To make such a pair of small dividers, take a piece of hard sheet brass
about 1/20" thick, ¼" wide, 1½" long, and shape it as shown at Fig.
3. It should be explained, the part cut from the sheet brass is shown
below the dotted line _k_, the portion above (_C_) being a round handle
turned from hard wood or ivory. The slot _l_ is sawn in, and two holes
drilled in the end to insert the needle points _i i_. In making the slot
_l_ we arrange to have the needle points come a little too close
together to agree with the degree spaces on the arcs _a a_ and _b b_. We
then put the small screw _j_ through one of the legs _D''_, and by
turning _j_, set the needle points _i i_ to exactly agree with the
degree spaces. As soon as the points _i i_ are set correctly, _j_ should
be soft soldered fast.

The degree spaces on _A_ are set off with these dividers and the spaces
on _A_ very carefully marked. The upper and outer arc _a a_ should have
the spaces cut with a graver line, while the lower one, _b b_ is best
permanently marked with a carefully-made prick punch. After the arc _a a_
is divided, the brass plate _A_ is cut back to this arc so the
divisions we have just made are on the edge. The object of having two
arcs on the plate _A_ is, if we desire to get at the number of degrees
contained in any arc of a 5" radius we lay the scale _A_ so the edge
agrees with the arc _a a_, and read off the number of degrees from the
scale. In setting dividers we employ the dotted spaces on the arc _b b_.


DELINEATING AN ESCAPE WHEEL.

[Illustration: Fig. 4]

We will now proceed to delineate an escape wheel for a detached lever.
We place a piece of good drawing-paper on our drawing-board and provide
ourselves with a very hard (HHH) drawing-pencil and a bottle of liquid
India ink. After placing our paper on the board, we draw, with the aid
of our T-square, a line through the center of the paper, as shown at
_m m_, Fig. 4. At 5½" from the lower margin of the paper we establish
the point _p_ and sweep the circle _n n_ with a radius of 5". We have
said nothing about stretching our paper on the drawing-board; still,
carefully-stretched paper is an important part of nice and correct
drawing. We shall subsequently give directions for properly stretching
paper, but for the present we will suppose the paper we are using is
nicely tacked to the face of the drawing-board with the smallest tacks
we can procure. The paper should not come quite to the edge of the
drawing-board, so as to interfere with the head of the T-square. We are
now ready to commence delineating our escape wheel and a set of pallets
to match.

The simplest form of the detached lever escapement in use is the one
known as the "ratchet-tooth lever escapement," and generally found in
English lever watches. This form of escapement gives excellent results
when well made; and we can only account for it not being in more general
use from the fact that the escape-wheel teeth are not so strong and
capable of resisting careless usage as the club-tooth escape wheel.

It will be our aim to convey broad ideas and inculcate general
principles, rather than to give specific instructions for doing "one
thing one way." The ratchet-tooth lever escapements of later dates
have almost invariably been constructed on the ten-degree
lever-and-pallet-action plan; that is, the fork and pallets were
intended to act through this arc. Some of the other specimens of this
escapement have larger arcs--some as high as twelve degrees.


PALLET-AND-FORK ACTION.

[Illustration: Fig. 5]

We illustrate at Fig. 5 what we mean by ten degrees of pallet-and-fork
action. If we draw a line through the center of the pallet staff, and
also through the center of the fork slot, as shown at _a b_, Fig. 5, and
allow the fork to vibrate five degrees each side of said lines _a b_, to
the lines _a c_ and _a c'_, the fork has what we term ten-degree pallet
action. If the fork and pallets vibrate six degrees on each side of the
line _a b_--that is, to the lines _a d_ and _a d'_--we have twelve
degrees pallet action. If we cut the arc down so the oscillation is only
four and one-quarter degrees on each side of _a b_, as indicated by the
lines _a s_ and _a s'_, we have a pallet-and-fork action of eight and
one-half degrees; which, by the way, is a very desirable arc for a
carefully-constructed escapement.

The controlling idea which would seem to rule in constructing a detached
lever escapement, would be to make it so the balance is free of the
fork; that is, detached, during as much of the arc of the vibration of
the balance as possible, and yet have the action thoroughly sound and
secure. Where a ratchet-tooth escapement is thoroughly well-made of
eight and one-half degrees of pallet-and-fork action, ten and one-half
degrees of escape-wheel action can be utilized, as will be explained
later on.

We will now resume the drawing of our escape wheel, as illustrated at
Fig. 4. In the drawing at Fig. 6 we show the circle _n n_, which
represents the periphery of our escape wheel; and in the drawing we are
supposed to be drawing it ten inches in diameter.

We produce the vertical line _m_ passing through the center _p_ of the
circle _n_. From the intersection of the circle _n_ with the line _m_
at _i_ we lay off thirty degrees on each side, and establish the points
_e f_; and from the center _p_, through these points, draw the radial
lines _p e'_ and _p f'_. The points _f e_, Fig. 6, are, of course, just
sixty degrees apart and represent the extent of two and one-half teeth
of the escape wheel. There are two systems on which pallets for lever
escapements are made, viz., equidistant lockings and circular pallets.
The advantages claimed for each system will be discussed subsequently.
For the first and present illustration we will assume we are to employ
circular pallets and one of the teeth of the escape wheel resting on the
pallet at the point _f_; and the escape wheel turning in the direction
of the arrow _j_. If we imagine a tooth as indicated at the dotted
outline at _D_, Fig. 6, pressing against a surface which coincides with
the radial line _p f_, the action would be in the direction of the line
_f h_ and at right angles to _p f_. If we reason on the action of the
tooth _D_, as it presses against a pallet placed at _f_, we see the
action is neutral.

[Illustration: Fig. 6]


ESTABLISHING THE CENTER OF PALLET STAFF.

[Illustration: Fig. 7]

With a fifteen-tooth escape wheel each tooth occupies twenty-four
degrees, and from the point _f_ to _e_ would be two and one-half
tooth-spaces. We show the dotted points of four teeth at _D D' D''D'''_.
To establish the center of the pallet staff we draw a line at
right angles to the line _p e'_ from the point _e_ so it intersects the
line _f h_ at _k_. For drawing a line at right angles to another line,
as we have just done, a hard-rubber triangle, shaped as shown at _C_,
Fig. 7, can be employed. To use such a triangle, we place it so the
right, or ninety-degrees angle, rests at _e_, as shown at the dotted
triangle _C_, Fig. 6, and the long side coincides with the radial line
_p e'_. If the short side of the hard-rubber triangle is too short, as
indicated, we place a short ruler so it rests against the edge, as shown
at the dotted line _g e_, Fig. 7, and while holding it securely down on
the drawing we remove the triangle, and with a fine-pointed pencil draw
the line _e g_, Fig. 6, by the short rule. Let us imagine a flat surface
placed at _e_ so its face was at right angles to the line _g e_, which
would arrest the tooth _D''_ after the tooth _D_ resting on _f_ had been
released and passed through an arc of twelve degrees. A tooth resting on
a flat surface, as imagined above, would also rest dead. As stated
previously, the pallets we are considering have equidistant locking
faces and correspond to the arc _l l_, Fig. 6.

In order to realize any power from our escape-wheel tooth, we must
provide an impulse face to the pallets faced at _f e_; and the problem
before us is to delineate these pallets so that the lever will be
propelled through an arc of eight and one-half degrees, while the escape
wheel is moving through an arc of ten and one-half degrees. We make the
arc of fork action eight and one-half degrees for two reasons--(1)
because most text-books have selected ten degrees of fork-and-pallet
action; (2) because most of the finer lever escapements of recent
construction have a lever action of less than ten degrees.


LAYING OUT ESCAPE-WHEEL TEETH.

To "lay out" or delineate our escape-wheel teeth, we continue our
drawing shown at Fig. 6, and reproduce this cut very nearly at Fig. 8.
With our dividers set at five inches, we sweep the short arc _a a'_ from
_f_ as a center. It is to be borne in mind that at the point _f_ is
located the extreme point of an escape-wheel tooth. On the arc _a a_ we
lay off from _p_ twenty-four degrees, and establish the point _b_; at
twelve degrees beyond _b_ we establish the point _c_. From _f_ we draw
the lines _f b_ and _f c_; these lines establishing the form and
thickness of the tooth _D_. To get the length of the tooth, we take in
our dividers one-half a tooth space, and on the radial line _p f_
establish the point _d_ and draw circle _d' d'_.

To facilitate the drawing of the other teeth, we draw the circles _d' c'_,
to which the lines _f b_ and _f c_ are tangent, as shown. We divide
the circle _n n_, representing the periphery of our escape wheel, into
fifteen spaces, to represent teeth, commencing at _f_ and continued as
shown at _o o_ until the entire wheel is divided. We only show four
teeth complete, but the same methods as produced these will produce them
all. To briefly recapitulate the instructions for drawing the teeth for
the ratchet-tooth lever escapement: We draw the face of the teeth at an
angle of twenty-four degrees to a radial line; the back of the tooth at
an angle of thirty-six degrees to the same radial line; and make teeth
half a tooth-space deep or long.

[Illustration: Fig. 8]

We now come to the consideration of the pallets and how to delineate
them. To this we shall add a careful analysis of their action. Let us,
before proceeding further, "think a little" over some of the factors
involved. To aid in this thinking or reasoning on the matter, let us
draw the heavy arc _l_ extending from a little inside of the circle _n_
at _f_ to the circle _n_ at _e_. If now we imagine our escape wheel to
be pressed forward in the direction of the arrow _j_, the tooth _D_
would press on the arc _l_ and be held. If, however, we should revolve
the arc _l_ on the center _k_ in the direction of the arrow _i_, the
tooth _D_ would _escape_ from the edge of _l_ and the tooth _D''_ would
pass through an arc (reckoning from the center _p_) of twelve degrees,
and be arrested by the inside of the arc _l_ at _e_. If we now should
reverse the motion and turn the arc _l_ backward, the tooth at _e_
would, in turn, be released and the tooth following after _D_ (but not
shown) would engage _l_ at _f_. By supplying motive to revolve the
escape wheel (_E_) represented by the circle _n_, and causing the arc
_l_ to oscillate back and forth in exact intervals of time, we should
have, in effect, a perfect escapement. To accomplish automatically such
oscillations is the problem we have now on hand.


HOW MOTION IS OBTAINED.

In clocks, the back-and-forth movement, or oscillating motion, is
obtained by employing a pendulum; in a movable timepiece we make use of
an equally-poised wheel of some weight on a pivoted axle, which device
we term a balance; the vibrations or oscillations being obtained by
applying a coiled spring, which was first called a "pendulum spring,"
then a "balance spring," and finally, from its diminutive size and coil
form, a "hairspring." We are all aware that for the motive power for
keeping up the oscillations of the escaping circle _l_ we must contrive
to employ power derived from the teeth _D_ of the escape wheel. About
the most available means of conveying power from the escape wheel to the
oscillating arc _l_ is to provide the lip of said arc with an inclined
plane, along which the tooth which is disengaged from _l_ at _f_ to
slide and move said arc _l_ through--in the present instance an arc of
eight and one-half degrees, during the time the tooth _D_ is passing
through ten and one-half degrees. This angular motion of the arc _l_ is
represented by the radial lines _k f'_ and _k r_, Fig. 8. We desire to
impress on the reader's mind the idea that each of these angular motions
is not only required to be made, but the motion of one mobile must
convey power to another mobile.

In this case the power conveyed from the mainspring to the escape wheel
is to be conveyed to the lever, and by the lever transmitted to the
balance. We know it is the usual plan adopted by text-books to lay down
a certain formula for drawing an escapement, leaving the pupil to work
and reason out the principles involved in the action. In the plan we
have adopted we propose to induct the reader into the why and how, and
point out to him the rules and methods of analysis of the problem, so
that he can, if required, calculate mathematically exactly how many
grains of force the fork exerts on the jewel pin, and also how much (or,
rather, what percentage) of the motive power is lost in various "power
leaks," like "drop" and lost motion. In the present case the mechanical
result we desire to obtain is to cause our lever pivoted at _k_ to
vibrate back and forth through an arc of eight and one-half degrees;
this lever not only to vibrate back and forth, but also to lock and hold
the escape wheel during a certain period of time; that is, through the
period of time the balance is performing its excursion and the jewel pin
free and detached from the fork.

We have spoken of paper being employed for drawings, but for very
accurate delineations we would recommend the horological student to make
drawings on a flat metal plate, after perfectly smoothing the surface
and blackening it by oxidizing.


PALLET-AND-FORK ACTION.

By adopting eight and one-half degrees pallet-and-fork action we can
utilize ten and one-half degrees of escape-wheel action. We show at _A A'_,
Fig. 9, two teeth of a ratchet-tooth escape wheel reduced one-half;
that is, the original drawing was made for an escape wheel ten inches in
diameter. We shall make a radical departure from the usual practice in
making cuts on an enlarged scale, for only such parts as we are talking
about. To explain, we show at Fig. 10 about one-half of an escape wheel
one eighth the size of our large drawing; and when we wish to show some
portion of such drawing on a larger scale we will designate such
enlargement by saying one-fourth, one-half or full size.

[Illustration: Fig. 9]

At Fig. 9 we show at half size that portion of our escapement embraced
by the dotted lines _d_, Fig. 10. This plan enables us to show very
minutely such parts as we have under consideration, and yet occupy but
little space. The arc _a_, Fig. 9, represents the periphery of the
escape wheel. On this line, ten and one-half degrees from the point of
the tooth _A_, we establish the point _c_ and draw the radial line
_c c'_. It is to be borne in mind that the arc embraced between the points
_b_ and _c_ represents the duration of contact between the tooth _A_ and
the entrance pallet of the lever. The space or short arc _c n_
represents the "drop" of the tooth.

This arc of one and one-half degrees of escape-wheel movement is a
complete loss of six and one-fourth per cent. of the entire power of the
mainspring, as brought down to the escapement; still, up to the present
time, no remedy has been devised to overcome it. All the other
escapements, including the chronometer, duplex and cylinder, are quite
as wasteful of power, if not more so. It is usual to construct
ratchet-tooth pallets so as to utilize but ten degrees of escape-wheel
action; but we shall show that half a degree more can be utilized by
adopting the eight and one-half degree fork action and employing a
double-roller safety action to prevent over-banking.

[Illustration: Fig. 10]

From the point _e_, which represents the center of the pallet staff, we
draw through _b_ the line _e f_. At one degree below _e f_ we draw the
line _e g_, and seven and one-half degrees below the line _e g_ we draw
the line _e h_. For delineating the lines _e g_, etc., correctly, we
employ a degree-arc; that is, on the large drawing we are making we
first draw the line _e b f_, Fig. 10, and then, with our dividers set at
five inches, sweep the short arc _i_, and on this lay off first one
degree from the intersection of _f e_ with the arc _i_, and through this
point draw the line _e g_.

From the intersection of the line _f e_ with the arc _i_ we lay off
eight and one-half degrees, and through this point draw the line _e h_.
Bear in mind that we are drawing the pallet at _B_ to represent one with
eight and one-half degrees fork-and-pallet action, and with equidistant
lockings. If we reason on the matter under consideration, we will see
the tooth _A_ and the pallet _B_, against which it acts, part or
separate when the tooth arrives at the point _c_; that is, after the
escape wheel has moved through ten and one-half degrees of angular
motion, the tooth drops from the impulse face of the pallet and falls
through one and one-half degrees of arc, when the tooth _A''_, Fig. 10,
is arrested by the exit pallet.

To locate the position of the inner angle of the pallet _B_, sweep the
short arc _l_ by setting the dividers so one point or leg rests at the
center _e_ and the other at the point _c_. Somewhere on this arc _l_ is
to be located the inner angle of our pallet. In delineating this angle,
Moritz Grossman, in his "Prize Essay on the Detached Lever Escapement,"
makes an error, in Plate III of large English edition, of more than his
entire lock, or about two degrees. We make no apologies for calling
attention to this mistake on the part of an authority holding so high a
position on such matters as Mr. Grossman, because a mistake is a
mistake, no matter who makes it.

We will say no more of this error at present, but will farther on show
drawings of Mr. Grossman's faulty method, and also the correct method of
drawing such a pallet. To delineate the locking face of our pallet, from
the point formed by the intersection of the lines _e g b b'_, Fig. 9, as
a center, we draw the line _j_ at an angle of twelve degrees to _b b''_.
In doing this we employ the same method of establishing the angle as we
made use of in drawing the lines _e g_ and _e h_, Fig. 10. The line _j_
establishes the locking face of the pallet _B_. Setting the locking face
of the pallet at twelve degrees has been found in practice to give a
safe "draw" to the pallet and keep the lever secure against the bank. It
will be remembered the face of the escape-wheel tooth was drawn at
twenty-four degrees to a radial line of the escape wheel, which, in this
instance, is the line _b b'_, Fig. 9. It will now be seen that the angle
of the pallet just halves this angle, and consequently the tooth _A_
only rests with its point on the locking face of the pallet. We do not
show the outlines of the pallet _B_, because we have not so far pointed
out the correct method of delineating it.


METHODS OF MAKING GOOD DRAWING INSTRUMENTS.

Perhaps we cannot do our readers a greater favor than to digress from
the study of the detached lever escapement long enough to say a few
words about drawing instruments and tablets or surfaces on which to
delineate, with due precision, mechanical designs or drawings. Ordinary
drawing instruments, even of the higher grades, and costing a good deal
of money, are far from being satisfactory to a man who has the proper
idea of accuracy to be rated as a first-class mechanic. Ordinary
compasses are obstinate when we try to set them to the hundredth of an
inch; usually the points are dull and ill-shapen; if they make a
puncture in the paper it is unsightly.

Watchmakers have one advantage, however, because they can very easily
work over a cheap set of drawing instruments and make them even superior
to anything they can buy at the art stores. To illustrate, let us take a
cheap pair of brass or German-silver five-inch dividers and make them
over into needle points and "spring set." To do this the points are cut
off at the line _a a_, Fig 11, and a steel tube is gold-soldered on each
leg. The steel tube is made by taking a piece of steel wire which will
fit a No. 16 chuck of a Whitcomb lathe, and drilling a hole in the end
about one-fourth of an inch deep and about the size of a No. 3 sewing
needle. We Show at Fig. 12 a view of the point _A'_, Fig. 11, enlarged,
and the steel tube we have just drilled out attached at _C_. About the
best way to attach _C_ is to solder. After the tube _C_ is attached a
hole is drilled through _A'_ at _d_, and the thumb-screw _d_ inserted.
This thumb-screw should be of steel, and hardened and tempered. The use
of this screw is to clamp the needle point. With such a device as the
tube _C_ and set-screw _d_, a No. 3 needle is used for a point; but for
drawings on paper a turned point, as shown at Fig 13, is to be
preferred. Such points can be made from a No. 3 needle after softening
enough to be turned so as to form the point _c_. This point at the
shoulder _f_ should be about 12/1000 of an inch, or the size of a
fourth-wheel pivot to an eighteen size movement.

[Illustration: Fig. 11]

[Illustration: Fig. 12]

[Illustration: Fig. 13]

[Illustration: Fig. 14]

The idea is, when drawing on paper the point _c_ enters the paper. For
drawing on metal the form of the point is changed to a simple cone, as
shown at _B'_ _c_, Fig. 13. such cones can be turned carefully, then
hardened and tempered to a straw color; and when they become dull, can
be ground by placing the points in a wire chuck and dressing them up
with an emery buff or an Arkansas slip. The opposite leg of the dividers
is the one to which is attached the spring for close setting of the
points.

In making this spring, we take a piece of steel about two and
one-fourth inches long and of the same width as the leg of the divider,
and attach it to the inside of the leg as shown at Fig. 14, where _D_
represents the spring and _A_ the leg of the dividers. The spring _D_
has a short steel tube _C''_ and set-screw _d''_ for a fine point like
_B_ or _B'_. In the lower end of the leg _A_, Fig. 14, is placed the
milled-head screw _g_, which serves to adjust the two points of the
dividers to very close distances. The spring _D_ is, of course, set so
it would press close to the leg _A_ if the screw _g_ did not force it
away.


SPRING AND ADJUSTING SCREW FOR DRAWING INSTRUMENTS.

[Illustration: Fig. 15]

It will be seen that we can apply a spring _D_ and adjusting screw
opposite to the leg which carries the pen or pencil point of all our
dividers if we choose to do so; but it is for metal drawing that such
points are of the greatest advantage, as we can secure an accuracy very
gratifying to a workman who believes in precision. For drawing circles
on metal, "bar compasses" are much the best, as they are almost entirely
free from spring, which attends the jointed compass. To make (because
they cannot be bought) such an instrument, take a piece of flat steel,
one-eighth by three-eighths of an inch and seven inches long, and after
turning and smoothing it carefully, make a slide half an inch wide, as
shown at Fig. 15, with a set-screw _h_ on top to secure it at any point
on the bar _E_. In the lower part of the slide _F_ is placed a steel
tube like _C_, shown in Figs. 12 and 14, with set-screw for holding
points like _B B'_, Fig. 13. At the opposite end of the bar _E_ is
placed a looped spring _G_, which carries a steel tube and point like
the spring _D_, Fig. 14. Above this tube and point, shown at _j_, Fig.
15, is placed an adjustment screw _k_ for fine adjustment. The inner end
of the screw _k_ rests against the end of the bar _E_. The tendency of
the spring _G_ is to close upon the end of _E_; consequently if we make
use of the screw _k_ to force away the lower end of _G_, we can set the
fine point in _j_ to the greatest exactness.

The spring _G_ is made of a piece of steel one-eighth of an inch
square, and secured to the bar _E_ with a screw and steady pins at _m_.
A pen and pencil point attachment can be added to the spring _G_; but in
case this is done it would be better to make another spring like _G_
without the point _j_, and with the adjusting screw placed at _l_. In
fitting pen and pencil points to a spring like _G_ it would probably be
economical to make them outright; that is, make the blades and screw for
the ruling pen and a spring or clamping tube for the pencil point.


CONSIDERATION OF DETACHED LEVER ESCAPEMENT RESUMED.

We will now, with our improved drawing instruments, resume the
consideration of the ratchet-tooth lever escapement. We reproduce at
Fig. 16 a portion of diagram III, from Moritz Grossmann's "Prize Essay
on the Detached Lever Escapement," in order to point out the error in
delineating the entrance pallet to which we previously called attention.
The cut, as we give it, is not quite one-half the size of Mr.
Grossmann's original plate.

In the cut we give the letters of reference employed the same as on the
original engraving, except where we use others in explanation. The
angular motion of the lever and pallet action as shown in the cut is ten
degrees; but in our drawing, where we only use eight and one-half
degrees, the same mistake would give proportionate error if we did not
take the means to correct it. The error to which we refer lies in
drawing the impulse face of the entrance pallet. The impulse face of
this pallet as drawn by Mr. Grossmann would not, from the action of the
engaging tooth, carry this pallet through more than eight degrees of
angular motion; consequently, the tooth which should lock on the exit
pallet would fail to do so, and strike the impulse face.

We would here beg to add that nothing will so much instruct a person
desiring to acquire sound ideas on escapements as making a large model.
The writer calls to mind a wood model of a lever escapement made by one
of the "boys" in the Elgin factory about a year or two after Mr.
Grossmann's prize essay was published. It went from hand to hand and did
much toward establishing sound ideas as regards the correct action of
the lever escapement in that notable concern.

If a horological student should construct a large model on the lines
laid down in Mr. Grossmann's work, the entrance pallet would be faulty
in form and would not properly perform its functions. Why? perhaps says
our reader. In reply let us analyze the action of the tooth _B_ as it
rests on the pallet _A_. Now, if we move this pallet through an angular
motion of one and one-half degrees on the center _g_ (which also
represents the center of the pallet staff), the tooth _B_ is disengaged
from the locking face and commences to slide along the impulse face of
the pallet and "drops," that is, falls from the pallet, when the inner
angle of the pallet is reached.

[Illustration: Fig. 16]

This inner angle, as located by Mr. Grossmann, is at the intersection of
the short arc _i_ with the line _g n_, which limits the ten-degree
angular motion of the pallets. If we carefully study the drawing, we
will see the pallet has only to move through eight degrees of angular
motion of the pallet staff for the tooth to escape, _because the tooth
certainly must be disengaged when the inner angle of the pallet reaches
the peripheral line a_. The true way to locate the position of the inner
angle of the pallet, is to measure down on the arc _i_ ten degrees from
its intersection with the peripheral line _a_ and locate a point to
which a line is drawn from the intersection of the line _g m_ with the
radial line _a c_, thus defining the inner angle of the entrance pallet.
We will name this point the point _x_.

It may not be amiss to say the arc _i_ is swept from the center _g_
through the point _u_, said point being located ten degrees from the
intersection of the radial _a c_ with the peripheral line _a_. It will
be noticed that the inner angle of the entrance pallet _A_ seems to
extend inward, beyond the radial line _a j_, that is, toward the pallet
center _g_, and gives the appearance of being much thicker than the exit
pallet _A'_; but we will see on examination that the extreme angle _x_
of the entrance pallet must move on the arc _i_ and, consequently, cross
the peripheral line _a_ at the point _u_. If we measure the impulse
faces of the two pallets _A A'_, we will find them nearly alike in
linear extent.

Mr. Grossmann, in delineating his exit pallet, brings the extreme angle
(shown at _4_) down to the periphery of the escape, as shown in the
drawing, where it extends beyond the intersection of the line _g f_ with
the radial line _a 3_. The correct form for the entrance pallet should
be to the dotted line _z x y_.

[Illustration: Fig. 17]

We have spoken of engaging and disengaging frictions; we do not know how
we can better explain this term than by illustrating the idea with a
grindstone. Suppose two men are grinding on the same stone; each has,
say, a cold chisel to grind, as shown at Fig. 17, where _G_ represents
the grindstone and _N N'_ the cold chisels. The grindstone is supposed
to be revolving in the direction of the arrow. The chisels _N_ and _N'_
are both being ground, but the chisel _N'_ is being cut much the more
rapidly, as each particle of grit of the stone as it catches on the
steel causes the chisel to hug the stone and bite in deeper and deeper;
while the chisel shown at _N_ is thrust away by the action of the grit.
Now, friction of any kind is only a sort of grinding operation, and the
same principles hold good.


THE NECESSITY FOR GOOD INSTRUMENTS.

It is to be hoped the reader who intends to profit by this treatise has
fitted up such a pair of dividers as those we have described, because it
is only with accurate instruments he can hope to produce drawings on
which any reliance can be placed. The drawing of a ratchet-tooth lever
escapement of eight and one-half degrees pallet action will now be
resumed. In the drawing at Fig. 18 is shown a complete delineation of
such an escapement with eight and one-half degrees of pallet action and
equidistant locking faces. It is, of course, understood the escape wheel
is to be drawn ten inches in diameter, and that the degree arcs shown in
Fig. 1 will be used.

We commence by carefully placing on the drawing-board a sheet of paper
about fifteen inches square, and then vertically through the center
draw the line _a' a''_. At some convenient position on this line is
established the point _a_, which represents the center of the escape
wheel. In this drawing it is not important that the entire escape wheel
be shown, inasmuch as we have really to do with but a little over sixty
degrees of the periphery of the escape wheel. With the dividers
carefully set at five inches, from _a_, as a center, we sweep the arc
_n n_, and from the intersection of the perpendicular line _a' a''_ with
the arc _n_ we lay off on each side thirty degrees from the brass degree
arc, and through the points thus established are drawn the radial lines
_a b'_ and _a d'_.


[Illustration: Fig. 18]

The point on the arc _n_ where it intersects with the line _b'_ is
termed the point _b_. At the intersection of the radial line _a d'_ is
established the point _d_. We take ten and one-half degrees in the
dividers, and from the point _b_ establish the point _c_, which embraces
the arc of the escape wheel which is utilized by the pallet action.
Through the point _b_ the line _h' h_ is drawn at right angles to the
line _a b'_. The line _j j'_ is also drawn at right angles to the line
_a d'_ through the point _d_. We now have an intersection of the lines
just drawn in common with the line _a a'_ at the point _g_, said point
indicating the center of the pallet action.

The dividers are now set to embrace the space between the points _b_ and
_g_ on the line _h' h_, and the arc _f f_ is swept; which, in proof of
the accuracy of the work, intersects the arc _n_ at the point _d_. This
arc coincides with the locking faces of both pallets. To lay out the
entrance pallet, the dividers are set to five inches, and from _g_ as a
center the short arc _o o_ is swept. On this arc one degree is laid off
below the line _h' h_, and the line _g i_ drawn. The space embraced
between the lines _h_ and _i_ on the arc _f_ represents the locking face
of the entrance pallet, and the point formed at the intersection of the
line _g i_ with the arc _f_ is called the point _p_. To give the proper
lock to the face of the pallet, from the point _p_ as a center is swept
the short arc _r r_, and from its intersection with the line _a b'_
twelve degrees are laid off and the line _b s_ drawn, which defines the
locking face of the entrance pallet. From _g_ as a center is swept the
arc _c' c'_, intersecting the arc _n n_ at _c_. On this arc (_c_) is
located the inner angle of the entrance pallet. The dividers are set to
embrace the space on the arc _c'_ between the lines _g h'_ and _g k_.
With this space in the dividers one leg is set at the point _c_,
measuring down on the arc _c'_ and establishing the point _t_. The
points _p_ and _t_ are then connected, and thus the impulse face of the
entrance pallet _B_ is defined. From the point _t_ is drawn the line
_t t'_, parallel to the line _b s_, thus defining the inner face of the
entrance pallet.


DELINEATING THE EXIT PALLET.

To delineate the exit pallet, sweep the short arc _u u_ (from _g_ as a
center) with the dividers set at five inches, and from the intersection
of this arc with the line _g j'_ set off eight and one-half degrees and
draw the line _g l_. At one degree below this line is drawn the line _g m_.
The space on the arc _f_ between these lines defines the locking
face of the exit pallet. The point where the line _g m_ intersects the
arc _f_ is named the point _x_. From the point _x_ is erected the line
_x w_, perpendicular to the line _g m_. From _x_ as a center, and with
the dividers set at five inches, the short arc _y y_ is swept, and on
this arc are laid off twelve degrees, and the line _x z_ is drawn, which
line defines the locking face of the exit pallet.

Next is taken ten and one-half degrees from the brass degree-scale, and
from the point _d_ on the arc _n_ the space named is laid off, and thus
is established the point _v_; and from _g_ as a center is swept the arc
_v' v'_ through the point _v_. It will be evident on a little thought,
that if the tooth _A'_ impelled the exit pallet to the position shown,
the outer angle of the pallet must extend down to the point _v_, on the
arc _v' v'_; consequently, we define the impulse face of this pallet by
drawing a line from point _x_ to _v_. To define the outer face of the
exit pallet, we draw the line _v e_ parallel to the line _x z_.

There are no set rules for drawing the general form of the pallet arms,
only to be governed by and conforming to about what we would deem
appropriate, and to accord with a sense of proportion and mechanical
elegance. Ratchet-tooth pallets are usually made in what is termed
"close pallets"; that is, the pallet jewel is set in a slot sawed in the
steel pallet arm, which is undoubtedly the strongest and most
serviceable form of pallet made. We shall next consider the
ratchet-tooth lever escapement with circular pallets and ten degrees of
pallet action.


DELINEATING CIRCULAR PALLETS.

To delineate "circular pallets" for a ratchet-tooth lever escapement, we
proceed very much as in the former drawing, by locating the point _A_,
which represents the center of the escape wheel, at some convenient
point, and with the dividers set at five inches, sweep the arc _m_, to
represent the periphery of the escape wheel, and then draw the vertical
line _A B'_, Fig. 19. We (as before) lay off thirty degrees on the arc
_m_ each side of the intersection of said arc with the line _A B'_, and
thus establish on the arc _m_ the points _a b_, and from _A_ as a center
draw through the points so established the radial lines _A a'_ and _A b'_.

We erect from the point _a_ a perpendicular to the line _A a_, and, as
previously explained, establish the pallet center at _B_. Inasmuch as we
are to employ circular pallets, we lay off to the left on the arc _m_,
from the point _a_, five degrees, said five degrees being half of the
angular motion of the escape wheel utilized in the present drawing, and
thus establish the point _c_, and from _A_ as a center draw through this
point the radial line _A c'_. To the right of the point _a_ we lay off
five degrees and establish the point _d_. To illustrate the underlying
principle of our circular pallets: with one leg of the dividers set at
_B_ we sweep through the points _c a d_ the arcs _c'' a'' d''_.

From _B_ as a center, we continue the line _B a_ to _f_, and with the
dividers set at five inches, sweep the short arc _e e_. From the
intersection of this arc with the line _B f_ we lay off one and a half
degrees and draw the line _B g_, which establishes the extent of the
lock on the entrance pallet. It will be noticed the linear extent of
the locking face of the entrance pallet is greater than that of the
exit, although both represent an angle of one and a half degrees.
Really, in practice, this discrepancy is of little importance, as the
same side-shake in banking would secure safety in either case.

[Illustration: Fig. 19]

The fault we previously pointed out, of the generally accepted method of
delineating a detached lever escapement, is not as conspicuous here as
it is where the pallets are drawn with equidistant locking faces; that
is, the inner angle of the entrance pallet (shown at _s_) does not have
to be carried down on the arc _d'_ as far to insure a continuous pallet
action of ten degrees, as with the pallets with equidistant locking
faces. Still, even here we have carried the angle _s_ down about half a
degree on the arc _d'_, to secure a safe lock on the exit pallet.


THE AMOUNT OF LOCK.

If we study the large drawing, where we delineate the escape wheel ten
inches in diameter, it will readily be seen that although we claim one
and a half degrees lock, we really have only about one degree, inasmuch
as the curve of the peripheral line _m_ diverges from the line _B f_,
and, as a consequence, the absolute lock of the tooth _C_ on the locking
face of the entrance pallet _E_ is but about one degree. Under these
conditions, if we did not extend the outer angle of the exit pallet at
_t_ down to the peripheral line _m_, we would scarcely secure one-half a
degree of lock. This is true of both pallets. We must carry the pallet
angles at _r s n t_ down on the circles _c'' d'_ if we would secure the
lock and impulse we claim; that is, one and a half degrees lock and
eight and a half degrees impulse.

Now, while the writer is willing to admit that a one-degree lock in a
sound, well-made escapement is ample, still he is not willing to allow
of a looseness of drawing to incorporate to the extent of one degree in
any mechanical matter demanding such extreme accuracy as the parts of a
watch. It has been claimed that such defects can, to a great extent, be
remedied by setting the escapement closer; that is, by bringing the
centers of the pallet staff and escape wheel nearer together. We hold
that such a course is not mechanical and, further, that there is not the
slightest necessity for such a policy.


ADVANTAGE OF MAKING LARGE DRAWINGS.

By making the drawings large, as we have already suggested and insisted
upon, we can secure an accuracy closely approximating perfection. As,
for instance, if we wish to get a lock of one and a half degrees on the
locking face of the entrance pallet _E_, we measure down on the arc
_c''_ from its intersection with the peripheral line _m_ one and a half
degrees, and establish the point _r_ and thus locate the outer angle of
the entrance pallet _E_, so there will really be one and a half degrees
of lock; and by measuring down on the arc _d'_ ten degrees from its
intersection with the peripheral line _m_, we locate the point _s_,
which determines the position of the inner angle of the entrance pallet,
and we know for a certainty that when this inner angle is freed from the
tooth it will be after the pallet (and, of course, the lever) has passed
through exactly ten degrees of angular motion.

For locating the inner angle of the exit pallet, we measure on the arc
_d'_, from its intersection with the peripheral line _m_, eight and a
half degrees, and establish the point _n_, which locates the position of
this inner angle; and, of course, one and a half degrees added on the
arc _d'_ indicates the extent of the lock on this pallet. Such drawings
not only enable us to theorize to extreme exactness, but also give us
proportionate measurements, which can be carried into actual
construction.


THE CLUB-TOOTH LEVER ESCAPEMENT.

We will now take up the club-tooth form of the lever escapement. This
form of tooth has in the United States and in Switzerland almost
entirely superceded the ratchet tooth. The principal reason for its
finding so much favor is, we think, chiefly owing to the fact that this
form of tooth is better able to stand the manipulations of the
able-bodied watchmaker, who possesses more strength than skill. We will
not pause now, however, to consider the comparative merits of the
ratchet and club-tooth forms of the lever escapement, but leave this
part of the theme for discussion after we have given full instructions
for delineating both forms.

With the ratchet-tooth lever escapement all of the impulse must be
derived from the pallets, but in the club-tooth escapement we can divide
the impulse planes between the pallets and the teeth to suit our fancy;
or perhaps it would be better to say carry out theories, because we have
it in our power, in this form of the lever escapement, to indulge
ourselves in many changes of the relations of the several parts. With
the ratchet tooth the principal changes we could make would be from
pallets with equidistant lockings to circular pallets. The club-tooth
escape wheel not only allows of circular pallets and equidistant
lockings, but we can divide the impulse between the pallets and the
teeth in such a way as will carry out many theoretical advantages which,
after a full knowledge of the escapement action is acquired, will
naturally suggest themselves. In the escapement shown at Fig. 20 we have
selected, as a very excellent example of this form of tooth, circular
pallets of ten degrees fork action and ten and a half degrees of
escape-wheel action.

It will be noticed that the pallets here are comparatively thin to those
in general use; this condition is accomplished by deriving the principal
part of the impulse from driving planes placed on the teeth. As relates
to the escape-wheel action of the ten and one-half degrees, which gives
impulse to the escapement, five and one-half degrees are utilized by the
driving planes on the teeth and five by the impulse face of the pallet.
Of the ten degrees of fork action, four and a half degrees relate to the
impulse face of the teeth, one and a half degrees to lock, and four
degrees to the driving plane of the pallets.

In delineating such a club-tooth escapement, we commence, as in former
examples, by first assuming the center of the escape wheel at _A_, and
with the dividers set at five inches sweeping the arc _a a_. Through _A_
we draw the vertical line _A B'_. On the arc _a a_, and each side of its
intersection with the line _A B'_, we lay off thirty degrees, as in
former drawings, and through the points so established on the arc _a a_
we draw the radial lines _A b_ and _A c_. From the intersection of the
radial line _A b_ with the arc _a_ we draw the line _h h_ at right
angles to _A b_. Where the line _h_ intersects the radial lines _A B'_
is located the center of the pallet staff, as shown at _B_. Inasmuch as
we decided to let the pallet utilize five degrees of escape-wheel
action, we take a space of two and a half degrees in the dividers, and
on the arc _a a_ lay off the said two and a half degrees to the left of
this intersection, and through the point so established draw the radial
line _A g_. From _B_ as a center we sweep the arc _d d_ so it passes
through the point of intersection of the arc _a_ with the line _A g_.

[Illustration: Fig. 20]

We again lay off two and a half degrees from the intersection of the
line _A b_ with the arc _a_, but this time to the right of said
intersection, and through the point so established, and from _B_ as a
center, we sweep the arc _e_. From the intersection of the radial line
_A g_ with the arc _a_ we lay off to the left five and a half degrees on
said arc, and through the point so established draw the radial line _A f_.
With the dividers set at five inches we sweep the short arc _m_ from
_B_ as a center. From the intersection of the line _h B h'_ with the
arc _m_ we lay off on said arc and above the line _h'_ four and a half
degrees, and through the point so established draw the line _B j_.

We next set the dividers so they embrace the space on the radial line _A b_
between its intersection with the line _B j_ and the center _A_, and
from _A_ as a center sweep the arc _i_, said arc defining the _addendum_
of the escape-wheel teeth. We draw a line from the intersection of the
radial line _A f_ with the arc _i_ to the intersection of the radial
line _A g_ with the arc _a_, and thus define the impulse face of the
escape-wheel tooth _D_. For defining the locking face of the tooth we
draw a line at an angle of twenty-four degrees to the line _A g_, as
previously described. The back of the tooth is defined with a curve
swept from some point on the addendum circle _i_, such as our judgment
will dictate.

In the drawing shown at Fig. 20 the radius of this curve was obtained by
taking eleven and a half degrees from the degree arc of 5" radius in the
dividers, and setting one leg at the intersection of the radial line _A f_
with the arc _i_, and placing the other on the line _i_, and allowing
the point so established to serve as a center, the arc was swept for the
back of the tooth, the small circle at _n_ denoting one of the centers
just described. The length for the face of the tooth was obtained by
taking eleven degrees from the degree arc just referred to and laying
that space off on the line _p_, which defined the face of the tooth. The
line _B k_ is laid off one and a half degrees below _B h_ on the arc
_m_. The extent of this arc on the arc _d_ defines the locking face of
the entrance pallet. We set off four degrees on the arc _m_ below the
line _B k_, and through the point so established draw the line _B l_. We
draw a line from the intersection of the line _A g_ with the line _c h_
to the intersection of the arc _e_ with the line _c l_, and define the
impulse face of the entrance pallet.


RELATIONS OF THE SEVERAL PARTS.

Before we proceed to delineate the exit pallet of our escapement, let us
reason on the relations of the several parts.

The club-tooth lever escapement is really the most complicated
escapement made. We mean by this that there are more factors involved in
the problem of designing it correctly than in any other known
escapement. Most--we had better say all, for there are no exceptions
which occur to us--writers on the lever escapement lay down certain
empirical rules for delineating the several parts, without giving
reasons for this or that course. For illustration, it is an established
practice among escapement makers to employ tangential lockings, as we
explained and illustrated in Fig. 16.

Now, when we adopt circular pallets and carry the locking face of the
entrance pallet around to the left two and a half degrees, the true
center for the pallet staff, if we employ tangent lockings, would be
located on a line drawn tangent to the circle _a a_ from its
intersection with the radial line _A k_, Fig. 21. Such a tangent is
depicted at the line _s l'_. If we reason on the situation, we will see
that the line _A k_ is not at right angles to the line _s l_; and,
consequently, the locking face of the entrance pallet _E_ has not really
the twelve-degree lock we are taught to believe it has.

[Illustration: Fig. 21]

We will not discuss these minor points further at present, but leave
them for subsequent consideration. We will say, however, that we could
locate the center of the pallet action at the small circle _B'_ above
the center _B_, which we have selected as our fork-and-pallet action,
and secure a perfectly sound escapement, with several claimed
advantages.

Let us now take up the delineation of the exit pallet. It is very easy
to locate the outer angle of this pallet, as this must be situated at
the intersection of the addendum circle _i_ and the arc _g_, and located
at _o_. It is also self-evident that the inner or locking angle must be
situated at some point on the arc _h_. To determine this location we
draw the line _B c_ from _B_ (the pallet center) through the
intersection of the arc _h_ with the pitch circle _a_.

Again, it follows as a self-evident fact, if the pallet we are dealing
with was locked, that is, engaged with the tooth _D''_, the inner angle
_n_ of the exit pallet would be one and a half degrees inside the pitch
circle _a_. With the dividers set at 5", we sweep the short arc _b b_,
and from the intersection of this arc with the line _B c_ we lay off ten
degrees, and through the point so established, from _B_, we draw the
line _B d_. Below the point of intersection of the line _B d_ with the
short arc _b b_ we lay off one and a half degrees, and through the point
thus established we draw the line _B e_.


LOCATING THE INNER ANGLE OF THE EXIT PALLET.

The intersection of the line _B e_ with the arc _h_, which we will term
the point _n_, represents the location of the inner angle of the exit
pallet. We have already explained how we located the position of the
outer angle at _o_. We draw the line _n o_ and define the impulse face
of the exit pallet. If we mentally analyze the problem in hand, we will
see that as the exit pallet vibrates through its ten degrees of arc the
line _B d_ and _B c_ change places, and the tooth _D''_ locks one and a
half degrees. To delineate the locking face of the exit pallet, we erect
a perpendicular to the line _B e_ from the point _n_, as shown by the
line _n p_.

From _n_ as a center we sweep the short arc _t t_, and from its
intersection with the line _n p_ we lay off twelve degrees, and through
the point so established we draw the line _n u_, which defines the
locking face of the exit pallet. We draw the line _o o'_ parallel with
_n u_ and define the outer face of said pallet. In Fig. 21 we have not
made any attempt to show the full outline of the pallets, as they are
delineated in precisely the same manner as those previously shown.

We shall next describe the delineation of a club-tooth escapement with
pallets having equidistant locking faces; and in Fig. 22 we shall show
pallets with much wider arms, because, in this instance, we shall derive
more of the impulse from the pallets than from the teeth. We do this to
show the horological student the facility with which the club-tooth
lever escapement can be manipulated. We wish also to impress on his mind
the facts that the employment of thick pallet arms and thin pallet arms
depends on the teeth of the escape wheel for its efficiency, and that
he must have knowledge enough of the principles of action to tell at a
glance on what lines the escapement was constructed.

Suppose, for illustration, we get hold of a watch which has thin pallet
arms, or stones, if they are exposed pallets, and the escape was
designed for pallets with thick arms. There is no sort of tinkering we
can do to give such a watch a good motion, except to change either the
escape wheel or the pallets. If we know enough of the lever escapement
to set about it with skill and judgment, the matter is soon put to
rights; but otherwise we can look and squint, open and close the
bankings, and tinker about till doomsday, and the watch be none the
better.


CLUB-TOOTH LEVER WITH EQUIDISTANT LOCKING FACES.

In drawing a club-tooth lever escapement with equidistant locking, we
commence, as on former occasions, by producing the vertical line _A k_,
Fig. 22, and establishing the center of the escape wheel at _A_, and
with the dividers set at 5" sweep the pitch circle _a_. On each side of
the intersection of the vertical line _A k_ with the arc _a_ we set off
thirty degrees on said arc, and through the points so established draw
the radial lines _A b_ and _A c_.

From the intersection of the radial line _A b_ with the arc _a_ lay off
three and a half degrees to the left of said intersection on the arc
_a_, and through the point so established draw the radial line _A e_.
From the intersection of the radial line _A b_ with the arc _a_ erect
the perpendicular line _f_, and at the crossing or intersection of said
line with the vertical line _A k_ establish the center of the pallet
staff, as indicated by the small circle _B_. From _B_ as a center sweep
the short arc _l_ with a 5" radius; and from the intersection of the
radial line _A b_ with the arc _a_ continue the line _f_ until it
crosses the short arc _l_, as shown at _f'_. Lay off one and a half
degrees on the arc _l_ below its intersection with the line _f'_, and
from _B_ as a center draw the line _B_ _i_ through said intersection.
From _B_ as a center, through the intersection of the radial line _A b_
and the arc _a_, sweep the arc _g_.

The space between the lines _B f'_ and _B i_ on the arc _g_ defines the
extent of the locking face of the entrance pallet _C_. The intersection
of the line _B f'_ with the arc _g_ we denominate the point _o_, and
from this point as a center sweep the short arc _p_ with a 5" radius;
and on this arc, from its intersection with the radial line _A b_, lay
off twelve degrees, and through the point so established, from _o_ as a
center, draw the radial line _o m_, said line defining the locking face
of the entrance pallet _C_.

[Illustration: Fig. 22]

It will be seen that this gives a positive "draw" of twelve degrees to
the entrance pallet; that is, counting to the line _B f'_. In this
escapement as delineated there is perfect tangential locking. If the
locking face of the entrance-pallet stone at _C_ was made to conform to
the radial line _A b_, the lock of the tooth _D_ at _o_ would be "dead";
that is, absolutely neutral. The tooth _D_ would press the pallet _C_ in
the direction of the arrow _x_, toward the center of the pallet staff
_B_, with no tendency on the part of the pallet to turn on its axis _B_.
Theoretically, the pallet with the locking face cut to coincide with the
line _A b_ would resist movement on the center _B_ in either direction
indicated by the double-headed arrow _y_.

A pallet at _C_ with a circular locking face made to conform to the arc
_g_, would permit movement in the direction of the double-headed arrow
_y_ with only mechanical effort enough to overcome friction. But it is
evident on inspection that a locking face on the line _A b_ would cause
a retrograde motion of the escape wheel, and consequent resistance, if
said pallet was moved in either direction indicated by the double-headed
arrow _y_. Precisely the same conditions obtain at the point _u_, which
holds the same relations to the exit pallet as the point _o_ does to the
entrance pallet _C_.


ANGULAR MOTION OF ESCAPE WHEEL DETERMINED.

The arc (three and a half degrees) of the circle _a_ embraced between
the radial lines _A b_ and _A e_ determines the angular motion of the
escape wheel utilized by the escape-wheel tooth. To establish and define
the extent of angular motion of the escape wheel utilized by the pallet,
we lay off seven degrees on the arc _a_ from the point _o_ and establish
the point _n_, and through the point _n_, from _B_ as a center, we sweep
the short arc _n'_. Now somewhere on this arc _n'_ will be located the
inner angle of the entrance pallet. With a carefully-made drawing,
having the escape wheel 10" in diameter, it will be seen that the arc
_a_ separates considerably from the line, _B f'_ where it crosses the
arc _n'_.

It will be remembered that when drawing the ratchet-tooth lever
escapement a measurement of eight and a half degrees was made on the arc
_n'_ down from its intersection with the pitch circle, and thus the
inner angle of the pallet was located. In the present instance the
addendum line _w_ becomes the controlling arc, and it will be further
noticed on the large drawing that the line _B h_ at its intersection
with the arc _n'_ approaches nearer to the arc _w_ than does the line
_B f'_ to the pitch circle _a_; consequently, the inner angle of the pallet
should not in this instance be carried down on the arc _n'_ so far to
correct the error as in the ratchet tooth.

Reason tells us that if we measure ten degrees down on the arc _n'_ from
its intersection with the addendum circle _w_ we must define the
position of the inner angle of the entrance pallet. We name the point so
established the point _r_. The outer angle of this pallet is located at
the intersection of the radial line _A b_ with the line _B i_; said
intersection we name the point _v_. Draw a line from the point _v_ to
the point _r_, and we define the impulse face of the entrance pallet;
and the angular motion obtained from it as relates to the pallet staff
embraces six degrees.

Measured on the arc _l_, the entire ten degrees of angular motion is as
follows: Two and a half degrees from the impulse face of the tooth, and
indicated between the lines _B h_ and _B f_; one and a half degrees lock
between the lines _B f'_ and _B i_; six degrees impulse from pallet
face, entrance between the lines _B i_ and _B j_.


A DEPARTURE FROM FORMER PRACTICES.

Grossmann and Britten, in all their delineations of the club-tooth
escapement, show the exit pallet as disengaged. To vary from this
beaten track we will draw our exit pallet as locked. There are other
reasons which prompt us to do this, one of which is, pupils are apt to
fall into a rut and only learn to do things a certain way, and that way
just as they are instructed.

To illustrate, the writer has met several students of the lever
escapement who could make drawings of either club or ratchet-tooth
escapement with the lock on the entrance pallet; but when required to
draw a pallet as illustrated at Fig. 23, could not do it correctly.
Occasionally one could do it, but the instances were rare. A still
greater poser was to request them to delineate a pallet and tooth when
the action of escaping was one-half or one-third performed; and it is
easy to understand that only by such studies the master workman can
thoroughly comprehend the complications involved in the club-tooth lever
escapement.


AN APT ILLUSTRATION.

As an illustration: Two draughtsmen, employed by two competing watch
factories, each designs a club-tooth escapement. We will further suppose
the trains and mainspring power used by each concern to be precisely
alike. But in practice the escapement of the watches made by one factory
would "set," that is, if you stopped the balance dead still, with the
pin in the fork, the watch would not start of itself; while the
escapement designed by the other draughtsman would not "set"--stop the
balance dead as often as you choose, the watch would start of itself.
Yet even to experienced workmen the escape wheels and pallets _looked_
exactly alike. Of course, there was a difference, and still none of the
text-books make mention of it.

For the present we will go on with delineating our exit pallet. The
preliminaries are the same as with former drawings, the instructions for
which we need not repeat. Previous to drawing the exit pallet, let us
reason on the matter. The point _r_ in Fig. 23 is located at the
intersection of pitch circle _a_ and the radial line _A c_; and this
will also be the point at which the tooth _C_ will engage the locking
face of the exit pallet.

This point likewise represents the advance angle of the engaging tooth.
Now if we measure on the arc _k_ (which represents the locking faces of
both pallets) downward one and a half degrees, we establish the lock of
the pallet _E_. To get this one and a half degrees defined on the arc
_k_, we set the dividers at 5", and from _B_ as a center sweep the
short arc _i_, and from the intersection of the arc _i_ with the line
_B e_ we lay off on said arc _i_ one and a half degrees, and through the
point so established draw the line _B f_.

Now the space on the arc _k_ between the lines _B e_ and _B f_ defines
the angular extent of the locking face. With the dividers set at 5" and
one leg resting at the point _r_, we sweep the short arc _t_, and from
the intersection of said arc with the line _A c_ we draw the line _n p_;
but in doing so we extend it (the line) so that it intersects the line
_B f_, and at said intersection is located the inner angle of the exit
pallet. This intersection we will name the point _n_.

[Illustration: Fig. 23]

From the intersection of the line _B e_ with the arc _i_ we lay off two
and a half degrees on said arc, and through the point so established we
draw the line _B g_. The intersection of this line with the arc _k_ we
name the point _z_. With one leg of our dividers set at _A_ we sweep the
arc _l_ so it passes through the point _z_. This last arc defines the
addendum of the escape-wheel teeth. From the point _r_ on the arc _a_ we
lay off three and a half degrees, and through the point so established
draw the line _A j_.


LOCATING THE OUTER ANGLE OF THE IMPULSE PLANES.

The intersection of this line with the addendum arc _l_ locates the
outer angle of the impulse planes of the teeth, and we name it the point
_x_. From the point _r_ we lay off on the arc _a_ seven degrees and
establish the point _v_, which defines the extent of the angular motion
of the escape wheel utilized by pallet. Through the point _v_, from _B_
as a center, we sweep the short arc _m_. It will be evident on a
moment's reflection that this arc _m_ must represent the path of
movement of the outer angle of the exit pallet, and if we measure down
ten degrees from the intersection of the arc _l_ with the arc _m_, the
point so established (which we name the point _s_) must be the exact
position of the outer angle of the pallet during locking. We have a
measure of ten degrees on the arc _m_, between the lines _B g_ and _B
h_, and by taking this space in the dividers and setting one leg at the
intersection of the arc _l_ with the arc _m_, and measuring down on _m_,
we establish the point _s_. Drawing a line from point _n_ to point _s_
we define the impulse face of the pallet.


MAKING AN ESCAPEMENT MODEL.

[Illustration: Fig. 24]

It is next proposed we apply the theories we have been considering and
make an enlarged model of an escapement, as shown at Figs. 24 and 25.
This model is supposed to have an escape wheel one-fifth the size of the
10" one we have been drawing. In the accompanying cuts are shown only
the main plate and bridges in full lines, while the positions of the
escape wheel and balance are indicated by the dotted circles _I B_. The
cuts are to no precise scale, but were reduced from a full-size drawing
for convenience in printing. We shall give exact dimensions, however, so
there will be no difficulty in carrying out our instructions in
construction.

[Illustration: Fig. 25]

Perhaps it would be as well to give a general description of the model
before taking up the details. A reduced side view of the complete model
is given at Fig. 26. In this cut the escapement model shown at Figs. 24
and 25 is sketched in a rough way at _R_, while _N_ shows a glass cover,
and _M_ a wooden base of polished oak or walnut. This base is recessed
on the lower side to receive an eight-day spring clock movement, which
supplies the motive power for the model. This base is recessed on top to
receive the main plate _A_, Fig. 24, and also to hold the glass shade
_N_ in position. The base _M_ is 2½" high and 8" diameter. The glass
cover _N_ can have either a high and spherical top, as shown, or, as
most people prefer, a flattened oval.

[Illustration: Fig. 26]

The main plate _A_ is of hard spring brass, 1/10" thick and 6" in
diameter; in fact, a simple disk of the size named, with slightly
rounded edges. The top plate, shown at _C_, Figs. 24 and 25, is 1/8"
thick and shaped as shown. This plate (_C_) is supported on two pillars
½" in diameter and 1¼" high. Fig. 25 is a side view of Fig. 24 seen
in the direction of the arrow _p_. The cock _D_ is also of 1/8" spring
brass shaped as shown, and attached by the screw _f_ and steady pins _s s_
to the top plate _C_. The bridge _F G_ carries the top pivots of
escape wheel and pallet staff, and is shaped as shown at the full
outline. This bridge is supported on two pillars ½" high and ½" in
diameter, one of which is shown at _E_, Fig. 25, and both at the dotted
circles _E E'_, Fig. 24.

To lay out the lower plate we draw the line _a a_ so it passes through
the center of _A_ at _m_. At 1.3" from one edge of _A_ we establish on
the line _a_ the point _d_, which locates the center of the escape
wheel. On the same line _a_ at 1.15" from _d_ we establish the point
_b_, which represents the center of the pallet staff. At the distance of
1.16" from _b_ we establish the point _c_, which represents the center
of the balance staff. To locate the pillars _H_, which support the top
plate _C_, we set the dividers at 2.58", and from the center _m_ sweep
the arc _n_.

From the intersection of this arc with the line _a_ (at _r_) we lay off
on said arc _n_ 2.1" and establish the points _g g'_, which locate the
center of the pillars _H H_. With the dividers set so one leg rests at
the center _m_ and the other leg at the point _d_, we sweep the arc _t_.
With the dividers set at 1.33" we establish on the arc _t_, from the
point _d_, the points _e e'_, which locate the position of the pillars
_E E'_. The outside diameter of the balance _B_ is 3-5/8" with the rim
3/16" wide and 5/16" deep, with screws in the rim in imitation of the
ordinary compensation balance.

Speaking of a balance of this kind suggests to the writer the trouble he
experienced in procuring material for a model of this kind--for the
balance, a pattern had to be made, then a casting made, then a machinist
turned the casting up, as it was too large for an American lathe. A
hairspring had to be specially made, inasmuch as a mainspring was too
short, the coils too open and, more particularly, did not look well.
Pallet jewels had to be made, and lapidists have usually poor ideas of
close measurements. Present-day conditions, however, will, no doubt,
enable the workman to follow our instructions much more readily.


MAKING THE BRIDGES.

In case the reader makes the bridges _C_ and _F_, as shown in Fig. 27,
he should locate small circles on them to indicate the position of the
screws for securing these bridges to the pillars which support them, and
also other small circles to indicate the position of the pivot holes _d b_
for the escape wheel and pallet staff. In practice it will be well to
draw the line _a a_ through the center of the main plate _A_, as
previously directed, and also establish the point _d_ as therein
directed.

The pivot hole _d'_ for the escape wheel, and also the holes at _e e_
and _b_, are now drilled in the bridge _F_. These holes should be about
1/16" in diameter. The same sized hole is also drilled in the main plate
_A_ at _d_. We now place a nicely-fitting steel pin in the hole _d'_ in
the bridge _F_ and let it extend into the hole _d_ in the main plate. We
clamp the bridge _F_ to _A_ so the hole _b_ comes central on the line
_a_, and using the holes _e e_ in _F_ as guides, drill or mark the
corresponding holes _e' e'_ and _b_ in the main plate for the pillars
_E E'_ and the pallet staff.

[Illustration: Fig. 27]

This plan will insure the escape wheel and pallet staff being perfectly
upright. The same course pursued with the plate _C_ will insure the
balance being upright. The pillars which support the bridges are shaped
as shown at Fig. 28, which shows a side view of one of the pillars which
support the top plate or bridge _C_. The ends are turned to ¼" in
diameter and extend half through the plate, where they are held by
screws, the same as in American movements.

[Illustration: Fig. 28]

The pillars (like _H_) can be riveted in the lower plate _A_, but we
think most workmen will find it more satisfactory to employ screws, as
shown at Fig. 29. The heads of such screws should be about 3/8" in
diameter and nicely rounded, polished and blued. We would not advise
jeweling the pivot holes, because there is but slight friction, except
to the foot of the balance pivot, which should be jeweled with a
plano-convex garnet.

[Illustration: Fig. 29]

IMITATION RUBIES FOR CAPPING THE TOP PIVOTS.

The top pivots to the escape wheel should be capped with imitation
rubies for appearance sake only, letting the cap settings be red gold,
or brass red gilded. If real twelve-karat gold is employed the cost will
not be much, as the settings are only about 3/8" across and can be
turned very thin, so they will really contain but very little gold. The
reason why we recommend imitation ruby cap jewels for the upper holes,
is that such jewels are much more brilliant than any real stone we can
get for a moderate cost. Besides, there is no wear on them.

The pallet jewels are also best made of glass, as garnet or any red
stone will look almost black in such large pieces. Red carnelian has a
sort of brick-red color, which has a cheap appearance. There is a new
phosphorus glass used by optical instrument makers which is intensely
hard, and if colored ruby-red makes a beautiful pallet jewel, which will
afford as much service as if real stones were used; they are no cheaper
than carnelian pallets, but much richer looking. The prettiest cap for
the balance is one of those foilback stones in imitation of a rose-cut
diamond.

[Illustration: Fig. 30]

[Illustration: Fig. 31]

In turning the staffs it is the best plan to use double centers, but a
piece of Stubs steel wire that will go into a No. 40 wire chuck, will
answer; in case such wire is used, a brass collet must be provided. This
will be understood by inspecting Fig. 30, where _L_ represents the Stubs
wire and _B N_ the brass collet, with the balance seat shown at _k_. The
escape-wheel arbor and pallet staff can be made in the same way. The
lower end of the escape wheel pivot is made about ¼" long, so that a
short piece of brass wire can be screwed upon it, as shown in Fig. 31,
where _h_ represents the pivot, _A_ the lower plate, and the dotted line
at _p_ the brass piece screwed on the end of the pivot. This piece _p_
is simply a short bit of brass wire with a female screw tapped into the
end, which screws on to the pivot. An arm is attached to _p_, as shown
at _T_. The idea is, the pieces _T p_ act like a lathe dog to convey the
power from one of the pivots of an old eight-day spring clock movement,
which is secured by screws to the lower side of the main plate _A_. The
plan is illustrated at Fig. 32, where _l_ represents pivot of the
eight-day clock employed to run the model. Counting the escape-wheel
pivot of the clock as one, we take the third pivot from this in the
clock train, placing the movement so this point comes opposite the
escape-wheel pivot of the model, and screw the clock movement fast to
the lower side of the plate _A_. The parts _T_, Fig. 33, are alike on
both pivots.

[Illustration: Fig. 32]

[Illustration: Fig. 33]


PROFITABLE FOR EXPLAINING TO A CUSTOMER.

To fully appreciate such a large escapement model as we have been
describing, a person must see it with its great balance, nearly 4"
across, flashing and sparkling in the show window in the evening, and
the brilliant imitation ruby pallets dipping in and out of the escape
wheel. A model of this kind is far more attractive than if the entire
train were shown, the mystery of "What makes it go?" being one of the
attractions. Such a model is, further, of great value in explaining to a
customer what you mean when you say the escapement of his watch is out
of order. Any practical workman can easily make an even $100 extra in a
year by making use of such a model.

For explaining to customers an extra balance cock can be used to show
how the jewels (hole and cap) are arranged. Where the parts are as large
as they are in the model, the customer can see and understand for
himself what is necessary to be done.

It is not to be understood that our advice to purchase the jewels for an
extra balance cock conflicts with our recommending the reader not to
jewel the holes of his model. The extra cock is to be shown, not for
use, and is employed solely for explaining to a customer what is
required when a pivot or jewel is found to be broken.


HOW LARGE SCREWS ARE MADE.

The screws which hold the plates in place should have heads about 3/8"
in diameter, to be in proportion to the scale on which the balance and
escape wheel are gotten up. There is much in the manner in which the
screw heads are finished as regards the elegance of such a model. A
perfectly flat head, no matter how highly polished, does not look well,
neither does a flattened conehead, like Fig. 35. The best head for this
purpose is a cupped head with chamfered edges, as shown at Fig. 34 in
vertical section. The center _b_ is ground and polished into a perfect
concave by means of a metal ball. The face, between the lines _a a_, is
polished dead flat, and the chamfered edge _a c_ finished a trifle
convex. The flat surface at _a_ is bright, but the concave _b_ and
chamfer at _c_ are beautifully blued. For a gilt-edged, double extra
head, the chamfer at _c_ can be "snailed," that is, ground with a
suitable lap before bluing, like the stem-wind wheels on some watches.

[Illustration: Fig. 34]

[Illustration: Fig. 35]


FANCY SCREWHEADS.

There are two easy methods of removing the blue from the flat part of
the screwhead at _a_. (1) Make a special holder for the screw in the end
of a cement brass, as shown at _E_, Fig. 36, and while it is slowly
revolving in the lathe touch the flat surface _a_ with a sharpened
pegwood wet with muriatic acid, which dissolves the blue coating of
oxide of iron. (2) The surface of the screwhead is coated with a very
thin coating of shellac dissolved in alcohol and thoroughly dried, or a
thin coating of collodion, which is also dried. The screw is placed in
the ordinary polishing triangle and the flat face at _a_ polished on a
tin lap with diamantine and oil. In polishing such surfaces the thinnest
possible coating of diamantine and oil is smeared on the lap--in fact,
only enough to dim the surface of the tin. It is, of course, understood
that it is necessary to move only next to nothing of the material to
restore the polish of the steel. The polishing of the other steel parts
is done precisely like any other steel work.

[Illustration: Fig. 36]

The regulator is of the Howard pattern. The hairspring stud is set in
the cock like the Elgin three-quarter-plate movement. The richest finish
for such a model is frosted plates and bridges. The frosting should not
be a fine mat, like a watch movement, but coarse-grained--in fact, the
grain of the frosting should be proportionate to the size of the
movement. The edges of the bridges and balance cock can be left smooth.
The best process for frosting is by acid. Details for doing the work
will now be given.

[Illustration: Fig. 37]

[Illustration: Fig. 38]

To do this frosting by acid nicely, make a sieve by tacking and gluing
four pieces of thin wood together, to make a rectangular box without a
bottom. Four pieces of cigar-box wood, 8" long by 1½" wide, answer
first rate. We show at _A A A A_, Fig. 37, such a box as if seen from
above; with a side view, as if seen in the direction of the arrow _a_,
at Fig. 38. A piece of India muslin is glued across the bottom, as shown
at the dotted lines _b b_. By turning up the edges on the outside of the
box, the muslin bottom can be drawn as tight as a drum head.


HOW TO DO ACID FROSTING.

To do acid frosting, we procure two ounces of gum mastic and place in
the square sieve, shown at Fig. 37. Usually more than half the weight of
gum mastic is in fine dust, and if not, that is, if the gum is in the
shape of small round pellets called "mastic tears," crush these into
dust and place the dust in _A_. Let us next suppose we wish to frost
the cock on the balance, shown at Fig. 39. Before we commence to frost,
the cock should be perfectly finished, with all the holes made, the
regulator cap in position, the screw hole made for the Howard regulator
and the index arc engraved with the letters S and F.

[Illustration: Fig. 39]

It is not necessary the brass should be polished, but every file mark
and scratch should be stoned out with a Scotch stone; in fact, be in the
condition known as "in the gray." It is not necessary to frost any
portion of the cock _C_, except the upper surface. To protect the
portion of the cock not to be frosted, like the edges and the back, we
"stop out" by painting over with shellac dissolved in alcohol, to which
a little lampblack is added. It is not necessary the coating of shellac
should be very thick, but it is important it should be well dried.


HOW TO PREPARE THE SURFACE.

For illustration, let us suppose the back and edges of the cock at Fig.
39 are coated with shellac and it is laid flat on a piece of paper about
a foot square to catch the excess of mastic. Holes should be made in
this paper and also in the board on which the paper rests to receive the
steady pins of the cock. We hold the sieve containing the mastic over
the cock and, gently tapping the box _A_ with a piece of wood like a
medium-sized file handle, shake down a little snowstorm of mastic dust
over the face of the cock _C_.

Exactly how much mastic dust is required to produce a nice frosting is
only to be determined by practice. The way to obtain the knack is to
frost a few scraps to "get your hand in." Nitric acid of full strength
is used, dipping the piece into a shallow dish for a few seconds. A
good-sized soup plate would answer very nicely for frosting the bottom
plate, which, it will be remembered, is 6" in diameter.


HOW TO ETCH THE SURFACE.

After the mastic is sifted on, the cock should be heated up to about
250° F., to cause the particles of mastic to adhere to the surface. The
philosophy of the process is, the nitric acid eats or dissolves the
brass, leaving a little brass island the size of the particle of mastic
which was attached to the surface. After heating to attach the particles
of mastic, the dipping in nitric acid is done as just described. Common
commercial nitric acid is used, it not being necessary to employ
chemically pure acid. For that matter, for such purposes the commercial
acid is the best.

After the acid has acted for fifteen or twenty seconds the brass is
rinsed in pure water to remove the acid, and dried by patting with an
old soft towel, and further dried by waving through the air. A little
turpentine on a rag will remove the mastic, but turpentine will not
touch the shellac coating. The surface of the brass will be found
irregularly acted upon, producing a sort of mottled look. To obtain a
nice frosting the process of applying the mastic and etching must be
repeated three or four times, when a beautiful coarse-grain mat or
frosting will be produced.

The shellac protection will not need much patching up during the three
or four bitings of acid, as the turpentine used to wash off the mastic
does not much affect the shellac coating. All the screw holes like _s s_
and _d_, also the steady pins on the back, are protected by varnishing
with shellac. The edges of the cocks and bridges should be polished by
rubbing lengthwise with willow charcoal or a bit of chamois skin
saturated with oil and a little hard rouge scattered upon it. The
frosting needs thorough scratch-brushing.

[Illustration: Fig. 40]

At Fig. 40 we show the balance cock of our model with modified form of
Howard regulator. The regulator bar _A_ and spring _B_ should be ground
smooth on one side and deeply outlined to perfect form. The regulator
cap _C_ is cut out to the correct size. These parts are of decarbonized
cast steel, annealed until almost as soft as sheet brass. It is not so
much work to finish these parts as one might imagine. Let us take the
regulator bar for an example and carry it through the process of making.
The strip of soft sheet steel on which the regulator bar is outlined is
represented by the dotted outline _b_, Fig. 41.

[Illustration: Fig. 41]

To cut out sheet steel rapidly we take a piece of smooth clock
mainspring about ¾" and 10" long and double it together, softening the
bending point with the lamp until the piece of mainspring assumes the
form shown at Fig. 42, where _c_ represents the piece of spring and
_H H_ the bench-vise jaws. The piece of soft steel is placed between the
limbs of _c c'_ of the old mainspring up to the line _a_, Fig. 41, and
clamped in the vise jaws. The superfluous steel is cut away with a sharp
and rather thin cold chisel.

[Illustration: Fig. 42]

The chisel is presented as shown at _G_, Fig. 43 (which is an end view
of the vise jaws _H H_ and regulator bar), and held to cut obliquely and
with a sort of shearing action, as illustrated in Fig. 42, where _A''_
represents the soft steel and _G_ the cold chisel. We might add that
Fig. 42 is a view of Fig. 43 seen in the direction of the arrow _f_. It
is well to cut in from the edge _b_ on the line _d_, Fig. 41, with a
saw, in order to readily break out the surplus steel and not bend the
regulator bar. By setting the pieces of steel obliquely in the vise, or
so the line _e_ comes even with the vise jaws, we can cut to more nearly
conform to the circular loop _A''_ of the regulator _A_.

[Illustration: Fig. 43]

The smooth steel surface of the bent mainspring _c_ prevents the vise
jaws from marking the soft steel of the regulator bar. A person who has
not tried this method of cutting out soft steel would not believe with
what facility pieces can be shaped. Any workman who has a universal face
plate to his lathe can turn out the center of the regulator bar to
receive the disk _C_, and also turn out the center of the regulator
spring _B_. What we have said about the regulator bar applies also to
the regulator spring _B_. This spring is attached to the cock _D_ by
means of two small screws at _n_.

The micrometer screw _F_ is tapped through _B''_ as in the ordinary
Howard regulator, and the screw should be about No. 6 of a Swiss
screw-plate. The wire from which such screw is made should be 1/10" in
diameter. The steel cap _C_ is fitted like the finer forms of Swiss
watches. The hairspring stud _E_ is of steel, shaped as shown, and comes
outlined with the other parts.


TO TEMPER AND POLISH STEEL.

The regulator bar should be hardened by being placed in a folded piece
of sheet iron and heated red hot, and thrown into cold water. The
regulator bar _A A'_ is about 3" long; and for holding it for
hardening, cut a piece of thin sheet iron 2½" by 3¼" and fold it
through the middle lengthwise, as indicated by the dotted line _g_, Fig.
44. The sheet iron when folded will appear as shown at Fig. 45. A piece
of flat sheet metal of the same thickness as the regulator bar should be
placed between the iron leaves _I I_, and the leaves beaten down with a
hammer, that the iron may serve as a support for the regulator during
heating and hardening. A paste made of castile soap and water applied to
the regulator bar in the iron envelope will protect it from oxidizing
much during the heating. The portions of the regulator bar marked _h_
are intended to be rounded, while the parts marked _m_ are intended to
be dead flat. The rounding is carefully done, first with a file and
finished with emery paper. The outer edge of the loop _A''_ is a little
rounded, also the inner edge next the cap _C_. This will be understood
by inspecting Fig. 46, where we show a magnified vertical section of the
regulator on line _l_, Fig. 40. The curvature should embrace that
portion of _A''_ between the radial lines _o o'_, and should, on the
model, not measure more than 1/40". It will be seen that the curved
surface of the regulator is sunk so it meets only the vertical edge of
the loop _A''_. For the average workman, polishing the flat parts _m_ is
the most difficult to do, and for this reason we will give entire
details. It is to be expected that the regulator bar will spring a
little in hardening, but if only a little we need pay no attention to
it.

[Illustration: Fig. 44]

[Illustration: Fig. 45]

[Illustration: Fig. 46]


HOW FLAT STEEL POLISHING IS DONE.

Polishing a regulator bar for a large model, such as we are building, is
only a heavy job of flat steel work, a little larger but no more
difficult than to polish a regulator for a sixteen-size watch. We would
ask permission here to say that really nice flat steel work is something
which only a comparatively few workmen can do, and, still, the process
is quite simple and the accessories few and inexpensive. First,
ground-glass slab 6" by 6" by ¼"; second, flat zinc piece 3¼" by
3¼" by ¼"; third, a piece of thick sheet brass 3" by 2" by 1/8";
and a bottle of Vienna lime. The glass slab is only a piece of plate
glass cut to the size given above. The zinc slab is pure zinc planed
dead flat, and the glass ground to a dead surface with another piece of
plate glass and some medium fine emery and water, the whole surface
being gone over with emery and water until completely depolished. The
regulator bar, after careful filing and dressing up on the edges with an
oilstone slip or a narrow emery buff, is finished as previously
described. We would add to the details already given a few words on
polishing the edges.

[Illustration: Fig. 47]

It is not necessary that the edges of steelwork, like the regulator bar
_B_, Fig. 47, should be polished to a flat surface; indeed, they look
better to be nicely rounded. Perhaps we can convey the idea better by
referring to certain parts: say, spring to the regulator, shown at _D_,
Fig. 40, and also the hairspring stud _E_. The edges of these parts look
best beveled in a rounded manner.

[Illustration: Fig. 48]

[Illustration: Fig. 49]

It is a little difficult to convey in words what is meant by "rounded"
manner. To aid in understanding our meaning, we refer to Figs. 48 and
49, which are transverse sections of _D_, Fig. 50, on the line _f_. The
edges of _D_, in Fig. 48, are simply rounded. There are no rules for
such rounding--only good judgment and an eye for what looks well. The
edges of _D_ as shown in Fig. 49 are more on the beveled order. In
smoothing and polishing such edges, an ordinary jeweler's steel burnish
can be used.

[Illustration: Fig. 50]


SMOOTHING AND POLISHING.

The idea in smoothing and polishing such edges is to get a fair gloss
without much attention to perfect form, inasmuch as it is the flat
surface _d_ on top which produces the impression of fine finish. If this
is flat and brilliant, the rounded edges, like _g c_ can really have
quite an inferior polish and still look well. For producing the flat
polish on the upper surface of the regulator bar _B_ and spring _D_, the
flat surface _d_, Figs. 48, 49, 51 and 52, we must attach the regulator
bar to a plate of heavy brass, as shown at Fig. 47, where _A_ represents
the brass plate, and _B_ the regulator bar, arranged for grinding and
polishing flat.

[Illustration: Fig. 51]

[Illustration: Fig. 52]

For attaching the regulator bar _B_ to the brass plate _A_, a good plan
is to cement it fast with lathe wax; but a better plan is to make the
plate _A_ of heavy sheet iron, something about 1/8" thick, and secure
the two together with three or four little catches of soft solder. It is
to be understood the edges of the regulator bar or the regulator spring
are polished, and all that remains to be done is to grind and polish the
flat face.

Two pieces _a a_ of the same thickness as the regulator bar are placed
as shown and attached to _A_ to prevent rocking. After _B_ is securely
attached to _A_, the regulator should be coated with shellac dissolved
in alcohol and well dried. The object of this shellac coating is to keep
the angles formed at the meeting of the face and side clean in the
process of grinding with oilstone dust and oil. The face of the
regulator is now placed on the ground glass after smearing it with oil
and oilstone dust. It requires but a very slight coating to do the work.

The grinding is continued until the required surface is dead flat, after
which the work is washed with soap and water and the shellac dissolved
away with alcohol. The final polish is obtained on the zinc lap with
Vienna lime and alcohol. Where lathe cement is used for securing the
regulator to the plate _A_, the alcohol used with the Vienna lime
dissolves the cement and smears the steel. Diamantine and oil are the
best materials for polishing when the regulator bar is cemented to the
plate _A_.


KNOWLEDGE THAT IS MOST ESSENTIAL.

_The knowledge most important for a practical working watchmaker to
possess is how to get the watches he has to repair in a shape to give
satisfaction to his customers._ No one will dispute the truth of the
above italicised statement. It is only when we seek to have limits set,
and define what such knowledge should consist of, that disagreement
occurs.

One workman who has read Grossmann or Saunier, or both, would insist on
all watches being made to a certain standard, and, according to their
ideas, all such lever watches as we are now dealing with should have
club-tooth escapements with equidistant lockings, ten degrees lever and
pallet action, with one and one-half degrees lock and one and one-half
degrees drop. Another workman would insist on circular pallets, his
judgment being based chiefly on what he had read as stated by some
author. Now the facts of the situation are that lever escapements vary
as made by different manufacturers, one concern using circular pallets
and another using pallets with equidistant lockings.

WHAT A WORKMAN SHOULD KNOW TO REPAIR A WATCH.

One escapement maker will divide the impulse equally between the tooth
and pallet; another will give an excess to the tooth. Now while these
matters demand our attention in the highest degree in a theoretical
sense, still, for such "know hows" as count in a workshop, they are of
but trivial importance in practice.

We propose to deal in detail with the theoretical consideration of
"thick" and "thin" pallets, and dwell exhaustively on circular pallets
and those with equidistant locking faces; but before we do so we wish to
impress on our readers the importance of being able to free themselves
of the idea that all lever escapements should conform to the rigid rules
of any dictum.


EDUCATE THE EYE TO JUDGE OF ANGULAR AS WELL AS LINEAR EXTENT.

For illustration: It would be easy to design a lever escapement that
would have locking faces which were based on the idea of employing
neither system, but a compromise between the two, and still give a good,
sound action. All workmen should learn to estimate accurately the extent
of angular motion, so as to be able to judge correctly of escapement
actions. It is not only necessary to know that a club-tooth escapement
should have one and one-half degrees drop, but the eye should be
educated, so to speak, as to be able to judge of angular as well as
linear extent.

[Illustration: Fig. 53]

Most mechanics will estimate the size of any object measured in inches
or parts of inches very closely; but as regards angular extent, except
in a few instances, we will find mechanics but indifferent judges. To
illustrate, let us refer to Fig. 53. Here we have the base line _A A'_
and the perpendicular line _a B_. Now almost any person would be able to
see if the angle _A a B_ was equal to _B a A'_; but not five in one
hundred practical mechanics would be able to estimate with even
tolerable accuracy the measure the angles made to the base by the lines
_b c d_; and still watchmakers are required in the daily practice of
their craft to work to angular motions and movements almost as important
as to results as diameters.

What is the use of our knowing that in theory an escape-wheel tooth
should have one and one-half degrees drop, when in reality it has three
degrees? It is only by educating the eye from carefully-made drawings;
or, what is better, constructing a model on a large scale, that we can
learn to judge of proper proportion and relation of parts, especially as
we have no convenient tool for measuring the angular motion of the fork
or escape wheel. Nor is it important that we should have, if the workman
is thoroughly "booked up" in the principles involved.

As we explained early in this treatise, there is no imperative necessity
compelling us to have the pallets and fork move through ten degrees any
more than nine and one-half degrees, except that experience has proven
that ten degrees is about the right thing for good results. In this day,
when such a large percentage of lever escapements have exposed pallets,
we can very readily manipulate the pallets to match the fork and roller
action. For that matter, in many instances, with a faulty lever
escapement, the best way to go about putting it to rights is to first
set the fork and roller so they act correctly, and then bring the
pallets to conform to the angular motion of the fork so adjusted.


FORK AND ROLLER ACTION.

Although we could say a good deal more about pallets and pallet action,
still we think it advisable to drop for the present this particular part
of the lever escapement and take up fork and roller action, because, as
we have stated, frequently the fork and roller are principally at fault.
In considering the action and relation of the parts of the fork and
roller, we will first define what is considered necessary to constitute
a good, sound construction where the fork vibrates through ten degrees
of angular motion and is supposed to be engaged with the roller by means
of the jewel pin for thirty degrees of angular motion of the balance.

There is no special reason why thirty degrees of roller action should be
employed, except that experience in practical construction has come to
admit this as about the right arc for watches of ordinary good, sound
construction. Manufacturers have made departures from this standard, but
in almost every instance have finally come back to pretty near these
proportions. In deciding on the length of fork and size of roller, we
first decide on the distance apart at which to place the center of the
balance and the center of the pallet staff. These two points
established, we have the length of the fork and diameter of the roller
defined at once.


HOW TO FIND THE ROLLER DIAMETER FROM THE LENGTH OF THE FORK.

To illustrate, let us imagine the small circles _A B_, Fig. 54, to
represent the center of a pallet staff and balance staff in the order
named. We divide this space into four equal parts, as shown, and the
third space will represent the point at which the pitch circles of the
fork and roller will intersect, as shown by the arc _a_ and circle _b_.
Now if the length of the radii of these circles stand to each other as
three to one, and the fork vibrates through an arc of ten degrees, the
jewel pin engaging such fork must remain in contact with said fork for
thirty degrees of angular motion of the balance.

[Illustration: Fig. 54]

Or, in other words, the ratio of angular motion of two _mobiles_ acting
on each must be in the same ratio as the length of their radii at the
point of contact. If we desire to give the jewel pin, or, in ordinary
horological phraseology, have a greater arc of roller action, we would
extend the length of fork (say) to the point _c_, which would be
one-fifth of the space between _A_ and _B_, and the ratio of fork to
roller action would be four to one, and ten degrees of fork action would
give forty degrees of angular motion to the roller--and such escapements
have been constructed.


WHY THIRTY DEGREES OF ROLLER ACTION IS ABOUT RIGHT.

Now we have two sound reasons why we should not extend the arc of
vibration of the balance: (_a_) If there is an advantage to be derived
from a detached escapement, it would surely be policy to have the arc of
contact, that is, for the jewel pin to engage the fork, as short an arc
as is compatible with a sound action. (_b_) It will be evident to any
thinking mechanic that the acting force of a fork which would carry the
jewel pin against the force exerted by the balance spring through an arc
of fifteen degrees, or half of an arc of thirty degrees, would fail to
do so through an arc of twenty degrees, which is the condition imposed
when we adopt forty degrees of roller action.

For the present we will accept thirty degrees of roller action as the
standard. Before we proceed to delineate our fork and roller we will
devote a brief consideration to the size and shape of a jewel pin to
perform well. In this matter there has been a broad field gone over,
both theoretically and in practical construction. Wide jewel pins, round
jewel pins, oval jewel pins have been employed, but practical
construction has now pretty well settled on a round jewel pin with about
two-fifths cut away. And as regards size, if we adopt the linear extent
of four degrees of fork or twelve degrees of roller action, we will find
it about right.


HOW TO SET A FORK AND ROLLER ACTION RIGHT.

As previously stated, frequently the true place to begin to set a lever
escapement right is with the roller and fork. But to do this properly we
should know when such fork and roller action is right and safe in all
respects. We will see on analysis of the actions involved that there are
three important actions in the fork and roller functions: (_a_) The fork
imparting perfect impulse through the jewel pin to the balance. (_b_)
Proper unlocking action. (_c_) Safety action. The last function is in
most instances sadly neglected and, we regret to add, by a large
majority of even practical workmen it is very imperfectly understood. In
most American watches we have ample opportunity afforded to inspect the
pallet action, but the fork and roller action is placed so that rigid
inspection is next to impossible.

The Vacheron concern of Swiss manufacturers were acute enough to see the
importance of such inspection, and proceeded to cut a circular opening
in the lower plate, which permitted, on the removal of the dial, a
careful scrutiny of the action of the roller and fork. While writing on
this topic we would suggest the importance not only of knowing how to
draw a correct fork and roller action, but letting the workman who
desires to be _au fait_ in escapements delineate and study the action of
a faulty fork and roller action--say one in which the fork, although of
the proper form, is too short, or what at first glance would appear to
amount to the same thing, a roller too small.

Drawings help wonderfully in reasoning out not only correct actions, but
also faulty ones, and our readers are earnestly advised to make such
faulty drawings in several stages of action. By this course they will
educate the eye to discriminate not only as to correct actions, but also
to detect those which are imperfect, and we believe most watchmakers
will admit that in many instances it takes much longer to locate a fault
than to remedy it after it has been found.

[Illustration: Fig. 55]

Let us now proceed to delineate a fork and roller. It is not imperative
that we should draw the parts to any scale, but it is a rule among
English makers to let the distance between the center of the pallet
staff and the center of the balance staff equal in length the chord of
ninety-six degrees of the pitch circle of the escape wheel, which, in
case we employ a pitch circle of 5" radius, would make the distance
between _A_ and _B_, Fig. 55, approximately 7½", which is a very fair
scale for study drawings.


HOW TO DELINEATE A FORK AND ROLLER.

To arrive at the proper proportions of the several parts, we divide the
space _A B_ into four equal parts, as previously directed, and draw the
circle _a_ and short arc _b_. With our dividers set at 5", from _B_ as a
center we sweep the short arc _c_. From our arc of sixty degrees, with a
5" radius, we take five degrees, and from the intersection of the right
line _A B_ with the arc _c_ we lay off on each side five degrees and
establish the points _d e_; and from _B_ as a center, through these
points draw the lines _B d'_ and _B e'_. Now the arc embraced between
these lines represents the angular extent of our fork action.

From _A_ as a center and with our dividers set at 5", we sweep the arc
_f_. From the scale of degrees we just used we lay off fifteen degrees
on each side of the line _A B_ on the arc _f_, and establish the points
_g h_. From _A_ as a center, through the points just established we draw
the radial lines _A g'_ and _A h'_. The angular extent between these
lines defines the limit of our roller action.

Now if we lay off on the arc _f_ six degrees each side of its
intersection with the line _A B_, we define the extent of the jewel pin;
that is, on the arc _f_ we establish the points _l m_ at six degrees
from the line _A B_, and through the points _l m_ draw, from _A_ as a
center, the radial lines _A l'_ and _A m'_. The extent of the space
between the lines _A l'_ and _A m'_ on the circle _a_ defines the size
of our jewel pin.


TO DETERMINE THE SIZE OF A JEWEL PIN.

[Illustration: Fig. 56]

To make the situation better understood, we make an enlarged drawing of
the lines defining the jewel pin at Fig. 56. At the intersection of the
line _A B_ with the arc _a_ we locate the point _k_, and from it as a
center we sweep the circle _i_ so it passes through the intersection of
the lines _A l'_ and _A m'_ with the arc _a_. We divide the radius of
the circle _i_ on the line _A B_ into five equal parts, as shown by the
vertical lines _j_. Of these five spaces we assume three as the extent
of the jewel pin, cutting away that portion to the right of the heavy
vertical line at _k_.

[Illustration: Fig. 57]

We will now proceed to delineate a fork and roller as the parts are
related on first contact of jewel pin with fork and initial with the
commencing of the act of unlocking a pallet. The position and relations
are also the same as at the close of the act of impulse. We commence the
drawing at Fig. 57, as before, by drawing the line _A B_ and the arcs
_a_ and _b_ to represent the pitch circles. We also sweep the arc _f_ to
enable us to delineate the line _A g'_. Next in order we draw our jewel
pin as shown at _D_. In drawing the jewel pin we proceed as at Fig. 56,
except we let the line _A g'_, Fig. 57, assume the same relations to the
jewel pin as _A B_ in Fig. 56; that is, we delineate the jewel pin as if
extending on the arc _a_ six degrees on each side of the line _A g'_,
Fig. 57.


THE THEORY OF THE FORK ACTION.

To aid us in reasoning, we establish the point _m_, as in Fig. 55, at
_m_, Fig. 57, and proceed to delineate another and imaginary jewel pin
at _D'_ (as we show in dotted outline). A brief reasoning will show that
in allowing thirty degrees of contact of the fork with the jewel pin,
the center of the jewel pin will pass through an arc of thirty degrees,
as shown on the arcs _a_ and _f_. Now here is an excellent opportunity
to impress on our minds the true value of angular motion, inasmuch as
thirty degrees on the arc _f_ is of more than twice the linear extent as
on the arc _a_.

Before we commence to draw the horn of the fork engaging the jewel pin
_D_, shown at full line in Fig. 57, we will come to perfectly understand
what mechanical relations are required. As previously stated, we assume
the jewel pin, as shown at _D_, Fig. 57, is in the act of encountering
the inner face of the horn of the fork for the end or purpose of
unlocking the engaged pallet. Now if the inner face of the horn of the
fork was on a radial line, such radial line would be _p B_, Fig. 57. We
repeat this line at _p_, Fig. 56, where the parts are drawn on a larger
scale.

To delineate a fork at the instant the last effort of impulse has been
imparted to the jewel pin, and said jewel pin is in the act of
separating from the inner face of the prong of the fork--we would also
call attention to the fact that relations of parts are precisely the
same as if the jewel pin had just returned from an excursion of
vibration and was in the act of encountering the inner face of the prong
of the fork in the act of unlocking the escapement.

We mentioned this matter previously, but venture on the repetition to
make everything clear and easily understood. We commence by drawing the
line _A B_ and dividing it in four equal parts, as on previous
occasions, and from _A_ and _B_ as centers draw the pitch circles _c d_.
By methods previously described, we draw the lines _A a_ and _A a'_,
also _B b_ and _B b'_ to represent the angular motion of the two
mobiles, viz., fork and roller action. As already shown, the roller
occupies twelve degrees of angular extent. To get at this conveniently,
we lay off on the arc by which we located the lines _A a_ and _A a'_ six
degrees above the line _A a_ and draw the line _A h_.

Now the angular extent on the arc _c_ between the lines _A a_ and _A h_
represents the radius of the circle defining the jewel pin. From the
intersection of the line _A a_ with the arc _c_ as a center, and with
the radius just named, we sweep the small circle _D_, Fig. 58, which
represents our jewel pin; we afterward cut away two-fifths and draw the
full line _D_, as shown. We show at Fig. 59 a portion of Fig. 58,
enlarged four times, to show certain portions of our delineations more
distinctly. If we give the subject a moment's consideration we will see
that the length of the prong _E_ of the lever fork is limited to such a
length as will allow the jewel pin _D_ to pass it.


HOW TO DELINEATE THE PRONGS OF A LEVER FORK.

[Illustration: Fig. 58]

[Illustration: Fig. 59]

To delineate this length, from _B_ as a center we sweep the short arc
_f_ so it passes through the outer angle _n_, Fig. 59, of the jewel pin.
This arc, carried across the jewel pin _D_, limits the length of the
opposite prong of the fork. The outer face of the prong of the fork can
be drawn as a line tangent to a circle drawn from _A_ as a center
through the angle _n_ of the jewel pin. Such a circle or arc is shown at
_o_, Figs. 58 and 59. There has been a good deal said as to whether the
outer edge of the prong of a fork should be straight or curved.

To the writer's mind, a straight-faced prong, like from _s_ to _m_, is
what is required for a fork with a single roller, while a fork with a
curved prong will be best adapted for a double roller. This subject will
be taken up again when we consider double-roller action. The extent or
length of the outer face of the prong is also an open subject, but as
there is but one factor of the problem of lever escapement construction
depending on it, when we name this and see this requirement satisfied we
have made an end of this question. The function performed by the outer
face of the prong of a fork is to prevent the engaged pallet from
unlocking while the guard pin is opposite to the passing hollow.

The inner angle _s_ of the horn of the fork must be so shaped and
located that the jewel pin will just clear it as it passes out of the
fork, or when it passes into the fork in the act of unlocking the
escapement. In escapements with solid bankings a trifle is allowed, that
is, the fork is made enough shorter than the absolute theoretical length
to allow for safety in this respect.


THE PROPER LENGTH OF A LEVER.

We will now see how long a lever must be to perform its functions
perfectly. Now let us determine at what point on the inner face of the
prong _E'_ the jewel pin parts from the fork, or engages on its return.
To do this we draw a line from the center _r_ (Fig. 59) of the jewel
pin, so as to meet the line _e_ at right angles, and the point _t_ so
established on the line _e_ is where contact will take place between the
jewel pin and fork.

It will be seen this point (_t_) of contact is some distance back of the
angle _u_ which terminates the inner face of the prong _E'_;
consequently, it will be seen the prongs _E E'_ of the fork can with
safety be shortened enough to afford a safe ingress or egress to the
jewel pin to the slot in the fork. As regards the length of the outer
face of the prong of the fork, a good rule is to make it one and a half
times the diameter of the jewel pin. The depth of the slot need be no
more than to free the jewel in its passage across the ten degrees of
fork action. A convenient rule as to the depth of the slot in a fork is
to draw the line _k_, which, it will be seen, coincides with the circle
which defines the jewel pin.


HOW TO DELINEATE THE SAFETY ACTION.

[Illustration: Fig. 60]

We will next consider a safety action of the single roller type. The
active or necessary parts of such safety action consist of a roller or
disk of metal, usually steel, shaped as shown in plan at _A_, Fig. 60.
In the edge of this disk is cut in front of the jewel pin a circular
recess shown at _a_ called the passing hollow. The remaining part of the
safety action is the guard pin shown at _N_ Figs. 61 and 62, which is
placed in the lever. Now it is to be understood that the sole function
performed by the guard pin is to strike the edge of the roller _A_ at
any time when the fork starts to unlock the engaged pallet, except when
the jewel pin is in the slot of the fork. To avoid extreme care in
fitting up the passing hollow, the horns of the fork are arranged to
strike the jewel pin and prevent unlocking in case the passing hollow is
made too wide. To delineate the safety action we first draw the fork and
jewel pin as previously directed and as shown at Fig. 63. The position
of the guard pin should be as close to the bottom of the slot of the
fork as possible and be safe. As to the size of the guard pin, it is
usual to make it about one-third or half the diameter of the jewel pin.
The size and position of the guard pin decided on and the small circle
_N_ drawn, to define the size and position of the roller we set our
dividers so that a circle drawn from the center _A_ will just touch the
edge of the small circle _N_, and thus define the outer boundary of our
roller, or roller table, as it is frequently called.

[Illustration: Fig. 61]

[Illustration: Fig. 62]

For deciding the angular extent of the passing hollow we have no fixed
rule, but if we make it to occupy about half more angular extent on the
circle _y_ than will coincide with the angular extent of the jewel pin,
it will be perfectly safe and effectual. We previously stated that the
jewel pin should occupy about twelve degrees of angular extent on the
circle _c_, and if we make the passing hollow occupy eighteen degrees
(which is one and a half the angular extent of the jewel pin) it will do
nicely. But if we should extend the width of the passing hollow to
twenty-four degrees it would do no harm, as the jewel pin would be well
inside the horn of the fork before the guard pin could enter the passing
hollow.

[Illustration: Fig. 63]

We show in Fig. 61 the fork as separated from the roller, but in Fig.
62, which is a side view, we show the fork and jewel pin as engaged.
When drawing a fork and roller action it is safe to show the guard pin
as if in actual contact with the roller. Then in actual construction, if
the parts are made to measure and agree with the drawing in the gray,
that is, before polishing, the process of polishing will reduce the
convex edge of the roller enough to free it.

It is evident if thought is given to the matter, that if the guard pin
is entirely free and does not touch the roller in any position, a
condition and relation of parts exist which is all we can desire. We are
aware that it is usual to give a considerable latitude in this respect
even by makers, and allow a good bit of side shake to the lever, but our
judgment would condemn the practice, especially in high-grade watches.


RESTRICT THE FRICTIONAL SURFACES.

Grossmann, in his essay on the detached lever escapement, adopts one and
a half degrees lock. Now, we think that one degree is ample; and we are
sure that every workman experienced in the construction of the finer
watches will agree with us in the assertion that we should in all
instances seek to reduce the extent of all frictional surfaces, no
matter how well jeweled. Acting under such advice, if we can reduce the
surface friction on the lock from one and a half degrees to one degree
or, better, to three-fourths of a degree, it is surely wise policy to do
so. And as regards the extent of angular motion of the lever, if we
reduce this to six degrees, exclusive of the lock, we would undoubtedly
obtain better results in timing.

We shall next consider the effects of opening the bankings too wide, and
follow with various conditions which are sure to come in the experience
of the practical watch repairer. It is to be supposed in this problem
that the fork and roller action is all right. The reader may say to
this, why not close the banking? In reply we would offer the supposition
that some workman had bent the guard pin forward or set a pallet stone
too far out.

We have now instructed our readers how to draw and construct a lever
escapement complete, of the correct proportions, and will next take up
defective construction and consider faults existing to a lesser or
greater degree in almost every watch. Faults may also be those arising
from repairs by some workman not fully posted in the correct form and
relation of the several parts which go to make up a lever escapement. It
makes no difference to the artisan called upon to put a watch in
perfect order as to whom he is to attribute the imperfection, maker or
former repairer; all the workman having the job in hand has to do is to
know positively that such a fault actually exists, and that it devolves
upon him to correct it properly.


BE FEARLESS IN REPAIRS, IF SURE YOU ARE RIGHT.

Hence the importance of the workman being perfectly posted on such
matters and, knowing that he is right, can go ahead and make the watch
as it should be. The writer had an experience of this kind years ago in
Chicago. A Jules Jurgensen watch had been in the hands of several good
workmen in that city, but it would stop. It was then brought to him with
a statement of facts given above. He knew there must be a fault
somewhere and searched for it, and found it in the exit pallet--a
certain tooth of the escape wheel under the right conditions would
sometimes not escape. It might go through a great many thousand times
and yet it might, and did sometimes, hold enough to stop the watch.

Now probably most of my fellow-workmen in this instance would have been
afraid to alter a "Jurgensen," or even hint to the owner that such a
thing could exist as a fault in construction in a watch of this
justly-celebrated maker. The writer removed the stone, ground a little
from the base of the offending pallet stone, replaced it, and all
trouble ended--no stops from that on.


STUDY OF AN ESCAPEMENT ERROR.

[Illustration: Fig. 64]

Now let us suppose a case, and imagine a full-plate American movement in
which the ingress or entrance pallet extends out too far, and in order
to have it escape, the banking on that side is opened too wide. We show
at Fig. 64 a drawing of the parts in their proper relations under the
conditions named. It will be seen by careful inspection that the jewel
pin _D_ will not enter the fork, which is absolutely necessary. This
condition very frequently exists in watches where a new pallet stone has
been put in by an inexperienced workman. Now this is one of the
instances in which workmen complain of hearing a "scraping" sound when
the watch is placed to the ear. The remedy, of course, lies in warming
up the pallet arms and pushing the stone in a trifle, "But how much?"
say some of our readers. There is no definite rule, but we will tell
such querists how they can test the matter.

Remove the hairspring, and after putting the train in place and securing
the plates together, give the winding arbor a turn or two to put power
on the train; close the bankings well in so the watch cannot escape on
either pallet. Put the balance in place and screw down the cock.
Carefully turn back the banking on one side so the jewel pin will just
pass out of the slot in the fork. Repeat this process with the opposite
banking; the jewel pin will now pass out on each side. Be sure the guard
pin does not interfere with the fork action in any way. The fork is now
in position to conform to the conditions required.


HOW TO ADJUST THE PALLETS TO MATCH THE FORK.

If the escapement is all right, the teeth will have one and a half
degrees lock and escape correctly; but in the instance we are
considering, the stone will not permit the teeth to pass, and must be
pushed in until they will. It is not a very difficult matter after we
have placed the parts together so we can see exactly how much the pallet
protrudes beyond what is necessary, to judge how far to push it back
when we have it out and heated. There is still an "if" in the problem we
are considering, which lies in the fact that the fork we are
experimenting with may be too short for the jewel pin to engage it for
ten degrees of angular motion.

This condition a man of large experience will be able to judge of very
closely, but the better plan for the workman is to make for himself a
test gage for the angular movement of the fork. Of course it will be
understood that with a fork which engages the roller for eight degrees
of fork action, such fork will not give good results with pallets ground
for ten degrees of pallet action; still, in many instances, a compromise
can be effected which will give results that will satisfy the owner of a
watch of moderate cost, and from a financial point of view it stands the
repairer in hand to do no more work than is absolutely necessary to keep
him well pleased.

We have just made mention of a device for testing the angular motion of
the lever. Before we take up this matter, however, we will devote a
little time and attention to the subject of jewel pins and how to set
them. We have heretofore only considered jewel pins of one form, that
is, a round jewel pin with two-fifths cut away. We assumed this form
from the fact that experience has demonstrated that it is the most
practicable and efficient form so far devised or applied. Subsequently
we shall take up the subject of jewel pins of different shapes.


HOW TO SET A JEWEL PIN AS IT SHOULD BE.

Many workmen have a mortal terror of setting a jewel pin and seem to
fancy that they must have a specially-devised instrument for
accomplishing this end. Most American watches have the hole for the
jewel pin "a world too wide" for it, and we have heard repeated
complaints from this cause. Probably the original object of this
accommodating sort of hole was to favor or obviate faults of pallet
action. Let us suppose, for illustration, that we have a roller with the
usual style of hole for a jewel pin which will take almost anything from
the size of a No. 12 sewing needle up to a round French clock pallet.

[Illustration: Fig. 65]

We are restricted as regards the proper size of jewel pin by the width
of the slot in the fork. Selecting a jewel which just fits the fork, we
can set it as regards its relation to the staff so it will cause the
pitch circle of the jewel pin to coincide with either of dotted circles
_a_ or _a'_, Fig. 65. This will perhaps be better understood by
referring to Fig. 66, which is a view of Fig. 65 seen in the direction
of the arrow _c_. Here we see the roller jewel at _D_, and if we bring
it forward as far as the hole in the roller will permit, it will occupy
the position indicated at the dotted lines; and if we set it in (toward
the staff) as far as the hole will allow, it will occupy the position
indicated by the full outline.

[Illustration: Fig. 66]

Now such other condition might very easily exist, that bringing the
jewel pin forward to the position indicated by the dotted lines at _D_,
Fig. 66, would remedy the defect described and illustrated at Fig. 64
without any other change being necessary. We do not assert, understand,
that a hole too large for the jewel pin is either necessary or
desirable--what we wish to convey to the reader is the necessary
knowledge so that he can profit by such a state if necessary. A hole
which just fits the jewel pin so the merest film of cement will hold it
in place is the way it should be; but we think it will be some time
before such rollers are made, inasmuch as economy appears to be a chief
consideration.


ABOUT JEWEL-PIN SETTERS.

To make a jewel-pin setter which will set a jewel pin straight is easy
enough, but to devise any such instrument which will set a jewel so as
to perfectly accord with the fork action is probably not practicable.
What the workman needs is to know from examination when the jewel pin is
in the proper position to perform its functions correctly, and he can
only arrive at this knowledge by careful study and thought on the
matter. If we make up our minds on examining a watch that a jewel pin is
"set too wide," that is, so it carries the fork over too far and
increases the lock to an undue degree, take out the balance, remove the
hairspring, warm the roller with a small alcohol lamp, and then with the
tweezers move the jewel pin in toward the staff.

[Illustration: Fig. 67]

[Illustration: Fig. 68]

[Illustration: Fig. 69]

[Illustration: Fig. 70]

No attempt should be made to move a jewel pin unless the cement which
holds the jewel is soft, so that when the parts cool off the jewel is as
rigid as ever. A very little practice will enable any workman who has
the necessary delicacy of touch requisite to ever become a good
watchmaker, to manipulate a jewel pin to his entire satisfaction with no
other setter than a pair of tweezers and his eye, with a proper
knowledge of what he wants to accomplish. To properly heat a roller for
truing up the jewel pin, leave it on the staff, and after removing the
hairspring hold the balance by the rim in a pair of tweezers, "flashing
it" back and forth through the flame of a rather small alcohol lamp
until the rim of the balance is so hot it can just be held between the
thumb and finger, and while at this temperature the jewel pin can be
pressed forward or backward, as illustrated in Fig. 66, and then a touch
or two will set the pin straight or parallel with the staff. Figs. 68
and 69 are self-explanatory. For cementing in a jewel pin a very
convenient tool is shown at Figs. 67 and 70. It is made of a piece of
copper wire about 1/16" in diameter, bent to the form shown at Fig. 67.
The ends _b b_ of the copper wire are flattened a little and recessed on
their inner faces, as shown in Fig. 70, to grasp the edges of the roller
_A_. The heat of an alcohol lamp is applied to the loop of the wire at
_g_ until the small bit of shellac placed in the hole _h_ melts. The
necessary small pieces of shellac are made by warming a bit of the gum
to near the melting point and then drawing the softened gum into a
filament the size of horse hair. A bit of this broken off and placed in
the hole _h_ supplies the cement necessary to fasten the jewel pin.
Figs. 68 and 69 will, no doubt, assist in a clear understanding of the
matter.


HOW TO MAKE AN ANGLE-MEASURING DEVICE.

We will now resume the consideration of the device for measuring the
extent of the angular motion of the fork and pallets. Now, before we
take this matter up in detail we wish to say, or rather repeat what we
have said before, which is to the effect that ten degrees of fork and
lever action is not imperative, as we can get just as sound an action
and precisely as good results with nine and a half or even nine degrees
as with ten, if other acting parts are in unison with such an arc of
angular motion. The chief use of such an angle-measuring device is to
aid in comparing the relative action of the several parts with a known
standard.

[Illustration: Fig. 71]

For use with full-plate movements about the best plan is a spring clip
or clasp to embrace the pallet staff below the pallets. We show at Fig.
71 such a device. To make it, take a rather large size of sewing
needle--the kind known as a milliner's needle is about the best. The
diameter of the needle should be about No. 2, so that at _b_ we can
drill and put in a small screw. It is important that the whole affair
should be very light. The length of the needle should be about 1-5/8",
in order that from the notch _a_ to the end of the needle _A'_ should be
1½". The needle should be annealed and flattened a little, to give a
pretty good grasp to the notch _a_ on the pallet staff.

Good judgment is important in making this clamp, as it is nearly
impossible to give exact measurements. About 1/40" in width when seen in
the direction of the arrow _j_ will be found to be about the right
width. The spring _B_ can be made of a bit of mainspring, annealed and
filed down to agree in width with the part _A_. In connection with the
device shown at Fig. 71 we need a movement-holder to hold the movement
as nearly a constant height as possible above the bench. The idea is,
when the clamp _A B_ is slipped on the pallet staff the index hand _A'_
will extend outward, as shown in Fig. 72, where the circle _C_ is
supposed to represent the top plate of a watch, and _A'_ the index hand.


HOW THE ANGULAR MOTION IS MEASURED.

[Illustration: Fig. 72]

Fig. 72 is supposed to be seen from above. It is evident that if we
remove the balance from the movement shown at _C_, leaving power on the
train, and with an oiling tool or hair broach move the lever back and
forth, the index hand _A'_ will show in a magnified manner the angular
motion of the lever. Now if we provide an index arc, as shown at _D_, we
can measure the extent of such motion from bank to bank.

[Illustration: Fig. 73]

[Illustration: Fig. 74]

To get up such an index arc we first make a stand as shown at _E F_,
Fig. 73. The arc _D_ is made to 1½" radius, to agree with the index
hand _A'_, and is divided into twelve degree spaces, six each side of a
zero, as shown at Fig. 74, which is an enlarged view of the index _D_ in
Fig. 72. The index arc is attached to a short bit of wire extending down
into the support _E_, and made adjustable as to height by the set-screw
_l_. Let us suppose the index arc is adjusted to the index hand _A'_,
and we move the fork as suggested; you see the hand would show exactly
the arc passed through from bank to bank, and by moving the stand _E F_
we can arrange so the zero mark on the scale stands in the center of
such arc. This, of course, gives the angular motion from bank to bank.
As an experiment, let us close the bankings so they arrest the fork at
the instant the tooth drops from each pallet. If this arc is ten
degrees, the pallet action is as it should be with the majority of
modern watches.


TESTING LOCK AND DROP WITH OUR NEW DEVICE.

Let us try another experiment: We carefully move the fork away from the
bank, and if after the index hand has passed through one and a half
degrees the fork flies over, we know the lock is right. We repeat the
experiment from the opposite bank, and in the same manner determine if
the lock is right on the other pallets. You see we have now the means
of measuring not only the angular motion of the lever, but the angular
extent of the lock. At first glance one would say that if now we bring
the roller and fork action to coincide and act in unison with the pallet
action, we would be all right; and so we would, but frequently this
bringing of the roller and fork to agree is not so easily accomplished.

It is chiefly toward this end the Waltham fork is made adjustable, so it
can be moved to or from the roller, and also that we can allow the
pallet arms to be moved, as we will try and explain. As we set the
bankings the pallets are all right; but to test matters, let us remove
the hairspring and put the balance in place. Now, if the jewel pin
passes in and out of the fork, it is to be supposed the fork and roller
action is all right. To test the fork and roller action we close the
banking a little on one side. If the fork and jewel pin are related to
each other as they should be, the jewel pin will not pass out of the
fork, nor will the engaged tooth drop from that pallet. This condition
should obtain on both pallets, that is, if the jewel pin will not pass
out of the fork on a given bank the tooth engaged on its pallet should
not drop.

We have now come to the most intricate and important problems which
relate to the lever escapement. However, we promise our readers that if
they will take the pains to follow closely our elucidations, to make
these puzzles plain. But we warn them that they are no easy problems to
solve, but require good, hard thinking. The readiest way to master this
matter is by means of such a model escapement as we have described. With
such a model, and the pallets made to clamp with small set-screws, and
roller constructed so the jewel pin could be set to or from the staff,
this matter can be reduced to object lessons. But study of the due
relation of the parts in good drawings will also master the situation.


A FEW EXPERIMENTS WITH OUR ANGLE-MEASURING DEVICE.

In using the little instrument for determining angular motion that we
have just described, care must be taken that the spring clamp which
embraces the pallet staff does not slip. In order to thoroughly
understand the methods of using this angle-measuring device, let us take
a further lesson or two.

We considered measuring the amount of lock on each pallet, and advised
the removal of the balance, because if we left the balance in we could
not readily tell exactly when the tooth passed on to the impulse plane;
but if we touch the fork lightly with an oiling tool or a hair broach,
moving it (the fork) carefully away from the bank and watching the arc
indicated by the hand _A_, Fig. 72, we can determine with great
exactness the angular extent of lock. The diagram at Fig. 75 illustrates
how this experiment is conducted. We apply the hair broach to the end of
the fork _M_, as shown at _L_, and gently move the fork in the direction
of the arrow _i_, watching the hand _A_ and note the number of degrees,
or parts of degrees, indicated by the hand as passed over before the
tooth is unlocked and passes on to the impulse plane and the fork flies
forward to the opposite bank. Now, the quick movement of the pallet and
fork may make the hand mark more or less of an arc on the index than one
of ten degrees, as the grasp may slip on the pallet staff; but the arc
indicated by the slow movement in unlocking will be correct.

[Illustration: Fig. 75]

By taking a piece of sharpened pegwood and placing the point in the slot
of the fork, we can test the fork to see if the drop takes place much
before the lever rests against the opposite bank. As we have previously
stated, the drop from the pallet should not take place until the lever
_almost_ rests on the banking pin. What the reader should impress on his
mind is that the lever should pass through about one and a half degrees
arc to unlock, and the remainder (eight and a half degrees) of the ten
degrees are to be devoted to impulse. But, understand, if the impulse
angle is only seven and a half degrees, and the jewel pin acts in
accordance with the rules previously given, do not alter the pallet
until you know for certain you will gain by it. An observant workman
will, after a little practice, be able to determine this matter.

We will next take up the double roller and fork action, and also
consider in many ways the effect of less angles of action than ten
degrees. This matter now seems of more importance, from the fact that we
are desirous to impress on our readers that _there is no valid reason
for adopting ten degrees of fork and roller action with the table
roller, except that about this number of degrees of action are required
to secure a reliable safety action_. With the double roller, as low as
six degrees fork and pallet action can be safely employed. In fork and
pallet actions below six degrees of angular motion, side-shake in pivot
holes becomes a dangerous factor, as will be explained further on. It is
perfectly comprehending the action of the lever escapement and then
being able to remedy defects, that constitute the master workman.


HOW TO MEASURE THE ANGULAR MOTION OF AN ESCAPE WHEEL.

[Illustration: Fig. 76]

We can also make use of our angle-testing device for measuring our
escape-wheel action, by letting the clasp embrace the arbor of the
escape wheel, instead of the pallet staff. We set the index arc as in
our former experiments, except we place the movable index _D_, Fig. 76,
so that when the engaged tooth rests on the locking face of a pallet,
the index hand stands at the extreme end of our arc of twelve degrees.
We next, with our pointed pegwood, start to move the fork away from the
bank, as before, we look sharp and see the index hand move backward a
little, indicating the "draw" on the locking face. As soon as the pallet
reaches the impulse face, the hand _A_ moves rapidly forward, and if the
escapement is of the club-tooth order and closely matched, the hand _A_
will pass over ten and a half degrees of angular motion before the drop
takes place.

[Illustration: Fig. 77]

We will warn our readers in advance, that if they make such a testing
device they will be astonished at the inaccuracy which they will find in
the escapements of so-called fine watches. The lock, in many instances,
instead of being one and a half degrees, will oftener be found to be
from two to four degrees, and the impulse derived from the escape wheel,
as illustrated at Fig. 76, will often fall below eight degrees. Such
watches will have a poor motion and tick loud enough to keep a policeman
awake. Trials with actual watches, with such a device as we have just
described, in conjunction with a careful study of the acting parts,
especially if aided by a large model, such as we have described, will
soon bring the student to a degree of skill unknown to the old-style
workman, who, if a poor escapement bothered him, would bend back the
banking pins or widen the slot in the fork.

We hold that educating our repair workmen up to a high knowledge of what
is required to constitute a high-grade escapement, will have a
beneficial effect on manufacturers. When we wish to apply our device to
the measurement of the escapement of three-quarter-plate watches, we
will require another index hand, with the grasping end bent downward, as
shown at Fig. 77. The idea with this form of index hand is, the
bent-down jaws _B'_, Fig. 77, grasp the fork as close to the pallet
staff as possible, making an allowance for the acting center by so
placing the index arc that the hand _A_ will read correctly on the index
_D_. Suppose, for instance, we place the jaws _B'_ inside the pallet
staff, we then place the index arc so the hand reads to the arc
indicated by the dotted arc _m_, Fig. 78, and if set outside of the
pallet staff, read by the arc _o_.

[Illustration: Fig. 78]


HOW A BALANCE CONTROLS THE TIMEKEEPING OF A WATCH.

We think a majority of the fine lever escapements made abroad in this
day have what is termed double-roller safety action. The chief gains to
be derived from this form of safety action are: (1) Reducing the arc of
fork and roller action; (2) reducing the friction of the guard point to
a minimum. While it is entirely practicable to use a table roller for
holding the jewel pin with a double-roller action, still a departure
from that form is desirable, both for looks and because as much of the
aggregate weight of a balance should be kept as far from the axis of
rotation as possible.

We might as well consider here as elsewhere, the relation the balance
bears to the train as a controlling power. Strictly speaking, _the
balance and hairspring are the time measurers_, the train serving only
two purposes: (_a_) To keep the balance in motion; (_b_) to classify and
record the number of vibrations of the balance. Hence, it is of
paramount importance that the vibrations of the balance should be as
untrammeled as possible; this is why we urge reducing the arc of
connection between the balance and fork to one as brief as is consistent
with sound results. With a double-roller safety action we can easily
reduce the fork action to eight degrees and the roller action to
twenty-four degrees.

Inasmuch as satisfactory results in adjustment depend very much on the
perfection of construction, we shall now dwell to some extent on the
necessity of the several parts being made on correct principles. For
instance, by reducing the arc of engagement between the fork and roller,
we lessen the duration of any disturbing influence of escapement action.

To resume the explanation of why it is desirable to make the staff and
all parts near the axis of the balance as light as possible, we would
say it is the moving portion of the balance which controls the
regularity of the intervals of vibration. To illustrate, suppose we have
a balance only 3/8" in diameter, but of the same weight as one in an
ordinary eighteen-size movement. We can readily see that such a balance
would require but a very light hairspring to cause it to give the usual
18,000 vibrations to the hour. We can also understand, after a little
thought, that such a balance would exert as much breaking force on its
pivots as a balance of the same weight, but ¾" in diameter acting
against a very much stronger hairspring. There is another factor in the
balance problem which deserves our attention, which factor is
atmospheric resistance. This increases rapidly in proportion to the
velocity.


HOW BAROMETRIC PRESSURE AFFECTS A WATCH.

The most careful investigators in horological mechanics have decided
that a balance much above 75/100" in diameter, making 18,000 vibrations
per hour, is not desirable, because of the varying atmospheric
disturbances as indicated by barometric pressure. A balance with all of
its weight as near the periphery as is consistent with strength, is what
is to be desired for best results. It is the moving matter composing the
balance, pitted against the elastic force of the hairspring, which we
have to depend upon for the regularity of the timekeeping of a watch,
and if we can take two grains' weight of matter from our roller table
and place them in the rim or screws of the balance, so as to act to
better advantage against the hairspring, we have disposed of these two
grains so as to increase the efficiency of the controlling power and not
increase the stress on the pivots.

[Illustration: Fig. 79]

We have deduced from the facts set forth, two axioms: (_a_) That we
should keep the weight of our balance as much in the periphery as
possible, consistent with due strength; (_b_) avoid excessive size from
the disturbing effect of the air. We show at _A_, Fig. 79, the shape of
the piece which carries the jewel pin. As shown, it consists of three
parts: (1) The socket _A_, which receives the jewel pin _a_; (2) the
part _A''_ and hole _b_, which goes on the balance staff; (3) the
counterpoise _A'''_, which makes up for the weight of the jewel socket
_A_, neck _A'_ and jewel pin. This counterpoise also makes up for the
passing hollow _C_ in the guard roller _B_, Fig. 80. As the piece _A_
is always in the same relation to the roller _B_, the poise of the
balance must always remain the same, no matter how the roller action is
placed on the staff. We once saw a double roller of nearly the shape
shown at Fig. 79, which had a small gold screw placed at _d_, evidently
for the purpose of poising the double rollers; but, to our thinking, it
was a sort of hairsplitting hardly worth the extra trouble. Rollers for
very fine watches should be poised on the staff before the balance is
placed upon it.

[Illustration: Fig. 80]

We shall next give detailed instructions for drawing such a double
roller as will be adapted for the large model previously described,
which, as the reader will remember, was for ten degrees of roller
action. We will also point out the necessary changes required to make it
adapted for eight degrees of fork action. We would beg to urge again the
advantages to be derived from constructing such a model, even for
workmen who have had a long experience in escapements, our word for it
they will discover a great many new wrinkles they never dreamed of
previously.

It is important that every practical watchmaker should thoroughly master
the theory of the lever escapement and be able to comprehend and
understand at sight the faults and errors in such escapements, which, in
the every-day practice of his profession, come to his notice. In no
place is such knowledge more required than in fork and roller action. We
are led to say the above chiefly for the benefit of a class of workmen
who think there is a certain set of rules which, if they could be
obtained, would enable them to set to rights any and all escapements. It
is well to understand that no such system exists and that, practically,
we must make one error balance another; and it is the "know how" to make
such faults and errors counteract each other that enables one workman to
earn more for himself or his employer in two days than another workman,
who can file and drill as well as he can, will earn in a week.


PROPORTIONS OF THE DOUBLE-ROLLER ESCAPEMENT.

The proportion in size between the two rollers in a double-roller
escapement is an open question, or, at least, makers seldom agree on it.
Grossmann shows, in his work on the lever escapement, two sizes: (1)
Half the diameter of the acting roller; (2) two-thirds of the size of
the acting roller. The chief fault urged against a smaller safety roller
is, that it necessitates longer horns to the fork to carry out the
safety action. Longer horns mean more metal in the lever, and it is the
conceded policy of all recent makers to have the fork and pallets as
light as possible. Another fault pertaining to long horns is, when the
horn does have to act as safety action, a greater friction ensues.

In all soundly-constructed lever escapements the safety action is only
called into use in exceptional cases, and if the watch was lying still
would theoretically never be required. Where fork and pallets are poised
on their arbor, pocket motion (except torsional) should but very little
affect the fork and pallet action of a watch, and torsional motion is
something seldom brought to act on a watch to an extent to make it
worthy of much consideration. In the double-roller action which we shall
consider, we shall adopt three-fifths of the pitch diameter of the
jewel-pin action as the proper size. Not but what the proportions given
by Grossmann will do good service; but we adopt the proportions named
because it enables us to use a light fork, and still the friction of the
guard point on the roller is but little more than where a guard roller
of half the diameter of the acting roller is employed.

The fork action we shall consider at present is ten degrees, but
subsequently we shall consider a double-roller action in which the fork
and pallet action is reduced to eight degrees. We shall conceive the
play between the guard point and the safety roller as one degree, which
will leave half a degree of lock remaining in action on the engaged
pallet.


THEORETICAL ACTION OF DOUBLE ROLLER CONSIDERED.

In the drawing at Fig. 81 we show a diagram of the action of the
double-roller escapement. The small circle at _A_ represents the center
of the pallet staff, and the one at _B_ the center of the balance staff.
The radial lines _A d_ and _A d'_ represent the arc of angular motion of
fork action. The circle _b b_ represents the pitch circle of the jewel
pin, and the circle at _c c_ the periphery of the guard or safety
roller. The points established on the circle _c c_ by intersection of
the radial lines _A d_ and _A d'_ we will denominate the points _h_ and
_h'_. It is at these points the end of the guard point of the fork will
terminate. In construction, or in delineating for construction, we show
the guard enough short of the points _h h'_ to allow the fork an angular
motion of one degree, from _A_ as a center, before said point would come
in contact with the safety roller.

[Illustration: Fig. 81]

We draw through the points _h h'_, from _B_ as a center, the radial
lines _B g_ and _B g'_. We measure this angle by sweeping the short arc
_i_ with any of the radii we have used for arc measurement in former
delineations, and find it to be a trifle over sixty degrees. To give
ourselves a practical object lesson, let us imagine that a real guard
point rests on the circle _c_ at _h_. Suppose we make a notch in the
guard roller represented by the circle _c_, to admit such imaginary
guard point, and then commence to revolve the circle _c_ in the
direction of the arrow _j_, letting the guard point rest constantly in
such notch. When the notch _n_ in _c_ has been carried through thirty
degrees of arc, counting from _B_ as a center, the guard point, as
relates to _A_ as a center, would only have passed through an arc of
five degrees. We show such a guard point and notch at _o n_. In fact, if
a jewel pin was set to engage the fork on the pitch circle _b a_, the
escapement would lock. To obviate such lock we widen the notch _n_ to
the extent indicated by the dotted lines _n'_, allowing the guard point
to fall back, so to speak, into the notch _n_, which really represents
the passing hollow. It is not to be understood that the extended notch
at _n_ is correctly drawn as regards position, because when the guard
point was on the line _A f_ the point _o_ would be in the center of the
extended notch, or passing hollow. We shall next give the details of
drawing the double roller, but before doing so we deemed it important to
explain the action of such guard points more fully than has been done
heretofore.


HOW TO DESIGN A DOUBLE-ROLLER ESCAPEMENT.

We have already given very desirable forms for the parts of a
double-roller escapement, consequently we shall now deal chiefly with
acting principles as regards the rollers, but will give, at Fig. 82, a
very well proportioned and practical form of fork. The pitch circle of
the jewel pin is indicated by the dotted circle _a_, and the jewel pin
of the usual cylindrical form, with two-fifths cut away. The safety
roller is three-fifths of the diameter of the pitch diameter of the
jewel-pin action, as indicated by the dotted circle _a_.

The safety roller is shown in full outline at _B'_, and the passing
hollow at _E_. It will be seen that the arc of intersection embraced
between the radial lines _B c_ and _B d_ is about sixty-one and a half
degrees for the roller, but the angular extent of the passing hollow is
only a little over thirty-two degrees. The passing hollow _E_ is located
and defined by drawing the radial line _B c_ from the center _B_ through
the intersection of radial line _A i_ with the dotted arc _b_, which
represents the pitch circle of the safety roller. We will name this
intersection the point _l_. Now the end of the guard point _C_
terminates at the point _l_, and the passing hollow _E_ extends on _b_
sixteen degrees on each side of the radial line _B c_.

[Illustration: Fig. 82]

The roller action is supposed to continue through thirty degrees of
angular motion of the balance staff, and is embraced on the circle _a_
between the radial line _B k_ and _B o_. To delineate the inner face of
the horn _p_ of the fork _F_ we draw the short arc _g_, from _A_ as a
center, and on said arc locate at two degrees from the center at _B_ the
point _f_. We will designate the upper angle of the outer face of the
jewel pin _D_ as the point _s_ and, from _A_ as a center, sweep through
this point _s_ the short arc _n n_. Parallel with the line _A i_ and at
the distance of half the diameter of the jewel pin _D_, we draw the
short lines _t t'_, which define the inner faces of the fork.

The intersection of the short line _t_ with the arc _n_ we will
designate the point _r_. With our dividers set to embrace the space
between the point _r_ and the point _f_, we sweep the arc which defines
the inner face of the prong of the fork. The space we just made use of
is practically the same as the radius of the circle _a_, and
consequently of the same curvature. Practically, the length of the guard
point _C'_ is made as long as will, with certainty, clear the safety
roller _B_ in all positions. While we set the point _f_ at two degrees
from the center _B_, still, in a well-constructed escapement, one and a
half degrees should be sufficient, but the extra half degree will do no
harm. If the roller _B'_ is accurately made and the guard point _C'_
properly fitted, the fork will not have half a degree of play.

The reader will remember that in the escapement model we described we
cut down the drop to one degree, being less by half a degree than
advised by Grossmann and Saunier. We also advised only one degree of
lock. In the perfected lever escapement, which we shall describe and
give working drawings for the construction of, we shall describe a
detached lever escapement with only eight degrees fork and pallet
action, with only three-fourths of a degree drop and three-fourths of a
degree lock, which we can assure our readers is easily within the limits
of practical construction by modern machinery.


HOW THE GUARD POINT IS MADE.

[Illustration: Fig. 83]

The guard point _C'_, as shown at Fig. 82, is of extremely simple
construction. Back of the slot of the fork, which is three-fifths of the
diameter of the jewel pin in depth, is made a square hole, as shown at
_u_, and the back end of the guard point _C_ is fitted to this hole so
that it is rigid in position. This manner of fastening the guard point
is equally efficient as that of attaching it with a screw, and much
lighter--a matter of the highest importance in escapement construction,
as we have already urged. About the best material for such guard points
is either aluminum or phosphor bronze, as such material is lighter than
gold and very rigid and strong. At Fig. 83 we show a side view of the
essential parts depicted in Fig. 82, as if seen in the direction of the
arrow _v_, but we have added the piece which holds the jewel pin _D_. A
careful study of the cut shown at Fig. 82 will soon give the horological
student an excellent idea of the double-roller action.

We will now take up and consider at length why Saunier draws his
entrance pallet with fifteen degrees draw and his exit pallet with only
twelve degrees draw. To make ourselves more conversant with Saunier's
method of delineating the lever escapement, we reproduce the essential
features of his drawing, Fig. 1, plate VIII, of his "Modern Horology,"
in which he makes the draw of the locking face of the entrance pallet
fifteen degrees and his exit pallet twelve degrees. In the cut shown at
Fig. 84 we use the same letters of reference as he employs. We do not
quote his description or directions for delineation because he refers to
so much matter which he has previously given in the book just referred
to. Besides we cannot entirely endorse his methods of delineations for
many reasons, one of which appears in the drawing at Fig. 84.

[Illustration: Fig. 84]


MORE ABOUT TANGENTIAL LOCKINGS.

Most writers endorse the idea of tangential lockings, and Saunier speaks
of the escapement as shown at Fig. 84 as having such tangential
lockings, which is not the case. He defines the position of the pallet
staff from the circle _t_, which represents the extreme length of the
teeth; drawing the radial lines _A D_ and _A E_ to embrace an arc of
sixty degrees, and establishing the center of his pallet staff _C_ at
the intersection of the lines _D C_ and _E C_, which are drawn at right
angles to the radial lines _A D_ and _A E_, and tangential to the circle
_t_.

Here is an error; the lines defining the center of the pallet staff
should have been drawn tangent to the circle _s_, which represents the
locking angle of the teeth. This would have placed the center of the
pallet staff farther in, or closer to the wheel. Any person can see at a
glance that the pallets as delineated are not tangential in a true
sense.

[Illustration: Fig. 85]

We have previously considered engaging friction and also repeatedly have
spoken of tangential lockings, but will repeat the idea of tangential
lockings at Fig. 85. A tangential locking is neutral, or nearly so, as
regards engaging friction. For illustration we refer to Fig. 85, where
_A_ represents the center of an escape wheel. We draw the radial lines
_A y_ and _A z_ so that they embrace sixty degrees of the arcs _s_ or
_t_, which correspond to similar circles in Fig. 84, and represent the
extreme extent of the teeth and likewise the locking angle of such
teeth. In fact, with the club-tooth escapement all that part of a tooth
which extends beyond the line _s_ should be considered the same as the
addendum in gear wheels. Consequently, a tangential locking made to
coincide with the center of the impulse plane, as recommended by
Saunier, would require the pallet staff to be located at _C'_ instead of
_C_, as he draws it. If the angle _k'_ of the tooth _k_ in Fig. 84 was
extended outward from the center _A_ so it would engage or rest on the
locking face of the entrance pallet as shown at Fig. 84, then the draw
of the locking angle would not be quite fifteen degrees; but it is
evident no lock can take place until the angle _a_ of the entrance
pallet has passed inside the circle _s_. We would say here that we have
added the letters _s_ and _t_ to the original drawings, as we have
frequently to refer to these circles, and without letters had no means
of designation. Before the locking angle _k'_ of the tooth can engage
the pallet, as shown in Fig. 84, the pallet must turn on the center _C_
through an angular movement of at least four degrees. We show the
situation in the diagram at Fig. 86, using the same letters of reference
for similar parts as in Fig. 84.

[Illustration: Fig. 86]

As drawn in Fig. 84 the angle of draft _G a I_ is equal to fifteen
degrees, but when brought in a position to act as shown at _G a' I'_,
Fig. 86, the draw is less even than twelve degrees. The angle _C a I_
remains constant, as shown at _C a' I'_, but the relation to the radial
_A G_ changes when the pallet moves through the angle _w C w'_, as it
must when locked. A tangential locking in the true sense of the meaning
of the phrase is a locking set so that a pallet with its face coinciding
with a radial line like _A G_ would be neutral, and the thrust of the
tooth would be tangent to the circle described by the locking angle of
the tooth. Thus the center _C_, Fig. 86, is placed on the line _w'_
which is tangent to the circle _s_; said line _w'_ also being at right
angles to the radial line _A G_.

The facts are, the problems relating to the club-tooth lever escapement
are very intricate and require very careful analysis, and without such
care the horological student can very readily be misled. Faulty
drawings, when studying such problems, lead to no end of errors, and
practical men who make imperfect drawings lead to the popular phrase,
"Oh, such a matter may be all right in theory, but will not work in
practice." We should always bear in mind that _theory, if right, must
lead practice_.


CORRECT DRAWING REQUIRED.

If we delineate our entrance pallet to have a draw of twelve degrees
when in actual contact with the tooth, and then construct in exact
conformity with such drawings, we will find our lever to "hug the banks"
in every instance. It is inattention to such details which produces the
errors of makers complained of by Saunier in section 696 of his "Modern
Horology," and which he attempts to correct by drawing the locking face
at fifteen degrees draw.

We shall show that neither _C_ nor _C'_, Fig. 85, is the theoretically
correct position for the pallet center for a tangential locking.

We will now take up the consideration of a club-tooth lever escapement
with circular pallets and tangential lockings; but previous to making
the drawings we must decide several points, among which are the
thickness of the pallet arms, which establishes the angular motion of
the escape wheel utilized by such pallet arms, and also the angular
motion imparted to the pallets by the impulse faces of the teeth. We
will, for the present, accept the thickness of the arms as being
equivalent to five degrees of angular extent of the pitch circle of the
escape wheel.

[Illustration: Fig. 87]

[Illustration: Fig. 88]

In making our drawings we commence, as on former occasions, by
establishing the center of our escape wheel at _A_, Fig. 87, and
sweeping the arc _a a_ to represent the pitch circle of such wheel.
Through the center _A_ we draw the vertical line _A B_, which is
supposed to also pass through the center of the pallet staff. The
intersection of the line _A B_ with the arc _a_ we term the point _d_,
and from this point we lay off on said arc _a_ thirty degrees each side
of said intersection, and thus establish the points _c b_. From _A_,
through the point _c_, we draw the line _A c c'_. On the arc _a a_ and
two and a half degrees to the left of the point _c_ we establish the
point _f_, which space represents half of the thickness of the entrance
pallet. From _A_ we draw through the point _f_ the line _A f f'_. From
_f_, and at right angles to said line _A f_, we draw the line _f e_
until it crosses the line _A B_.

Now this line _f e_ is tangent to the arc _a_ from the point _f_, and
consequently a locking placed at the point _f_ is a true tangential
locking; and if the resting or locking face of a pallet was made to
coincide with the line _A f'_, such locking face would be strictly
"dead" or neutral. The intersection of the line _f e_ with the line _A
B_ we call the point _C_, and locate at this point the center of our
pallet staff. According to the method of delineating the lever
escapement by Moritz Grossmann the tangent line for locating the center
of the pallet staff is drawn from the point _c_, which would locate the
center of the pallet staff at the point _h_ on the line _A B_.

Grossmann, in delineating his locking face for the draw, shows such face
at an angle of twelve degrees to the radial line _A f'_, when he should
have drawn it twelve degrees to an imaginary line shown at _f i_, which
is at right angles to the line _f h_. To the writer's mind this is not
just as it should be, and may lead to misunderstanding and bad
construction. We should always bear in mind the fact that the basis of a
locking face is a neutral plane placed at right angles to the line of
thrust, and the "draw" comes from a locking face placed at an angle to
such neutral plane. A careful study of the diagram at Fig. 88 will give
the reader correct ideas. If a tooth locks at the point _c_, the
tangential thrust would be on the line _c h'_, and a neutral locking
face would be on the line _A c_.


NEUTRAL LOCKINGS.

To aid in explanation, let us remove the pallet center to _D_; then the
line of thrust would be _c D_ and a neutral locking face would coincide
with the line _m m_, which is at right angles to the line _c D_. If we
should now make a locking face with a "draw" and at an angle to the line
_c D_, say, for illustration, to correspond to the line _c c'_ (leaving
the pallet center at _D_), we would have a strong draw and also a cruel
engaging friction.

If, however, we removed the engaging tooth, which we have just conceived
to be at _c_, to the point _k_ on the arc _a' a'_, Fig. 88, the pallet
center _D_ would then represent a tangential locking, and a neutral
pallet face would coincide with the radial line _A k'_; and a locking
face with twelve degrees draw would coincide nearly with the line _l_.
Let us next analyze what the effect would be if we changed the pallet
center to _h'_, Fig. 88, leaving the engaging tooth still at _k_. In
this instance the line _l l_ would then coincide with a neutral locking
face, and to obtain the proper draw we should delineate the locking face
to correspond to the line _k n_, which we assume to be twelve degrees
from _k l_.

It is not to be understood that we insist on precisely twelve degrees
draw from a neutral plane for locking faces for lever pallets. What we
do insist upon, however, is a "safe and sure draw" for a lever pallet
which will hold a fork to the banks and will also return it to such
banks if by accident the fork is moved away. We are well aware that it
takes lots of patient, hard study to master the complications of the
club-tooth lever escapement, but it is every watchmaker's duty to
conquer the problem. The definition of "lock," in the detached lever
escapement, is the stoppage or arrest of the escape wheel of a watch
while the balance is left free or detached to perform the greater
portion of its arc of vibration. "Draw" is a function of the locking
parts to preserve the fork in the proper position to receive and act on
the jewel pin of the balance.

It should be borne in mind in connection with "lock" and "draw," that
the line of thrust as projected from the locked tooth of the escape
wheel should be as near tangential as practicable. This maxim applies
particularly to the entrance pallet. We would beg to add that
practically it will make but little odds whether we plant the center of
our pallet staff at _C_ or _h_, Fig. 87, provided we modify the locking
and impulse angles of our pallets to conform to such pallet center. But
it will not do to arrange the parts for one center and then change to
another.


PRACTICAL HINTS FOR LEVER ESCAPEMENTS.

Apparently there seems to be a belief with very many watchmakers that
there is a set of shorthand rules for setting an escapement, especially
in American watches, which, if once acquired, conquers all
imperfections. Now we wish to disabuse the minds of our readers of any
such notions. Although the lever escapement, as adopted by our American
factories, is constructed on certain "lines," still these lines are
subject to modifications, such as may be demanded for certain defects of
construction. If we could duplicate every part of a watch movement
perfectly, then we could have certain rules to go by, and fixed
templets could be used for setting pallet stones and correcting other
escapement faults.

Let us now make an analysis of the action of a lever escapement. We show
at Fig. 89 an ordinary eighteen-size full-plate lever with fork and
pallets. The dotted lines _a b_ are supposed to represent an angular
movement of ten degrees. Now, it is the function of the fork to carry
the power of the train to the balance. How well the fork performs its
office we will consider subsequently; for the present we are dealing
with the power as conveyed to the fork by the pallets as shown at Fig.
89.

[Illustration: Fig. 89]

The angular motion between the lines _a c_ (which represents the lock)
is not only absolutely lost--wasted--but during this movement the train
has to retrograde; that is, the dynamic force stored in the momentum of
the balance has to actually turn the train backward and against the
force of the mainspring. True, it is only through a very short arc, but
the necessary force to effect this has to be discounted from the power
stored in the balance from a former impulse. For this reason we should
make the angular motion of unlocking as brief as possible. Grossmann, in
his essay, endorses one and a half degrees as the proper lock.

In the description which we employed in describing the large model for
illustrating the action of the detached lever escapement, we cut the
lock to one degree, and in the description of the up-to-date lever
escapement, which we shall hereafter give, we shall cut the lock down to
three-quarters of a degree, a perfection easily to be attained by modern
tools and appliances. We shall also cut the drop down to three-quarters
of a degree. By these two economies we more than make up for the power
lost in unlocking. With highly polished ruby or sapphire pallets ten
degrees of draw is ample. But such draw must positively be ten degrees
from a neutral locking face, not an escapement drawn on paper and
called ten degrees, but when actually measured would only show eight and
a half or nine degrees.


THE PERFECTED LEVER ESCAPEMENT.

With ten degrees angular motion of the lever and one and a half degrees
lock, we should have eight and a half degrees impulse. The pith of the
problem, as regards pallet action, for the practical workman can be
embodied in the following question: What proportion of the power derived
from the twelve degrees of angular motion of the escape wheel is really
conveyed to the fork? The great leak of power as transmitted by the
lever escapement to the balance is to be found in the pallet action, and
we shall devote special attention to finding and stopping such leaks.


WHEN POWER IS LOST IN THE LEVER ESCAPEMENT.

If we use a ratchet-tooth escape wheel we must allow at least one and a
half degrees drop to free the back of the tooth; but with a club-tooth
escape wheel made as can be constructed by proper skill and care, the
drop can be cut down to three-quarters of a degree, or one-half of the
loss with the ratchet tooth. We do not wish our readers to imagine that
such a condition exists in most of the so-called fine watches, because
if we take the trouble to measure the actual drop with one of the little
instruments we have described, it will be found that the drop is seldom
less than two, or even three degrees.

If we measure the angular movement of the fork while locked, it will
seldom be found less than two or three degrees. Now, we can all
understand that the friction of the locking surface has to be counted as
well as the recoil of the draw. Locking friction is seldom looked after
as carefully as the situation demands. Our factories make the impulse
face of the pallets rounded, but leave the locking face flat. We are
aware this condition is, in a degree, necessary from the use of exposed
pallets. In many of the English lever watches with ratchet teeth, the
locking faces are made cylindrical, but with such watches the pallet
stones, as far as the writer has seen, are set "close"; that is, with
steel pallet arms extending above and below the stone.

There is another feature of the club-tooth lever escapement that next
demands our attention which we have never seen discussed. We refer to
arranging and disposing of the impulse of the escape wheel to meet the
resistance of the hairspring. Let us imagine the dotted line _A d_, Fig.
89, to represent the center of action of the fork. We can readily see
that the fork in a state of rest would stand half way between the two
banks from the action of the hairspring, and in the pallet action the
force of the escape wheel, one tooth of which rests on the impulse face
of a pallet, would be exerted against the elastic force of the
hairspring. If the force of the mainspring, as represented by the
escape-wheel tooth, is superior to the power of the hairspring, the
watch starts itself. The phases of this important part of the detached
lever escapement will be fully discussed.


ABOUT THE CLUB-TOOTH ESCAPEMENT.

We will now take up a study of the detached lever escapement as relates
to pallet action, with the point specially in view of constructing an
escapement which cannot "set" in the pocket, or, in other words, an
escapement which will start after winding (if run down) without shaking
or any force other than that supplied by the train as impelled by the
mainspring. In the drawing at Fig. 90 we propose to utilize eleven
degrees of escape-wheel action, against ten and a half, as laid down by
Grossmann. Of this eleven degrees we propose to divide the impulse arc
of the escape wheel in six and five degrees, six to be derived from the
impulse face of the club tooth and five from the impulse plane of the
pallet.

The pallet action we divide into five and four, with one degree of lock.
Five degrees of pallet action is derived from the impulse face of the
tooth and four from the impulse face of the pallet. The reader will
please bear in mind that we do not give these proportions as imperative,
because we propose to give the fullest evidence into the reader's hands
and enable him to judge for himself, as we do not believe in laying down
imperious laws that the reader must accept on our assertion as being
correct. Our idea is rather to furnish the proper facts and put him in a
situation to know for himself.

The reader is urged to make the drawings for himself on a large scale,
say, an escape wheel 10" pitch diameter. Such drawings will enable him
to realize small errors which have been tolerated too much in drawings
of this kind. The drawings, as they appear in the cut, are one-fourth
the size recommended, and many of the lines fail to show points we
desire to call attention to. As for instance, the pallet center at _B_
is tangential to the pitch circle _a_ from the point of tooth contact at
_f_. To establish this point we draw the radial lines _A c_ and _A d_
from the escape-wheel center _A_, as shown, by laying off thirty degrees
on each side of the intersection of the vertical line _i_ (passing
through the centers _A B_) with the arc _a_, and then laying off two and
a half degrees on _a_ and establishing the point _f_, and through _f_
from the center _A_ draw the radial line _A f'_. Through the point _f_
we draw the tangent line _b' b b''_, and at the intersection of the line
_b_ with _i_ we establish the center of our pallet staff at _B_. At two
and a half degrees from the point _c_ we lay off two and a half degrees
to the right of said point and establish the point _n_, and draw the
radial line _A n n'_, which establishes the extent of the arc of angular
motion of the escape wheel utilized by the pallet arm.

[Illustration: Fig. 90]

We have now come to the point where we must exercise our reasoning
powers a little. We know the locking angle of the escape-wheel tooth
passes on the arc _a_, and if we utilize the impulse face of the tooth
for five degrees of pallet or lever motion we must shape it to this end.
We draw the short arc _k_ through the point _n_, knowing that the inner
angle of the pallet stone must rest on this arc wherever it is situated.
As, for instance, when the locking face of the pallet is engaged, the
inner angle of the pallet stone must rest somewhere on this arc (_k_)
inside of _a_, and the extreme outer angle of the impulse face of the
tooth must part with the pallet on this arc _k_.


HOW TO LOCATE THE PALLET ACTION.

With the parts related to each other as shown in the cut, to establish
where the inner angle of the pallet stone is located in the drawing, we
measure down on the arc _k_ five degrees from its intersection with _a_,
and establish the point _s_. The line _B b_, Fig. 90, as the reader will
see, does not coincide with the intersection of the arcs _a_ and _k_,
and to conveniently get at the proper location for the inner angle of
our pallet stone, we draw the line _B b'_, which passes through the
point _n_ located at the intersection of the arc _a_ with the arc _k_.
From _B_ as a center we sweep the short arc _j_ with any convenient
radius of which we have a sixty-degree scale, and from the intersection
of _B b'_ with _j_ we lay off five degrees and draw the line _B s'_,
which establishes the point _s_ on the arc _k_. As stated above, we
allow one degree for lock, which we establish on the arc _o_ by laying
off one degree on the arc _j_ below its intersection with the line _B
b_. We do not show this line in the drawing, from the fact that it comes
so near to _B b'_ that it would confuse the reader. Above the arc _a_ on
the arc _k_ at five degrees from the point _n_ we establish the point
_l_, by laying off five degrees on the arc _j_ above the intersection of
the line _B b_ with _j_.

The point _l_, Fig. 90, establishes where the outer angle of the tooth
will pass the arc _k_ to give five degrees of angular motion to the
lever. From _A_ as a center we sweep the arc _m_, passing through the
point _l_. The intersection of the arc _m_ with the line _A h_ we call
the point _r_, and by drawing the right line _r f_ we delineate the
impulse face of the tooth. On the arc _o_ and one degree below its
intersection with the line _B b_ we establish the point _t_, and by
drawing a right line from _t_ to _s_ we delineate the impulse face of
our entrance pallet.


"ACTION" DRAWINGS.

One great fault with most of our text books on horology lies in the fact
that when dealing with the detached lever escapement the drawings show
only the position of the pallets when locked, and many of the conditions
assumed are arrived at by mental processes, without making the proper
drawings to show the actual relation of the parts at the time such
conditions exist. For illustration, it is often urged that there is a
time in the action of the club-tooth lever escapement action when the
incline on the tooth and the incline on the pallet present parallel
surfaces, and consequently endure excessive friction, especially if the
oil is a little thickened.

We propose to make drawings to show the exact position and relation of
the entrance pallet and tooth at three intervals viz: (1) Locked; (2)
the position of the parts when the lever has performed one-half of its
angular motion; (3) when half of the impulse face of the tooth has
passed the pallet. The position of the entrance pallet when locked is
sufficiently well shown in Fig. 90 to give a correct idea of the
relations with the entrance pallet; and to conform to statement (2), as
above. We will now delineate the entrance pallet, not in actual contact,
however, with the pallet, because if we did so the lines we employed
would become confused. The methods we use are such that _we can
delineate with absolute correctness either a pallet or tooth at any
point in its angular motion_.

We have previously given instructions for drawing the pallet locked; and
to delineate the pallet after five degrees of angular motion, we have
only to conceive that we substitute the line _s'_ for the line _b'_. All
angular motions and measurements for pallet actions are from the center
of the pallet staff at _B_. As we desire to now delineate the entrance
pallet, it has passed through five degrees of angular motion and the
inner angle _s_ now lies on the pitch circle of the escape wheel, the
angular space between the lines _b' s'_ being five degrees, the line
_b''_ reducing the impulse face to four degrees.


DRAWING AN ESCAPEMENT TO SHOW ANGULAR MOTION.

To delineate our locking face we draw a line at right angles to the line
_B b''_ from the point _t_, said point being located at the intersection
of the arc _o_ with the line _B b''_. To draw a line perpendicular to
_B b''_ from the point _t_, we take a convenient space in our dividers and
establish on the line _B b''_ the points _x x'_ at equal distances from
the point _t_. We open the dividers a little (no special distance) and
sweep the short arcs _x'' x'''_, as shown at Fig. 91. Through the
intersection of the short arcs _x'' x'''_ and to the point _t_ we draw
the line _t y_. The reader will see from our former explanations that
the line _t y_ represents the neutral plane of the locking face, and
that to have the proper draw we must delineate the locking face of our
pallet at twelve degrees. To do this we draw the line _t x'_ at twelve
degrees to the line _t y_, and proceed to outline our pallet faces as
shown. We can now understand, after a moment's thought, that we can
delineate the impulse face of a tooth at any point or place we choose by
laying off six degrees on the arc _m_, and drawing radial lines from _A_
to embrace such arc. To illustrate, suppose we draw the radial lines
_w' w''_ to embrace six degrees on the arc _a_. We make these lines
contiguous to the entrance pallet _C_ for convenience only. To delineate
the impulse face of the tooth, we draw a line extending from the
intersection of the radial line _A' w'_ with the arc _m_ to the
intersection of the arc _a_ with the radial line _A w''_.

[Illustration: Fig. 91]

We next desire to know where contact will take place between the
wheel-tooth _D_ and pallet _C_. To determine this we sweep, with our
dividers set so one leg rests at the escape-wheel center _A_ and the
other at the outer angle _t_ of the entrance pallet, the short arc _t' w_.
Where this arc intersects the line _w_ (which represents the impulse
face of the tooth) is where the outer angle _t_ of the entrance pallet
_C_ will touch the impulse face of the tooth. To prove this we draw the
radial line _A v_ through the point where the short arc _t t'_ passes
through the impulse face _w_ of the tooth _D_. Then we continue the line
_w_ to _n_, to represent the impulse face of the tooth, and then measure
the angle _A w n_ between the lines _w n_ and _v A_, and find it to be
approximately sixty-four degrees. We then, by a similar process, measure
the angle _A t s'_ and find it to be approximately sixty-six degrees.
When contact ensues between the tooth _D_ and pallet _C_ the tooth _D_
will attack the pallet at the point where the radial line _A v_ crosses
the tooth face. We have now explained how we can delineate a tooth or
pallet at any point of its angular motion, and will next explain how to
apply this knowledge in actual practice.


PRACTICAL PROBLEMS IN THE LEVER ESCAPEMENT.

To delineate our entrance pallet after one-half of the engaged tooth has
passed the inner angle of the entrance pallet, we proceed, as in former
illustrations, to establish the escape-wheel center at _A_, and from it
sweep the arc _b_, to represent the pitch circle. We next sweep the
short arcs _p s_, to represent the arcs through which the inner and
outer angles of the entrance pallet move. Now, to comply with our
statement as above, we must draw the tooth as if half of it has passed
the arc _s_.

To do this we draw from _A_ as a center the radial line _A j_, passing
through the point _s_, said point _s_ being located at the intersection
of the arcs _s_ and _b_. The tooth _D_ is to be shown as if one half of
it has passed the point _s_; and, consequently, if we lay off three
degrees on each side of the point _s_ and establish the points _d m_, we
have located on the arc _b_ the angular extent of the tooth to be drawn.
To aid in our delineations we draw from the center _A_ the radial lines
_A d'_ and _A m'_, passing through the points _d m_. The arc _a_ is next
drawn as in former instructions and establishes the length of the
addendum of the escape-wheel teeth, the outer angle of our escape-wheel
tooth being located at the intersection of the arc _a_ with the radial
line _A d'_.

As shown in Fig. 92, the impulse planes of the tooth _D_ and pallet _C_
are in contact and, consequently, in parallel planes, as mentioned on
page 91. It is not an easy matter to determine at exactly what degree of
angular motion of the escape wheel such condition takes place; because
to determine such relation mathematically requires a knowledge of higher
mathematics, which would require more study than most practical men
would care to bestow, especially as they would have but very little use
for such knowledge except for this problem and a few others in dealing
with epicycloidal curves for the teeth of wheels.

For all practical purposes it will make no difference whether such
parallelism takes place after eight or nine degrees of angular motion of
the escape wheel subsequent to the locking action. The great point, as
far as practical results go, is to determine if it takes place at or
near the time the escape wheel meets the greatest resistance from the
hairspring. We find by analysis of our drawing that parallelism takes
place about the time when the tooth has three degrees of angular motion
to make, and the pallet lacks about two degrees of angular movement for
the tooth to escape. It is thus evident that the relations, as shown in
our drawing, are in favor of the train or mainspring power over
hairspring resistance as three is to two, while the average is only as
eleven to ten; that is, the escape wheel in its entire effort passes
through eleven degrees of angular motion, while the pallets and fork
move through ten degrees. The student will thus see we have arranged to
give the train-power an advantage where it is most needed to overcome
the opposing influence of the hairspring.

[Illustration: Fig. 92]

As regards the exalted adhesion of the parallel surfaces, we fancy there
is more harm feared than really exists, because, to take the worst view
of the situation, such parallelism only exists for the briefest
duration, in a practical sense, because theoretically these surfaces
never slide on each other as parallel planes. Mathematically
considered, the theoretical plane represented by the impulse face of
the tooth approaches parallelism with the plane represented by the
impulse face of the pallet, arrives at parallelism and instantly passes
away from such parallelism.


TO DRAW A PALLET IN ANY POSITION.

As delineated in Fig. 92, the impulse planes of the tooth and pallet are
in contact; but we have it in our power to delineate the pallet at any
point we choose between the arcs _p s_. To describe and illustrate the
above remark, we say the lines _B e_ and _B f_ embrace five degrees of
angular motion of the pallet. Now, the impulse plane of the pallet
occupies four of these five degrees. We do not draw a radial line from
_B_ inside of the line _B e_ to show where the outer angle of the
impulse plane commences, but the reader will see that the impulse plane
is drawn one degree on the arc _p_ below the line _B e_. We continue the
line _h h_ to represent the impulse face of the tooth, and measure the
angle _B n h_ and find it to be twenty-seven degrees. Now suppose we
wish to delineate the entrance pallet as if not in contact with the
escape-wheel tooth--for illustration, say, we wish the inner angle of
the pallet to be at the point _v_ on the arc _s_. We draw the radial
line _B l_ through _v_; and if we draw another line so it passes through
the point _v_ at an angle of twenty-seven degrees to _B l_, and continue
said line so it crosses the arc _p_, we delineate the impulse face of
our pallet.

We measure the angle _i n B_, Fig. 92, and find it to be seventy-four
degrees; we draw the line _v t_ to the same angle with _v B_, and we
define the inner face of our pallet in the new position. We draw a line
parallel with _v t_ from the intersection of the line _v y_ with the arc
_p_, and we define our locking face. If now we revolve the lines we have
just drawn on the center _B_ until the line _l B_ coincides with the
line _f B_, we will find the line _y y_ to coincide with _h h_, and the
line _v v'_ with _n i_.


HIGHER MATHEMATICS APPLIED TO THE LEVER ESCAPEMENT.

We have now instructed the reader how to delineate either tooth or
pallet in any conceivable position in which they can be related to each
other. Probably nothing has afforded more efficient aid to practical
mechanics than has been afforded by the graphic solution of abstruce
mathematical problems; and if we add to this the means of correction by
mathematical calculations which do not involve the highest mathematical
acquirements, we have approached pretty close to the actual requirements
of the practical watchmaker.

[Illustration: Fig. 93]

To better explain what we mean, we refer the reader to Fig. 93, where we
show preliminary drawings for delineating a lever escapement. We wish to
ascertain by the graphic method the distance between the centers of
action of the escape wheel and the pallet staff. We make our drawing
very carefully to a given scale, as, for instance, the radius of the arc
_a_ is 5". After the drawing is in the condition shown at Fig. 93 we
measure the distance on the line _b_ between the points (centers) _A B_,
and we thus by graphic means obtain a measure of the distance between _A
B_. Now, by the use of trigonometry, we have the length of the line _A
f_ (radius of the arc _a_) and all the angles given, to find the length
of _f B_, or _A B_, or both _f B_ and _A B_. By adopting this policy we
can verify the measurements taken from our drawings. Suppose we find by
the graphic method that the distance between the points _A B_ is 5.78",
and by trigonometrical computation find the distance to be 5.7762". We
know from this that there is .0038" to be accounted for somewhere; but
for all practical purposes either measurement should be satisfactory,
because our drawing is about thirty-eight times the actual size of the
escape wheel of an eighteen-size movement.


HOW THE BASIS FOR CLOSE MEASUREMENTS IS OBTAINED.

Let us further suppose the diameter of our actual escape wheel to be
.26", and we were constructing a watch after the lines of our drawing.
By "lines," in this case, we mean in the same general form and ratio of
parts; as, for illustration, if the distance from the intersection of
the arc _a_ with the line _b_ to the point _B_ was one-fifteenth of the
diameter of the escape wheel, this ratio would hold good in the actual
watch, that is, it would be the one-fifteenth part of .26". Again,
suppose the diameter of the escape wheel in the large drawing is 10" and
the distance between the centers _A B_ is 5.78"; to obtain the actual
distance for the watch with the escape wheel .26" diameter, we make a
statement in proportion, thus: 10 : 5.78 :: .26 to the actual distance
between the pivot holes of the watch. By computation we find the
distance to be .15". These proportions will hold good in every part of
actual construction.

All parts--thickness of the pallet stones, length of pallet arms,
etc.--bear the same ratio of proportion. We measure the thickness of the
entrance pallet stone on the large drawing and find it to be .47"; we
make a similar statement to the one above, thus: 10 : .47 :: .26 to the
actual thickness of the real pallet stone. By computation we find it to
be .0122". All angular relations are alike, whether in the large drawing
or the small pallets to match the actual escape wheel .26" in diameter.
Thus, in the pallet _D_, Fig. 93, the impulse face, as reckoned from _B_
as a center, would occupy four degrees.


MAKE A LARGE ESCAPEMENT MODEL.

Reason would suggest the idea of having the theoretical keep pace and
touch with the practical. It has been a grave fault with many writers on
horological matters that they did not make and measure the abstractions
which they delineated on paper. We do not mean by this to endorse the
cavil we so often hear--"Oh, that is all right in theory, but it will
not work in practice." If theory is right, practice must conform to it.
The trouble with many theories is, they do not contain all the elements
or factors of the problem.

[Illustration: Fig. 94]

Near the beginning of this treatise we advised our readers to make a
large model, and described in detail the complete parts for such a
model. What we propose now is to make adjustable the pallets and fork to
such a model, in order that we can set them both right and wrong, and
thus practically demonstrate a perfect action and also the various
faults to which the lever escapement is subject. The pallet arms are
shaped as shown at _A_, Fig. 94. The pallets _B B'_ can be made of steel
or stone, and for all practical purposes those made of steel answer
quite as well, and have the advantage of being cheaper. A plate of sheet
brass should be obtained, shaped as shown at _C_, Fig. 95. This plate is
of thin brass, about No. 18, and on it are outlined the pallet arms
shown at Fig. 94.

[Illustration: Fig. 95]

[Illustration: Fig. 96]

[Illustration: Fig. 97]

[Illustration: Fig. 98]

To make the pallets adjustable, they are set in thick disks of sheet
brass, as shown at _D_, Figs. 95, 96 and 97. At the center of the plate
_C_ is placed a brass disk _E_, Fig. 98, which serves to support the
lever shown at Fig. 99. This disk _E_ is permanently attached to the
plate _C_. The lever shown at Fig. 99 is attached to the disk _E_ by two
screws, which pass through the holes _h h_. If we now place the brass
pieces _D D'_ on the plate _C_ in such a way that the pallets set in
them correspond exactly to the pallets as outlined on the plate _C_, we
will find the action of the pallets to be precisely the same as if the
pallet arms _A A'_, Fig. 94, were employed.

[Illustration: Fig. 99]

To enable us to practically experiment with and to fully demonstrate all
the problems of lock, draw, drop, etc., we make quite a large hole in
_C_ where the screws _b_ come. To explain, if the screws _b b_ were
tapped directly into _C_, as they are shown at Fig. 95, we could only
turn the disk _D_ on the screw _b_; but if we enlarge the screw hole in
_C_ to three or four times the natural diameter, and then place the nut
_e_ under _C_ to receive the screw _b_, we can then set the disks _D D'_
and pallets _B B'_ in almost any relation we choose to the escape wheel,
and clamp the pallets fast and try the action. We show at Fig. 97 a view
of the pallet _B'_, disk _D'_ and plate _C_ (seen in the direction of
the arrow _c_) as shown in Fig. 95.


PRACTICAL LESSONS WITH FORK AND PALLET ACTION.

It will be noticed in Fig. 99 that the hole _g_ for the pallet staff in
the lever is oblong; this is to allow the lever to be shifted back and
forth as relates to roller and fork action. We will not bother about
this now, and only call attention to the capabilities of such
adjustments when required. At the outset we will conceive the fork _F_
attached to the piece _E_ by two screws passing through the holes _h h_,
Fig. 99. Such an arrangement will insure the fork and roller action
keeping right if they are put right at first. Fig. 100 will do much to
aid in conveying a clear impression to the reader.

The idea of the adjustable features of our escapement model is to show
the effects of setting the pallets wrong or having them of bad form. For
illustration, we make use of a pallet with the angle too acute, as shown
at _B'''_, Fig. 101. The problem in hand is to find out by mechanical
experiments and tests the consequences of such a change. It is evident
that the angular motion of the pallet staff will be increased, and that
we shall have to open one of the banking pins to allow the engaging
tooth to escape. To trace out _all_ the consequences of this one little
change would require a considerable amount of study, and many drawings
would have to be made to illustrate the effects which would naturally
follow only one such slight change.

[Illustration: Fig. 100]

[Illustration: Fig. 101]

Suppose, for illustration, we should make such a change in the pallet
stone of the entrance pallet; we have increased the angle between the
lines _k l_ by (say) one and a half degrees; by so doing we would
increase the lock on the exit pallet to three degrees, provided we were
working on a basis of one and a half degrees lock; and if we pushed back
the exit pallet so as to have the proper degree of lock (one and a half)
on it, the tooth which would next engage the entrance pallet would not
lock at all, but would strike the pallet on the impulse instead of on
the locking face. Again, such a change might cause the jewel pin to
strike the horn of the fork, as indicated at the dotted line _m_, Fig.
99.

Dealing with such and similar abstractions by mental process requires
the closest kind of reasoning; and if we attempt to delineate all the
complications which follow even such a small change, we will find the
job a lengthy one. But with a large model having adjustable parts we
provide ourselves with the means for the very best practical solution,
and the workman who makes and manipulates such a model will soon master
the lever escapement.


QUIZ PROBLEMS IN THE DETACHED LEVER ESCAPEMENT.

Some years ago a young watchmaker friend of the writer made, at his
suggestion, a model of the lever escapement similar to the one
described, which he used to "play with," as he termed it--that is, he
would set the fork and pallets (which were adjustable) in all sorts of
ways, right ways and wrong ways, so he could watch the results. A
favorite pastime was to set every part for the best results, which was
determined by the arc of vibration of the balance. By this sort of
training he soon reached that degree of proficiency where one could no
more puzzle him with a bad lever escapement than you could spoil a meal
for him by disarranging his knife, fork and spoon.

Let us, as a practical example, take up the consideration of a short
fork. To represent this in our model we take a lever as shown at Fig.
99, with the elongated slot for the pallet staff at _g_. To facilitate
the description we reproduce at Fig. 102 the figure just mentioned, and
also employ the same letters of reference. We fancy everybody who has
any knowledge of the lever escapement has an idea of exactly what a
"short fork" is, and at the same time it would perhaps puzzle them a
good deal to explain the difference between a short fork and a roller
too small.

[Illustration: Fig. 102]

[Illustration: Fig. 103]

In our practical problems, as solved on a large escapement model, say we
first fit our fork of the proper length, and then by the slot _g_ move
the lever back a little, leaving the bankings precisely as they were.
What are the consequences of this slight change? One of the first
results which would display itself would be discovered by the guard pin
failing to perform its proper functions. For instance, the guard pin
pushed inward against the roller would cause the engaged tooth to pass
off the locking face of the pallet, and the fork, instead of returning
against the banking, would cause the guard pin to "ride the roller"
during the entire excursion of the jewel pin. This fault produces a
scraping sound in a watch. Suppose we attempt to remedy the fault by
bending forward the guard pin _b_, as indicated by the dotted outline
_b'_ in Fig. 103, said figure being a side view of Fig. 102 seen in the
direction of the arrow _a_. This policy would prevent the engaged pallet
from passing off of the locking face of the pallet, but would be
followed by the jewel pin not passing fully into the fork, but striking
the inside face of the prong of the fork at about the point indicated by
the dotted line _m_. We can see that if the prong of the fork was
extended to about the length indicated by the outline at _c_, the action
would be as it should be.

To practically investigate this matter to the best advantage, we need
some arrangement by which we can determine the angular motion of the
lever and also of the roller and escape wheel. To do this, we provide
ourselves with a device which has already been described, but of smaller
size, for measuring fork and pallet action. The device to which we
allude is shown at Figs. 104, 105 and 106. Fig. 104 shows only the index
hand, which is made of steel about 1/20" thick and shaped as shown. The
jaws _B''_ are intended to grasp the pallet staff by the notches _e_,
and hold by friction. The prongs _l l_ are only to guard the staff so it
will readily enter the notch _e_. The circle _d_ is only to enable us to
better hold the hand _B_ flat.

[Illustration: Fig. 104]


HOW TO MEASURE ESCAPEMENT ANGLES.

From the center of the notches _e_ to the tip of the index hand _B'_ the
length is 2". This distance is also the radius of the index arc _C_.
This index arc is divided into thirty degrees, with three or four
supplementary degrees on each side, as shown. For measuring pallet
action we only require ten degrees, and for roller action thirty
degrees. The arc _C_, Fig. 105, can be made of brass and is about 1½"
long by ¼" wide; said arc is mounted on a brass wire about 1/8"
diameter, as shown at _k_, Fig. 106, which is a view of Fig. 105 seen in
the direction of the arrow _i_. This wire _k_ enters a base shown at
_D E_, Fig. 106, which is provided with a set-screw at _j_ for holding
the index arc at the proper height to coincide with the hand _B_.

[Illustration: Fig. 105]

[Illustration: Fig. 106]

A good way to get up the parts shown in Fig. 106 is to take a disk of
thick sheet brass about 1" in diameter and insert in it a piece of brass
wire about ¼" diameter and 3/8" long, through which drill axially a
hole to receive the wire _k_. After the jaws _B''_ are clamped on the
pallet staff, we set the index arc _C_ so the hand _B'_ will indicate
the angular motion of the pallet staff. By placing the index hand _B_
on the balance staff we can get at the exact angular duration of the
engagement of the jewel pin in the fork.

Of course, it is understood that this instrument will also measure the
angles of impulse and lock. Thus, suppose the entire angular motion of
the lever from bank to bank is ten degrees; to determine how much of
this is lock and how much impulse, we set the index arc _C_ so that the
hand _B'_ marks ten degrees for the entire motion of the fork, and when
the escapement is locked we move the fork from its bank and notice by
the arc _C_ how many degrees the hand indicated before it passed of its
own accord to the opposite bank. If we have more than one and a half
degrees of lock we have too much and should seek to remedy it. How? It
is just the answers to such questions we propose to give by the aid of
our big model.


DETERMINATION OF "RIGHT" METHODS.

"Be sure you are right, then go ahead," was the advice of the celebrated
Davie Crockett. The only trouble in applying this motto to watchmaking
is to know when you are right. We have also often heard the remark that
there was only one right way, but any number of wrong ways. Now we are
inclined to think that most of the people who hold to but one right way
are chiefly those who believe all ways but their own ways are wrong.
Iron-bound rules are seldom sound even in ethics, and are utterly
impracticable in mechanics.

We have seen many workmen who had learned to draw a lever escapement of
a given type, and lived firm in the belief that all lever escapements
were wrong which were not made so as to conform to this certain method.
One workman believes in equidistant lockings, another in circular
pallets; each strong in the idea that their particular and peculiar
method of designing a lever escapement was the only one to be tolerated.
The writer is free to confess that he has seen lever escapements of both
types, that is, circular pallets and equidistant lockings, which gave
excellent results.

Another mooted point in the lever escapement is, to decide between the
merits of the ratchet and the club-tooth escape wheel. English makers,
as a rule, hold to the ratchet tooth, while Continental and American
manufacturers favor the club tooth. The chief arguments in favor of the
ratchet tooth are: (_a_) It will run without oiling the pallets; (_b_)
in case the escape wheel is lost or broken it is more readily replaced,
as all ratchet-tooth escape wheels are alike, either for circular
pallets or equidistant lockings. The objections urged against it are:
(_a_) Excessive drop; (_b_) the escape wheel, being frail, is liable to
be injured by incompetent persons handling it; (_c_) this escapement in
many instances does require to have the pallets oiled.


ESCAPEMENTS COMPARED.

(_a_) That a ratchet-tooth escape wheel requires more drop than a club
tooth must be admitted without argument, as this form of tooth requires
from one-half to three-fourths of a degree more drop than a club tooth;
(_b_) as regards the frailty of the teeth we hold this as of small
import, as any workman who is competent to repair watches would never
injure the delicate teeth of an escape wheel; (_c_) ratchet-tooth lever
escapements will occasionally need to have the pallets oiled. The writer
is inclined to think that this defect could be remedied by proper care
in selecting the stone (ruby or sapphire) and grinding the pallets in
such a way that the escape-wheel teeth will not act against the
foliations with which all crystalline stones are built up.

All workmen who have had an extended experience in repair work are well
aware that there are some lever escapements in which the pallets
absolutely require oil; others will seem to get along very nicely
without. This applies also to American brass club-tooth escapements;
hence, we have so much contention about oiling pallets. The writer does
not claim to know positively that the pallet stones are at fault because
some escapements need oiling, but the fact must admit of explanation
some way, and is this not at least a rational solution? All persons who
have paid attention to crystallography are aware that crystals are built
up, and have lines of cleavage. In the manufacture of hole jewels, care
must be taken to work with the axis of crystallization, or a smooth hole
cannot be obtained.

The advantages claimed for the club-tooth escapement are many; among
them may be cited (_a_) the fact that it utilizes a greater arc of
impulse of the escape wheel; (_b_) the impulse being divided between the
tooth and the pallet, permits greater power to be utilized at the close
of the impulse. This feature we have already explained. It is no doubt
true that it is more difficult to match a set of pallets with an escape
wheel of the club-tooth order than with a ratchet tooth; still the
writer thinks that this objection is of but little consequence where a
workman knows exactly what to do and how to do it; in other words, is
sure he is right, and can then go ahead intelligently.

It is claimed by some that all American escape wheels of a given grade
are exact duplicates; but, as we have previously stated, this is not
exactly the case, as they vary a trifle. So do the pallet jewels vary a
little in thickness and in the angles. Suppose we put in a new escape
wheel and find we have on the entrance pallet too much drop, that is,
the tooth which engaged this pallet made a decided movement forward
before the tooth which engaged the exit pallet encountered the locking
face of said pallet. If we thoroughly understand the lever escapement we
can see in an instant if putting in a thicker pallet stone for entrance
pallet will remedy the defect. Here again we can study the effects of a
change in our large model better than in an escapement no larger than is
in an ordinary watch.


HOW TO SET PALLET STONES.

There have been many devices brought forward to aid the workman in
adjusting the pallet stones to lever watches. Before going into the
details of any such device we should thoroughly understand exactly what
we desire to accomplish. In setting pallet stones we must take into
consideration the relation of the roller and fork action. As has already
been explained, the first thing to do is to set the roller and fork
action as it should be, without regard in a great degree to pallet
action.

[Illustration: Fig. 107]

To explain, suppose we have a pallet stone to set in a full-plate
movement. The first thing to do is to close the bankings so that the
jewel pin will not pass out of the slot in the fork on either side; then
gradually open the bankings until the jewel pin will pass out. This will
be understood by inspecting Fig. 107, where _A A'_ shows a lever fork as
if in contact with both banks, and the jewel pin, represented at _B
B''_, just passes the angle _a c'_ of the fork. The circle described by
the jewel pin _B_ is indicated by the arc _e_. It is well to put a
slight friction under the balance rim, in order that we can try the
freedom of the guard pin. As a rule, all the guard pin needs is to be
free and not touch the roller. The entire point, as far as setting the
fork and bankings is concerned, is to have the fork and roller action
sound. For all ordinary lever escapements the angular motion of the
lever banked in as just described should be _about_ ten degrees. As
explained in former examples, if the fork action is entirely sound and
the lever only vibrates through an arc of nine degrees, it is quite as
well to make the pallets conform to this arc as to make the jewel pin
carry the fork through full ten degrees. Again, if the lever vibrates
through eleven degrees, it is as well to make the pallets conform to
this arc.

The writer is well aware that many readers will cavil at this idea and
insist that the workman should bring all the parts right on the basis of
ten degrees fork and lever action. In reply we would say that no
escapement is perfect, and it is the duty of the workman to get the best
results he can for the money he gets for the job. In the instance given
above, of the escapement with nine degrees of lever action, when the
fork worked all right, if we undertook to give the fork the ten degrees
demanded by the stickler for accuracy we would have to set out the jewel
pin or lengthen the fork, and to do either would require more time than
it would to bring the pallets to conform to the fork and roller action.
It is just this knowing how and the decision to act that makes the
difference in the workman who is worth to his employer twelve or
twenty-five dollars per week.

We have described instruments for measuring the angle of fork and pallet
action, but after one has had experience he can judge pretty nearly and
then it is seldom necessary to measure the angle of fork action as long
as it is near the proper thing, and then bring the pallets to match the
escape wheel after the fork and roller action is as it should be--that
is, the jewel pin and fork work free, the guard pin has proper freedom,
and the fork vibrates through an arc of about ten degrees.

Usually the workman can manipulate the pallets to match the escape wheel
so that the teeth will have the proper lock and drop at the right
instant, and again have the correct lock on the next succeeding pallet.
The tooth should fall but a slight distance before the tooth next in
action locks it, because all the angular motion the escape wheel makes
except when in contact with the pallets is just so much lost power,
which should go toward giving motion to the balance.

There seems to be a little confusion in the use of the word "drop" in
horological phrase, as it is used to express the act of parting of the
tooth with the pallet. The idea will be seen by inspecting Fig. 108,
where we show the tooth _D_ and pallet _C_ as about parting or dropping.
When we speak of "banking up to the drop" we mean we set the banking
screws so that the teeth will just escape from each pallet. By the term
"fall" we mean the arc the tooth passes through before the next pallet
is engaged. This action is also illustrated at Fig. 108, where the tooth
_D_, after dropping from the pallet _C_, is arrested at the position
shown by the dotted outline. We designate this arc by the term "fall,"
and we measure this motion by its angular extent, as shown by the dotted
radial lines _i f_ and _i g_. As we have explained, this fall should
only extend through an arc of one and a half degrees, but by close
escapement matching this arc can be reduced to one degree, or even a
trifle less.

[Illustration: Fig. 108]

We shall next describe an instrument for holding the escape wheel and
pallets while adjusting them. As shown at Fig. 107, the fork _A'_ is
banked a little close and the jewel pin as shown would, in some
portions, rub on _C'_, making a scraping sound.


HOW TO MAKE AN ESCAPEMENT MATCHING TOOL.

[Illustration: Fig. 109]

A point has now been reached where we can use an escapement matcher to
advantage. There are several good ones on the market, but we can make
one very cheaply and also add our own improvements. In making one, the
first thing to be provided is a movement holder. Any of the three-jaw
types of such holders will answer, provided the jaws hold a movement
plate perfectly parallel with the bed of the holder. This will be better
understood by inspecting Fig. 109, which is a side view of a device of
this kind seen edgewise in elevation. In this _B_ represents the bed
plate, which supports three swing jaws, shown at _C_, Figs. 109 and 110.
The watch plate is indicated by the parallel dotted lines _A_, Fig. 109.
The seat _a_ of the swing jaws _C_ must hold the watch plate _A_ exactly
parallel with the bed plate _B_. In the cheap movement holders these
seats (_a_) are apt to be of irregular heights, and must be corrected
for our purpose. We will take it for granted that all the seats _a_ are
of precisely the same height, measured from _B_, and that a watch plate
placed in the jaws _C_ will be held exactly parallel with the said bed
_B_. We must next provide two pillars, shown at _D E_, Figs. 109 and
111. These pillars furnish support for sliding centers which hold the
top pivots of the escape wheel and pallet staff while we are testing the
depths and adjusting the pallet stones. It will be understood that these
pillars _D E_ are at right angles to the plane of the bed _B_, in order
that the slides like _G N_ on the pillars _D E_ move exactly vertical.
In fact, all the parts moving up and down should be accurately made, so
as not to destroy the depths taken from the watch plate _A_. Suppose, to
illustrate, that we place the plate _A_ in position as shown, and insert
the cone point _n_, Figs. 109 and 112, in the pivot hole for the pallet
staff, adjusting the slide _G N_ so that the cone point rests accurately
in said pivot hole. It is further demanded that the parts _I H F G N D_
be so constructed and adjusted that the sliding center _I_ moves truly
vertical, and that we can change ends with said center _I_ and place the
hollow cone end _m_, Fig. 112, so it will receive the top pivot of the
pallet staff and hold it exactly upright.

[Illustration: Fig. 110]

[Illustration: Fig. 111]

[Illustration: Fig. 112]

The idea of the sliding center _I_ is to perfectly supply the place of
the opposite plate of the watch and give us exactly the same practical
depths as if the parts were in their place between the plates of the
movement. The foot of the pillar _D_ has a flange attached, as shown at
_f_, which aids in holding it perfectly upright. It is well to cut a
screw on _D_ at _D'_, and screw the flange _f_ on such screw and then
turn the lower face of _f_ flat to aid in having the pillar _D_
perfectly upright.


DETAILS OF FITTING UP ESCAPEMENT MATCHER.

It is well to fit the screw _D'_ loosely, so that the flange _f_ will
come perfectly flat with the upper surface of the base plate _B_. The
slide _G N_ on the pillar _D_ can be made of two pieces of small brass
tube, one fitting the pillar _D_ and the other the bar _F_. The slide _G
N_ is held in position by the set screw _g_, and the rod _F_ by the set
screw _h_.

[Illustration: Fig. 113]

[Illustration: Fig. 114]

The piece _H_ can be permanently attached to the rod _F_. We show
separate at Figs. 113 and 114 the slide _G N_ on an enlarged scale from
Fig. 109. Fig. 114 is a view of Fig. 113 seen in the direction of the
arrow _e_. All joints and movable parts should work free, in order that
the center _I_ may be readily and accurately set. The parts _H F_ are
shown separate and enlarged at Figs. 115 and 116. The piece _H_ can be
made of thick sheet brass securely attached to _F_ in such a way as to
bring the V-shaped groove at right angles to the axis of the rod _F_. It
is well to make the rod _F_ about 1/8" in diameter, while the sliding
center _I_ need not be more than 1/16" in diameter. The cone point _n_
should be hardened to a spring temper and turned to a true cone in an
accurately running wire chuck.

[Illustration: Fig. 115]

[Illustration: Fig. 116]

The hollow cone end _m_ of _I_ should also be hardened, but this is best
done after the hollow cone is turned in. The hardening of both ends
should only be at the tips. The sliding center _I_ can be held in the
V-shaped groove by two light friction springs, as indicated at the
dotted lines _s s_, Fig. 115, or a flat plate of No. 24 or 25 sheet
brass of the size of _H_ can be employed, as shown at Figs. 116 and 117,
where _o_ represents the plate of No. 24 brass, _p p_ the small screws
attaching the plate _o_ to _H_, and _k_ a clamping screw to fasten _I_
in position. It will be found that the two light springs _s s_, Fig. 115
will be the most satisfactory. The wire legs, shown at _L_, will aid in
making the device set steady. The pillar _E_ is provided with the same
slides and other parts as described and illustrated as attached to _D_.
The position of the pillars _D_ and _E_ are indicated at Fig. 110.

[Illustration: Fig. 117]

[Illustration: Fig. 118]

We will next tell how to flatten _F_ to keep _H_ exactly vertical. To
aid in explanation, we will show (enlarged) at Fig. 118 the bar _F_
shown in Fig. 109. In flattening such pieces to prevent turning, we
should cut away about two-fifths, as shown at Fig. 119, which is an end
view of Fig. 118 seen in the direction of the arrow _c_. In such
flattening we should not only cut away two-fifths at one end, but we
must preserve this proportion from end to end. To aid in this operation
we make a fixed gage of sheet metal, shaped as shown at _I_, Fig. 120.

[Illustration: Fig. 119]


ESCAPEMENT MATCHING DEVICE DESCRIBED.

[Illustration: Fig. 120]

In practical construction we first file away about two-fifths of _F_ and
then grind the flat side on a glass slab to a flat, even surface and, of
course, equal thickness from end to end. We reproduce the sleeve _G_ as
shown at Fig. 113 as if seen from the left and in the direction of the
axis of the bar _F_. To prevent the bar _F_ turning on its axis, we
insert in the sleeve _G_ a piece of wire of the same size as _F_ but
with three-fifths cut away, as shown at _y_, Fig. 121. This piece _y_ is
soldered in the sleeve _G_ so its flat face stands vertical. To give
service and efficiency to the screw _h_, we thicken the side of the
sleeve _F_ by adding the stud _w_, through which the screw _h_ works. A
soft metal plug goes between the screw _h_ and the bar _F_, to prevent
_F_ being cut up and marred. It will be seen that we can place the top
plate of a full-plate movement in the device shown at Fig. 109 and set
the vertical centers _I_ so the cone points _n_ will rest in the pivot
holes of the escape wheel and pallets. It is to be understood that the
lower side of the top plate is placed uppermost in the movement holder.

[Illustration: Fig. 121]

If we now reverse the ends of the centers _I_ and let the pivots of the
escape wheel and pallet staff rest in the hollow cones of these centers
_I_, we have the escape wheel and pallets in precisely the same position
and relation to each other as if the lower plate was in position. It is
further to be supposed that the balance is in place and the cock screwed
down, although the presence of the balance is not absolutely necessary
if the banking screws are set as directed, that is, so the jewel pin
will just freely pass in and out of the fork.


HOW TO SET PALLET STONES.

We have now come to setting or manipulating the pallet stones so they
will act in exact conjunction with the fork and roller. To do this we
need to have the shellac which holds the pallet stones heated enough to
make it plastic. The usual way is to heat a piece of metal and place it
in close proximity to the pallets, or to heat a pair of pliers and clamp
the pallet arms to soften the cement.

Of course, it is understood that the movement holder cannot be moved
about while the stones are being manipulated. The better way is to set
the movement holder on a rather heavy plate of glass or metal, so that
the holder will not jostle about; then set the lamp so it will do its
duty, and after a little practice the setting of a pair of pallet stones
to perfectly perform their functions will take but a few minutes. In
fact, if the stones will answer at all, three to five minutes is as much
time as one could well devote to the adjustment. The reader will see
that if the lever is properly banked all he has to do is to set the
stones so the lock, draw and drop are right, when the entire escapement
is as it should be, and will need no further trial or manipulating.




CHAPTER II.

THE CYLINDER ESCAPEMENT.


There is always in mechanical matters an underlying combination of
principles and relations of parts known as "theory." We often hear the
remark made that such a thing may be all right in theory, but will not
work in practice. This statement has no foundation in fact. If a given
mechanical device accords strictly with theory, it will come out all
right practically. _Mental conceptions_ of a machine are what we may
term their theoretical existence.

When we make drawings of a machine mentally conceived, we commence its
mechanical construction, and if we make such drawings to scale, and add
a specification stating the materials to be employed, we leave only the
merest mechanical details to be carried out; the brain work is done and
only finger work remains to be executed.

With these preliminary remarks we will take up the consideration of the
cylinder escapement invented by Robert Graham about the year 1720. It is
one of the two so-called frictional rest dead-beat escapements which
have come into popular use, the other being the duplex. Usage, or, to
put it in other words, experience derived from the actual manufacture of
the cylinder escapement, settled the best forms and proportions of the
several parts years ago. Still, makers vary slightly on certain lines,
which are important for a man who repairs such watches to know and be
able to carry out, in order to put them in a condition to perform as
intended by the manufacturers. It is not knowing these lines which
leaves the average watchmaker so much at sea. He cuts and moves and
shifts parts about to see if dumb luck will not supply the correction he
does not know how to make. This requisite knowledge does not consist so
much in knowing how to file or grind as it does in discriminating where
such application of manual dexterity is to be applied. And right here
let us make a remark to which we will call attention again later on. The
point of this remark lies in the question--How many of the so-called
practical watchmakers could tell you what proportion of a cylinder
should be cut away from the half shell? How many could explain the
difference between the "real" and "apparent" lift? Comparatively few,
and yet a knowledge of these things is as important for a watchmaker as
it is for a surgeon to understand the action of a man's heart or the
relations of the muscles to the bones.


ESSENTIAL PARTS OF THE CYLINDER ESCAPEMENT.

The cylinder escapement is made up of two essential parts, viz.: the
escape wheel and the cylinder. The cylinder escape wheel in all modern
watches has fifteen teeth, although Saunier, in his "Modern Horology,"
delineates a twelve-tooth wheel for apparently no better reason than
because it was more easily drawn. We, in this treatise, will consider
both the theoretical action and the practical construction, but more
particularly the repair of this escapement in a thorough and complete
manner.

At starting out, we will first agree on the names of the several parts
of this escapement, and to aid us in this we will refer to the
accompanying drawings, in which Fig. 122 is a side elevation of a
cylinder complete and ready to have a balance staked on to it. Fig. 123
shows the cylinder removed from the balance collet. Figs. 124 and 125
show the upper and lower plugs removed from the cylinder. Fig. 126 is a
horizontal section of Fig. 122 on the line _i_. Fig. 127 is a side view
of one tooth of a cylinder escape wheel as if seen in the direction of
the arrow _f_ in Fig. 126. Fig. 128 is a top view of two teeth of a
cylinder escape wheel. The names of the several parts usually employed
are as follows:

         _A._--Upper or Main Shell.
        _A'._--Half Shell.
       _A''._--Column.
      _A'''._--Small Shell.
  _B B' B''._--Balance Collet.
         _G._--Upper Plug.
         _H._--Lower Plug.
         _g._--Entrance Lip of Cylinder.
         _h._--Exit Lip of Cylinder.
         _c._--Banking Slot.
         _C._--Tooth.
         _D._--U arm.
         _E._--Stalk of Pillar.
         _I._--U space.
         _l._--Point of Tooth.
         _k._--Heel of Tooth.

The cylinder escapement has two engagements or actions, during the
passage of each tooth; that is, one on the outside of the cylinder and
one on the inside of the shell. As we shall show later on, the cylinder
escapement is the only positively dead-beat escapement in use, all
others, even the duplex, having a slight recoil during the process of
escaping.

When the tooth of a cylinder escape wheel while performing its
functions, strikes the cylinder shell, it rests dead on the outer or
inner surface of the half shell until the action of the balance spring
has brought the lip of the cylinder so that the impulse face of the
tooth commences to impart motion or power to the balance.

[Illustration: Fig. 122]

[Illustration: Fig. 123]

[Illustration: Fig. 124]

[Illustration: Fig. 125]

[Illustration: Fig. 126]

[Illustration: Fig. 127]

[Illustration: Fig. 128]

Most writers on horological matters term this act the "lift," which name
was no doubt acquired when escapements were chiefly confined to pendulum
clocks. Very little thought on the matter will show any person who
inspects Fig. 126 that if the tooth _C_ is released or escapes from the
inside of the half shell of the cylinder _A_, said cylinder must turn or
revolve a little in the direction of the arrow _j_, and also that the
next succeeding tooth of the escape wheel will engage the cylinder on
the outside of the half shell, falling on the dead or neutral portion of
said cylinder, to rest until the hairspring causes the cylinder to turn
in the opposite direction and permitting the tooth now resting on the
outside of the cylinder to assume the position shown on the drawing.

The first problem in our consideration of the theoretical action of the
cylinder escapement, is to arrange the parts we have described so as to
have these two movements of the escape wheel of like angular values. To
explain what we mean by this, we must premise by saying, that as our
escape wheel has fifteen teeth and we make each tooth give two impulses
in alternate directions we must arrange to have these half-tooth
movements exactly alike, or, as stated above, of equal angular values;
and also each impulse must convey the same power or force to the
balance. All escape wheels of fifteen teeth acting by half impulses must
impel the balance during twelve degrees (minus the drop) of escape-wheel
action; or, in other words, when a tooth passes out of the cylinder from
the position shown at Fig. 126, the form of the impulse face of the
tooth and the shape of the exit lip of the cylinder must be such during
twelve degrees (less the drop) of the angular motion of the escape
wheel. The entire power of such an escape wheel is devoted to giving
impulse to the balance.

The extent of angular motion of the balance during such impulse is, as
previously stated, termed the "lifting angle." This "lifting angle" is
by horological writers again divided into real and apparent lifts. This
last division is only an imaginary one, as the real lift is the one to
be studied and expresses the arc through which the impulse face of the
tooth impels the balance during the act of escaping, and so, as we shall
subsequently show, should no more be counted than in the detached lever
escapement, where a precisely similar condition exists, but is never
considered or discussed.

We shall for the present take no note of this lifting angle, but confine
ourselves to the problem just named, of so arranging and designing our
escape-wheel teeth and cylinder that each half of the tooth space shall
give equal impulses to the balance with the minimum of drop. To do this
we will make a careful drawing of an escape-wheel tooth and cylinder on
an enlarged scale; our method of making such drawings will be on a new
and original system, which is very simple yet complete.


DRAWING THE CYLINDER ESCAPEMENT.

All horological--and for that matter all mechanical--drawings are based
on two systems of measurements: (1) Linear extent; (2) angular movement.
For the first measurement we adopt the inch and its decimals; for the
second we adopt degrees, minutes and seconds. For measuring the latter
the usual plan is to employ a protractor, which serves the double
purpose of enabling us to lay off and delineate any angle and also to
measure any angle obtained by the graphic method, and it is thus by this
graphic method we propose to solve very simply some of the most
abstruce problems in horological delineations. As an instance, we
propose to draw our cylinder escapement with no other instruments than a
steel straight-edge, showing one-hundredths of an inch, and a pair of
dividers; the degree measurement being obtained from arcs of sixty
degrees of radii, as will be explained further on.

In describing the method for drawing the cylinder escapement we shall
make a radical departure from the systems usually laid down in
text-books, and seek to simplify the formulas which have heretofore been
given for such delineations. In considering the cylinder escapement we
shall pursue an analytical course and strive to build up from the
underlying principles. In the drawings for this purpose we shall
commence with one having an escape wheel of 10" radius, and our first
effort will be the primary drawing shown at Fig. 129. Here we establish
the point _A_ for the center of our escape wheel, and from this center
sweep the short arc _a a_ with a 10" radius, to represent the
circumference of our escape wheel. From _A_ we draw the vertical line
_A B_, and from the intersection of said line with the arc _a a_ we lay
off twelve degree spaces on each side of the line _A B_ on said arc _a_
and establish the points _b c_. From _A_ as a center we draw through
the points _b c_ the radial lines _b' c'_.

To define the face of the incline to the teeth we set our dividers to
the radius of any of the convenient arcs of sixty degrees which we have
provided, and sweep the arc _t t_. From the intersection of said arc
with the line _A b'_ we lay off on said arc sixty-four degrees and
establish the point _g_ and draw the line _b g_. Why we take sixty-four
degrees for the angle _A b g_ will be explained later on, when we are
discussing the angular motion of the cylinder. By dividing the eleventh
degree from the point _b_ on the arc _a a_ into thirds and taking two of
them, we establish the point _y_ and draw the radial line _A y'_. Where
this line _A y'_ intersects the line _b g_ we name the point _n_, and in
it is located the point of the escape-wheel tooth. That portion of the
line _b g_ which lies between the points _b_ and _n_ represents the
measure of the inner diameter of the cylinder, and also the length of
the chord of the arc which rounds the impulse face of the tooth. We
divide the space _b n_ into two equal portions and establish the point
_e_, which locates the position of the center of the cylinder. From _A_
as a center and through the point _e_ we sweep the arc _e' e'_, and it
is on this line that the points establishing the center of the cylinder
will in every instance be located. From _A_ as a center, through the
point _n_ we sweep the arc _k_, and on this line we locate the points of
the escape-wheel teeth. For delineating the curved impulse faces of the
escape-wheel teeth we draw from the point _e_ and at right angles to the
line _b g_ the line _e o_. We next take in our dividers the radius of
the arc _k_, and setting one leg at either of the points _b_ or _n_,
establish with the other leg the point _p'_ on the line _e o_, and from
the point _p'_ as a center we sweep the arc _b v n_, which defines the
curve of the impulse faces of the teeth. From _A_ as a center through
the point _p'_ we sweep the arc _p_, and in all instances where we
desire to delineate the curved face of a tooth we locate either the
position of the point or the heel of such tooth, and setting one leg of
our dividers at such point, the other leg resting on the arc _p_, we
establish the center from which to sweep the arc defining the face of
said tooth.


ADVANTAGES GAINED IN SHAPING.

The reason for giving a curved form to the impulse face of the teeth of
cylinder escape wheels are somewhat intricate, and the problem involves
several factors. That there are advantages in so shaping the incline or
impulse face is conceded, we believe, by all recent manufacturers. The
chief benefit derived from such curved impulse faces will be evident
after a little thought and study of the situation and relation of parts
as shown in Fig. 129. It will be seen on inspection that the angular
motion imparted to the cylinder by the impulse face of the tooth when
curved as shown, is greater during the first half of the twelve degrees
of escape-wheel action than during the last half, thus giving the escape
wheel the advantage at the time the balance spring increases its
resistance to the passage of the escape-wheel tooth across the lip of
the cylinder. Or, in other words, as the ratio of resistance of the
balance spring increases, in a like ratio the curved form of the impulse
face of the tooth gives greater power to the escape-wheel action in
proportion to the angular motion of the escape wheel. Hence, in actual
service it is found that cylinder watches with curved impulse planes to
the escape-wheel teeth are less liable to set in the pocket than the
teeth having straight impulse faces.


THE OUTER DIAMETER OF THE CYLINDER.

[Illustration: Fig. 129]

To define the remainder of the form of our escape-wheel tooth we will
next delineate the heel. To do this we first define the outer diameter
of our cylinder, which is the extent from the point _n_ to _c_, and
after drawing the line _n c_ we halve the space and establish the point
_x_, from which point as a center we sweep the circle _w w_, which
defines the outer circumference of our cylinder. With our dividers set
to embrace the extent from the point _n_ to the point _c_ we set one leg
at the point _b_, and with the other leg establish on the arc _k_ the
point _h_. We next draw the line _b h_, and from the point _b_ draw the
line _b f_ at right angle to the line _b h_. Our object for drawing
these lines is to define the heel of our escape-wheel tooth by a right
angle line tangent to the circle _w_, from the point _b_; which circle
_w_ represents the curve of the outer circumference of the cylinder. We
shape the point of the tooth as shown to give it the proper stability,
and draw the full line _j_ to a curve from the center _A_. We have now
defined the form of the upper face of the tooth. How to delineate the U
arms will be taken up later on, as, in the present case, the necessary
lines would confuse our drawing.

We would here take the opportunity to say that there is a great latitude
taken by makers as regards the extent of angular impulse given to the
cylinder, or, as it is termed, the "actual lift." This latitude governs
to a great extent the angle _A b g_, which we gave as sixty-four degrees
in our drawing. It is well to understand that the use of sixty-four
degrees is based on no hard-and-fast rules, but varies back and forth,
according as a greater or lesser angle of impulse or lift is employed.

In practical workshop usage the impulse angle is probably more easily
estimated by the ratio between the diameter of the cylinder and the
measured (by lineal measure) height of the impulse plane. Or, to be more
explicit, we measure the radial extent from the center _A_ between the
arcs _a k_ on the line _A b_, and use this for comparison with the outer
diameter of the cylinder.

We can readily see that as we increase the height of the heel of the
impulse face of our tooth we must also increase the angle of impulse
imparted to the cylinder. With the advantages of accurate micrometer
calipers now possessed by the horological student it is an easy matter
to get at the angular extent of the real lift of any cylinder. The
advantage of such measuring instruments is also made manifest in
determining when the proper proportion of the cylinder is cut away for
the half shell.

[Illustration: Fig. 130]

In the older methods of watchmaking it was a very common rule to say,
let the height of the incline of the tooth be one-seventh of the outer
diameter of the cylinder, and at the same time the trade was furnished
with no tools except a clumsy douzieme gage; but with micrometer
calipers which read to one-thousandths of an inch such rules can be
definitely carried into effect and not left to guess work. Let us
compare the old method with the new: Suppose we have a new cylinder to
put in; we have the old escape wheel, but the former cylinder is gone.
The old-style workman would take a round broach and calculate the size
of the cylinder by finding a place where the broach would just go
between the teeth, and the size of the broach at this point was supposed
to be the outer diameter of the cylinder. By our method we measure the
diameter of the escape wheel in thousandths of an inch, and from this
size calculate exactly what the diameter of the new cylinder should be
in thousandths of an inch. Suppose, to further carry out our comparison,
the escape wheel which is in the watch has teeth which have been stoned
off to permit the use of a cylinder which was too small inside, or, in
fact, of a cylinder too small for the watch: in this case the broach
system would only add to the trouble and give us a cylinder which would
permit too much inside drop.


DRAWING A CYLINDER.

We have already instructed the pupil how to delineate a cylinder escape
wheel tooth and we will next describe how to draw a cylinder. As already
stated, the center of the cylinder is placed to coincide with the center
of the chord of the arc which defines the impulse face of the tooth.
Consequently, if we design a cylinder escape wheel tooth as previously
described, and setting one leg of our compasses at the point _e_ which
is situated at the center of the chord of the arc which defines the
impulse face of the tooth and through the points _d_ and _b_ we define
the inside of our cylinder. We next divide the chord _d b_ into eight
parts and set our dividers to five of these parts, and from _e_ as a
center sweep the circle _h_ and define the outside of our cylinder. From
_A_ as a center we draw the radial line _A e'_. At right angles to the
line _A e'_ and through the point _e_ we draw the line from _e_ as a
center, and with our dividers set to the radius of any of the convenient
arcs which we have divided into sixty degrees, we sweep the arc _i_.
Where this arc intersects the line _f_ we term the point _k_, and from
this point we lay off on the arc _i_ 220 degrees, and draw the line
_l e l'_, which we see coincides with the chord of the impulse face of the
tooth. We set our dividers to the same radius by which we sweep the arc
_i_ and set one leg at the point _b_ for a center and sweep the arc
_j'_. If we measure this arc from the point _j'_ to intersection of said
arc _j'_ with the line _l_ we will find it to be sixty-four degrees,
which accounts for our taking this number of degrees when we defined the
face of our escape-wheel tooth, Fig. 129.

There is no reason why we should take twenty-degrees for the angle _k e
l_ except that the practical construction of the larger sizes of
cylinder watches has established the fact that this is about the right
angle to employ, while in smaller watches it frequently runs up as high
as twenty-five. Although the cylinder is seemingly a very simple
escapement, it is really a very abstruce one to follow out so as to
become familiar with all of its actions.


THE CYLINDER PROPER CONSIDERED.

[Illustration: Fig. 131]

We will now proceed and consider the cylinder proper, and to aid us in
understanding the position and relation of the parts we refer to Fig.
131, where we repeat the circles _d_ and _h_, shown in Fig. 130, which
represents the inside and outside of the cylinder. We have here also
repeated the line _f_ of Fig. 130 as it cuts the cylinder in half, that
is, divides it into two segments of 180 degrees each. If we conceive of
a cylinder in which just one-half is cut away, that is, the lips are
bounded by straight radial lines, we can also conceive of the relation
and position of the parts shown in Fig. 130. The first position of which
we should take cognizance is, the tooth _D_ is moved back to the left so
as to rest on the outside of our cylinder. The cylinder is also supposed
to stand so that the lips correspond to the line _f_. On pressing the
tooth _D_ forward the incline of the tooth would attack the entrance
lip of the cylinder at just about the center of the curved impulse face,
imparting to the cylinder twenty degrees of angular motion, but the
point of the tooth at _d_ would exactly encounter the inner angle of the
exit lip, and of course the cylinder would afford no rest for the tooth;
hence, we see the importance of not cutting away too much of the half
shell of the cylinder.

But before we further consider the action of the tooth _D_ in its action
as it passes the exit lip of the cylinder we must finish with the action
of the tooth on the entrance lip. A very little thought and study of
Fig. 130 will convince us that the incline of the tooth as it enters the
cylinder will commence at _t_, Fig. 130, but at the close of the action
the tooth parts from the lip on the inner angle. Now it is evident that
it would require greater force to propel the cylinder by its inner angle
than by the outer one. To compensate for this we round the edge of the
entrance lip so that the action of the tooth instead of commencing on
the outer angle commences on the center of the edge of the entrance lip
and also ends its action on the center of the entrance lip. To give
angular extent enough to the shell of the cylinder to allow for rounding
and also to afford a secure rest for the tooth inside the cylinder, we
add six degrees to the angular extent of the entrance lip of the
cylinder shell, as indicated on the arc _o'_, Fig. 131, three of these
degrees being absorbed for rounding and three to insure a dead rest for
the tooth when it enters the cylinder.


WHY THE ANGULAR EXTENT IS INCREASED.

Without rounding the exit lip the action of the tooth on its exit would
be entirely on the inner angle of the shell. To obviate this it is the
usual practice to increase the angular extent of the cylinder ten
degrees, as shown on the arc _o'_ between the lines _f_ and _p_, Fig.
131. Why we should allow ten degrees on the exit lip and but six degrees
on the entrance lip will be understood by observing Fig. 130, where the
radial lines _s_ and _r_ show the extent of angular motion of the
cylinder, which would be lost if the tooth commenced to act on the inner
angle and ended on the outer angle of the exit lip. This arc is a little
over six degrees, and if we add a trifle over three degrees for rounding
we would account for the ten degrees between the lines _f_ and _p_, Fig.
131. It will now be seen that the angular extent is 196 degrees. If we
draw the line _w_ we can see in what proportion the measurement should
be made between the outer diameter of the cylinder and the measure of
the half shell. It will be seen on measurement that the distance between
the center _e_ and the line _w_ is about one-fifteenth part of the outer
diameter of the cylinder and consequently with a cylinder which measures
45/1000 of an inch in diameter, now the half shell should measure half
of the entire diameter of the cylinder plus one-fifteenth part of such
diameter, or 25½ thousandths of an inch.

After these proportions are understood and the drawing made, the eye
will get accustomed to judging pretty near what is required; but much
the safer plan is to measure, where we have the proper tools for doing
so. Most workmen have an idea that the depth or distance at which the
cylinder is set from the escape wheel is a matter of adjustment; while
this is true to a certain extent, still there is really only one
position for the center of the cylinder, and that is so that the center
of the pivot hole coincides exactly with the center of the chord to the
curve of the impulse face of the tooth or the point _e_, Fig. 130. Any
adjustment or moving back and forth of the chariot to change the depth
could only be demanded where there was some fault existing in the
cylinder or where it had been moved out of its proper place by some
genius as an experiment in cylinder depths. It will be evident on
observing the drawing at Fig. 131 that when the cylinder is performing
an arc of vibration, as soon as the entrance lip has passed the point
indicated by the radial line _e x_ the point of the escape-wheel tooth
will commence to act on the cylinder lip and continue to do so through
an arc of forty degrees, or from the lines _x_ to _l_.


MAKING A WORKING MODEL.

To practically study the action of the cylinder escapement it is well to
make a working model. It is not necessary that such a model should
contain an entire escape wheel; all that is really required is two teeth
cut out of brass of the proper forms and proportions and attached to the
end of an arm 4-7/8" long with studs riveted to the U arms to support
the teeth. This U arm is attached to the long arm we have just
mentioned. A flat ring of heavy sheet brass is shaped to represent a
short transverse section of a cylinder. This segment is mounted on a
yoke which turns on pivots. In making such a model we can employ all the
proportions and exact forms of the larger drawings made on a ten-inch
radius. Such a model becomes of great service in learning the
importance of properly shaping the lips of the cylinder. And right here
we beg to call attention to the fact that in the ordinary repair shop
the proper shape of cylinder lips is entirely neglected.


PROPER SHAPE OF CYLINDER LIPS.

The workman buys a cylinder and whether the proper amount is cut away
from the half shell, or the lips, the correct form is entirely ignored,
and still careful attention to the form of the cylinder lips adds full
ten per cent. to the efficiency of the motive force as applied to the
cylinder. In making study drawings of the cylinder escapement it is not
necessary to employ paper so large that we can establish upon it the
center of the arc which represents the periphery of our escape wheel, as
we have at our disposal two plans by which this can be obviated. First,
placing a bit of bristol board on our drawing-board in which we can set
one leg of our dividers or compasses when we sweep the peripheral arc
which we use in our delineations; second, making three arcs in brass or
other sheet metal, viz.: the periphery of the escape wheel, the arc
passing through the center of the chord of the arc of the impulse face
of the tooth, and the arc passing through the point of the escape-wheel
tooth. Of these plans we favor the one of sticking a bit of cardboard on
the drawing board outside of the paper on which we are making our
drawing.

[Illustration: Fig. 132]

At Fig. 132 we show the position and relation of the several parts just
as the tooth passes into the shell of the cylinder, leaving the lip of
the cylinder just as the tooth parted with it. The half shell of the
cylinder as shown occupies 196 degrees or the larger arc embraced
between the radial lines _k_ and _l_. In drawing the entrance lip the
acting face is made almost identical with a radial line except to round
the corners for about one-third the thickness of the cylinder shell. No
portion, however, of the lip can be considered as a straight line, but
might be described as a flattened curve.

[Illustration: Fig. 133]

A little study of what would be required to get the best results after
making such a drawing will aid the pupil in arriving at the proper
shape, especially when he remembers that the thickness of the cylinder
shell of a twelve-line watch is only about five one-thousandths of an
inch. But because the parts are small we should not shirk the problem of
getting the most we possibly can out of a cylinder watch.

The extent of arc between the radial lines _k f_, as shown in Fig. 132,
is four degrees. Although in former drawings we showed the angular
extent added as six degrees, as we show the lip _m_ in Fig. 132, two
degrees are lost in rounding. The space _k f_ on the egress or exit side
is intended to be about four degrees, which shows the extent of lock. We
show at Fig. 133 the tooth _D_ just having passed out of the cylinder,
having parted with the exit lip _p_.

In making this drawing we proceed as with Fig. 132 by establishing a
center for our radius of 10" outside of our drawing paper and drawing
the line _A A_ to such center and sweeping the arcs _a b c_. We
establish the point _e_, which represents the center of our cylinder, as
before. We take the space to represent the radial extent of the outside
of our cylinder in our dividers and from _e_ as a center sweep a fine
pencil line, represented by the dotted line _t_ in our drawing; and
where this circle intersects the arc _a_ we name it the point _s_; and
it is at this point the heel of our escape-wheel tooth must part with
the exit lip of the cylinder. From _e_ as a center and through the point
_s_ we draw the line _e l''_. With our dividers set to the radius of any
convenient arc which we have divided into degrees, we sweep the short
arc _d'_. The intersection of this arc with the line _e l''_ we name the
point _u_; and from _e_ as a center we draw the radial line _e u f'_. We
place the letter _f''_ in connection with this line because it (the
line) bears the same relations to the half shell of the cylinder shown
in Fig. 133 that the line _f_ does to the half shell (_D_) shown in Fig.
132. We draw the line _f'' f'''_, Fig. 133, which divides the cylinder
into two segments of 180 degrees each. We take the same space in our
dividers with which we swept the interior of the cylinder in Fig. 132
and sweep the circle _v_, Fig. 133. From _e_ as a center we sweep the
short arc _d''_, Fig. 133, and from its intersection of the line _f''_
we lay off six degrees on said arc _d''_ and draw the line _e' k''_,
which defines the angular extent of our entrance lip to the half shell
of the cylinder in Fig. 133. We draw the full lines of the cylinder as
shown.

We next delineate the heel of the tooth which has just passed out of the
cylinder, as shown at _D'_, Fig. 133. We now have a drawing showing the
position of the half shell of the cylinder just as the tooth has passed
the exit lip. This drawing also represents the position of the half
shell of the cylinder when the tooth rests against it on the outside. If
we should make a drawing of an escape-wheel tooth shaped exactly as the
one shown at Fig. 132 and the point of the tooth resting at _x_, we
would show the position of a tooth encountering the cylinder after a
tooth which has been engaged in the inside of the shell has passed out.
By following the instructions now given, we can delineate a tooth in any
of its relations with the cylinder shell.


DELINEATING AN ESCAPE-WHEEL TOOTH WHILE IN ACTION.

We will now go through the operation of delineating an escape-wheel
tooth while in action. The position we shall assume is the one in which
the cylinder and escape-wheel tooth are in the relation of the passage
of half the impulse face of the tooth into the cylinder. To do this is
simple enough: We first produce the arcs _a b c_, Fig. 133, as directed,
and then proceed to delineate a tooth as in previous instances. To
delineate our cylinder in the position we have assumed above, we take
the space between the points _e d_ in our dividers and setting one leg
at _d_ establish the point _g_, to represent the center of our cylinder.
If we then sweep the circle _h_ from the center of _g_ we define the
inner surface of the shell of our cylinder.

Strictly speaking, we have not assumed the position we stated, that is,
the impulse face of the tooth as passing half way into the cylinder. To
comply strictly with our statement, we divide the chord of the impulse
face of the tooth _A_ into eight equal spaces, as shown. Now as each of
these spaces represent the thickness of the cylinder, if we take in our
dividers four of these spaces and half of another, we have the radius of
a circle passing the center of the cylinder shell. Consequently, if with
this space in our dividers we set the leg at _d_, we establish on the
arc _b_ the point _i_. We locate the center of our cylinder when
one-half of an entering tooth has passed into the cylinder. If now from
the new center with our dividers set at four of the spaces into which we
have divided the line _e f_ we can sweep a circle representing the inner
surface of the cylinder shell, and by setting our dividers to five of
these spaces we can, from _i_ as a center, sweep an arc representing the
outside of the cylinder shell. For all purposes of practical study the
delineation we show at Fig. 133 is to be preferred, because, if we carry
out all the details we have described, the lines would become confused.
We set our dividers at five of the spaces on the line _e f_ and from _g_
as a center sweep the circle _j_, which delineates the outer surface of
our cylinder shell.

Let us now, as we directed in our former instructions, draw a flattened
curve to represent the acting surface of the entrance lip of our
cylinder as if it were in direct contact with the impulse face of the
tooth. To delineate the exit lip we draw from the center _g_, Fig. 134,
to the radial line _g k_, said line passing through the point of contact
between the tooth and entrance lip of the cylinder. Let us next continue
this line on the opposite side of the point _g_, as shown at _g k'_, and
we thus bisect the cylinder shell into two equal parts of 180 degrees
each. As we previously explained, the entire extent of the cylinder half
shell is 196 degrees. We now set our dividers to the radius of any
convenient arc which we have divided into degrees, and from _g_ as a
center sweep the short arc _l l_, and from the intersection of this arc
with the line _g k'_ we lay off sixteen degrees on the said arc _l_ and
establish the point _n_, from _g_ as a center draw the radial line _g
n'_. Take ten degrees from the same parent arc and establish the point
_m_, then draw the line _g m'_. Now the arc on the circles _h j_ between
the lines _g n'_ and _g m_ limits the extent of the exit lip of the
cylinder and the arc between the lines _g k'_ and _g m'_ represents the
locking surface of the cylinder shell.

[Illustration: Fig. 134]

To delineate the U arms we refer to Fig. 135. Here, again, we draw the
arc _a b c_ and delineate a tooth as before. From the point _e_ located
at the heel of the tooth we draw the radial line _e e'_. From the point
_e_ we lay off on the arc _a_ five degrees and establish the point _p_;
we halve this space and draw the short radial line _p' s'_ and _p s_.
From the point _e_ on the arc _A_ we lay off twenty-four degrees and
establish the point _t_, which locates the heel of the next tooth in
advance of _A_. At two and a half degrees to the right of the point _t_
we locate the point _r_ and draw the short radial line _r s_. On the arc
_b_ and half way between the lines _p s_ and _r s_, we establish the
point _u_, and from it as a center we sweep the arc _v_ defining the
curve of the U arms.

We have now given minute instructions for drawing a cylinder escapement
in all its details except the extent of the banking slot of the
cylinder, which is usually made to embrace an angular extent of 270
degrees; consequently, the pillar of the cylinder will not measure more
than ninety degrees of angular extent.

There is no escapement constructed where carefully-made drawings tend
more to perfect knowledge of the action than the cylinder. But it is
necessary with the pupil to institute a careful analysis of the actions
involved. In writing on a subject of this kind it is extremely
perplexing to know when to stop; not that there is so much danger of
saying too much as there is not having the words read with attention.

As an illustration, let us consider the subject of depth between the
cylinder and the escape wheel. As previously stated, 196 degrees of
cylinder shell should be employed; but suppose we find a watch in which
the half shell has had too much cut away, so the tooth on entering the
half shell after parting with the entrance lip does not strike dead on
the inside of the shell, but encounters the edge of the exit lip. In
this case the impulse of the balance would cause the tooth to slightly
retrograde and the watch would go but would lack a good motion. In such
an instance a very slight advance of the chariot would remedy the
fault--not perfectly remedy it, but patch up, so to speak--and the watch
would run.

[Illustration: Fig. 135]

In this day, fine cylinder watches are not made, and only the common
kind are met with, and for this reason the student should familiarize
himself with all the imaginary faults which could occur from bad
construction. The best way to do this is to delineate what he (the
student) knows to be a faulty escapement, as, for instance, a cylinder
in which too much of the half shell is cut away; but in every instance
let the tooth be of the correct form. Then delineate an escapement in
which the cylinder is correct but the teeth faulty; also change the
thickness of the cylinder shell, so as to make the teeth too short. This
sort of practice makes the pupil think and study and he will acquire a
knowledge which will never be forgotten, but always be present to aid
him in the puzzles to which the practical watchmaker is every day
subject.

The ability to solve these perplexing problems determines in a great
degree the worth of a man to his employer, in addition to establishing
his reputation as a skilled workman. The question is frequently asked,
"How can I profitably employ myself in spare time?" It would seem that a
watchmaker could do no better than to carefully study matters
horological, striving constantly to attain a greater degree of
perfection, for by so doing his earning capacity will undoubtedly be
increased.




CHAPTER III.

THE CHRONOMETER ESCAPEMENT.


Undoubtedly "the detent," or, as it is usually termed, "the chronometer
escapement," is the most perfect of any of our portable time measurers.
Although the marine chronometer is in a sense a portable timepiece,
still it is not, like a pocket watch, capable of being adjusted to
positions. As we are all aware, the detent escapement is used in fine
pocket watches, still the general feeling of manufacturers is not
favorable to it. Much of this feeling no doubt is owing to the
mechanical difficulties presented in repairing the chronometer
escapements when the detent is broken, and the fact that the spring
detent could not be adjusted to position. We shall have occasion to
speak of position adjustments as relate to the chronometer escapement
later on.


ADVANTAGES OF THE CHRONOMETER.

We will proceed now to consider briefly the advantages the detent
escapement has over all others. It was soon discovered in constructing
portable timepieces, that to obtain the best results the vibrations of
the balance should be as free as possible from any control or influence
except at such times as it received the necessary impulse to maintain
the vibrations at a constant arc. This want undoubtedly led to the
invention of the detent escapement. The early escapements were all
frictional escapements, i.e., the balance staff was never free from
the influence of the train. The verge escapement, which was undoubtedly
the first employed, was constantly in contact with the escape wheel, and
was what is known as a "recoiling beat," that is, the contact of the
pallets actually caused the escape wheel to recoil or turn back. Such
escapements were too much influenced by the train, and any increase in
power caused the timepiece to gain. The first attempt to correct this
imperfection led to the invention and introduction of the fusee, which
enabled the watchmaker to obtain from a coiled spring nearly equal power
during the entire period of action. The next step in advance was the
"dead-beat escapement," which included the cylinder and duplex. In these
frictional escapements the balance staff locked the train while the
balance performed its arc of vibration.

FRICTIONAL ESCAPEMENTS IN HIGH FAVOR.

These frictional escapements held favor with many eminent watchmakers
even after the introduction of the detached escapements. It is no more
than natural we should inquire, why? The idea with the advocates of the
frictional rest escapements was, the friction of the tooth acted as a
_corrective_, and led no doubt to the introduction of going-barrel
watches. To illustrate, suppose in a cylinder watch we increase the
motive power, such increase of power would not, as in the verge
escapement, increase the rapidity of the vibrations; it might, in fact,
cause the timepiece to run slower from the increased friction of the
escape-wheel tooth on the cylinder; also, in the duplex escapement the
friction of the locking tooth on the staff retards the vibrations.

Dr. Hooke, the inventor of the balance spring, soon discovered it could
be manipulated to isochronism, i.e., so arcs of different extent would
be formed in equal time. Of course, the friction-rest escapement
requiring a spring to possess different properties from one which would
be isochronal with a perfectly detached escapement, these two frictional
escapements also differing, the duplex requiring other properties from
what would isochronize a spring for a cylinder escapement. Although
pocket watches with duplex and cylinder escapements having balances
compensated for heat and cold and balance springs adjusted to
isochronism gave very good results, careful makers were satisfied that
an escapement in which the balance was detached and free to act during
the greater proportion of the arc of vibration and uncontrolled by any
cause, would do still better, and this led to the detent escapement.


FAULTS IN THE DETENT ESCAPEMENT.

As stated previously, the detent escapement having pronounced faults in
positions which held it back, it is probable it would never have been
employed in pocket watches to any extent if it had not acquired such a
high reputation in marine chronometers. Let us now analyze the
influences which surround the detent escapement in a marine chronometer
and take account of the causes which are combined to make it an accurate
time measurer, and also take cognizance of other interfering causes
which have a tendency to prevent desired results. First, we will imagine
a balance with its spring such as we find in fine marine chronometers.
It has small pivots running in highly-polished jewels; such pivots are
perfectly cylindrical, and no larger than are absolutely necessary to
endure the task imposed upon them--of carrying the weight of the balance
and endure careful handling.

To afford the necessary vibrations a spring is fitted, usually of a
helical form, so disposed as to cause the balance to vibrate in arcs
back and forth in equal time, _provided these arcs are of equal extent_.
It is now to be taken note of that we have it at our disposal and option
to make these arcs equal in time duration, i.e., to make the long or
short arcs the quickest or to synchronize them. We can readily
comprehend we have now established a very perfect measure of short
intervals of time. We can also see if we provide the means of
maintaining these vibrations and counting them we should possess the
means of counting the flights of time with great accuracy. The
conditions which surround our balance are very constant, the small
pivots turning in fine hard jewels lubricated with an oil on which
exposure to the action of the air has little effect, leaves but few
influences which can interfere with the regular action of our balance.
We add to the influences an adjustable correction for the disturbances
of heat and cold, and we are convinced that but little could be added.


ANTAGONISTIC INFLUENCES.

In this combination we have pitted two antagonistic forces against each
other, viz., the elasticity of the spring and the weight and inertia of
the balance; both forces are theoretically constant and should produce
constant results. The mechanical part of the problem is simply to afford
these two forces perfect facilities to act on each other and compel each
to realize its full effect. We must also devise mechanical means to
record the duration of each conflict, that is, the time length of each
vibration. Many years have been spent in experimenting to arrive at the
best propositions to employ for the several parts to obtain the best
practical results. Consequently, in designing a chronometer escapement
we must not only draw the parts to a certain form, but consider the
quality and weight of material to employ.

To illustrate what we have just said, suppose, in drawing an escape
wheel, we must not only delineate the proper angle for the acting face
of the tooth, but must also take cognizance of the thickness of the
tooth. By thickness we mean the measurement of extent of the tooth in
the direction of the axis of the escape wheel. An escape-wheel tooth
might be of the best form to act in conveying power to the balance and
yet by being too thin soon wear or produce excessive friction. How thick
an escape wheel should be to produce best results, is one of the many
matters settled only by actual workshop experience.


FACTORS THAT MUST BE CONSIDERED.

Even this experience is in every instance modified by other influences.
To illustrate: Let us suppose in the ordinary to-day marine chronometer
the escape-wheel teeth exerted a given average force, which we set down
as so many grains. Now, if we should employ other material than
hammer-hardened brass for an escape wheel it would modify the thickness;
also, if we should decrease the motive power and increase the arc of
impulse. Or, if we should diminish the extent of the impulse arc and add
to the motive force, every change would have a controlling influence. In
the designs we shall employ, it is our purpose to follow such
proportions as have been adopted by our best makers, in all respects,
including form, size and material. We would say, however, there has been
but little deviation with our principal manufacturers of marine
chronometers for the last twenty years as regards the general principle
on which they were constructed, the chief aim being to excel in the
perfection of the several parts and the care taken in the several
adjustments.

Before we proceed to take up the details of constructing a chronometer
escapement we had better master the names for the several parts. We show
at Fig. 136 a complete plan of a chronometer escapement as if seen from
the back, which is in reality the front or dial side of the "top plate."
The chronometer escapement consists of four chief or principal parts,
viz.: The escape wheel, a portion of which is shown at _A_; the impulse
roller _B_; unlocking or discharging roller _C_, and the detent _D_.
These principal parts are made up of sub-parts: thus, the escape wheel
is composed of arms, teeth, recess and collet, the recess being the
portion of the escape wheel sunk, to enable us to get wide teeth actions
on the impulse pallet. The collet is a brass bush on which the wheel is
set to afford better support to the escape wheel than could be obtained
by the thinned wheel if driven directly on the pinion arbor. The impulse
roller is composed of a cylindrical steel collet _B_, the impulse pallet
_d_ (some call it the impulse stone), the safety recess _b b_. The
diameter of the impulse collet is usually one-half that of the escape
wheel. This impulse roller is staked directly on the balance staff, and
its perfection of position assured by resting against the foot of the
shoulder to which the balance is secured. This will be understood by
inspecting Fig. 137, which is a vertical longitudinal section of a
chronometer balance staff, the lower side of the impulse roller being
cupped out at _c_ with a ball grinder and finished a ball polish.

[Illustration: Fig. 136]

[Illustration: Fig. 137]

It will be seen the impulse roller is staked flat against the hub _E_ of
the balance staff. The unlocking roller, or, as it is also called, the
discharging roller, _C_, is usually thinner than the impulse roller and
has a jewel similar to the impulse jewel _a_ shown at _f_. This roller
is fitted by friction to the lower part of the balance staff and for
additional security has a pipe or short socket _e_ which embraces the
balance staff at _g_. The pipe _e_ is usually flattened on opposite
sides to admit of employing a special wrench for turning the discharging
roller in adjusting the jewel for opening the escapement at the proper
instant to permit the escape wheel to act on the impulse jewel _a_. The
parts which go to make up the detent _D_ consist of the "detent foot"
_F_, the detent spring _h_, the detent blade _i_, the jewel pipe _j_,
the locking jewel (or stone) _s_, the "horn" of the detent _k_, the
"gold spring" (also called the auxiliary and lifting spring) _m_. This
lifting or gold spring _m_ should be made as light and thin as possible
and stand careful handling.

We cannot impress on our readers too much the importance of making a
chronometer detent light. Very few detents, even from the hands of our
best makers, are as light as they might be. We should in such
construction have very little care for clumsy workmen who may have to
repair such mechanism. This feature should not enter into consideration.

We should only be influenced by the feeling that we are working for best
results, and it is acting under this influence that we devote so much
time to establishing a correct idea of the underlying principles
involved in a marine chronometer, instead of proceeding directly to the
drawing of such an escapement and give empirical rules for the length of
this or the diameter of that. As, for instance, in finishing the detent
spring _h_, suppose we read in text books the spring should be reduced
in thickness, so that a weight of one pennyweight suspended from the
pipe _j_ will deflect the detent ¼". This is a rule well enough for
people employed in a chronometer factory, but for the horological
student such fixed rules (even if remembered) would be of small use.
What the student requires is sound knowledge of the "whys," in order
that he may be able to thoroughly master this escapement.


FUNCTIONS OF THE DETENT.

We can see, after a brief analysis of the principles involved, that the
functions required of the detent _D_ are to lock the escape wheel _A_
and hold it while the balance performs its excursion, and that the
detent or recovering spring _h_ must have sufficient strength and power
to perform two functions: (1) Return the locking stone _s_ back to the
proper position to arrest and hold the escape wheel; (2) the spring _h_
must also be able to resist, without buckling or cockling, the thrust of
the escape wheel, represented by the arrows _p o_. Now we can readily
understand that the lighter we make the parts _i j k m_, the weaker the
spring _h_ can be. You say, perhaps, if we make it too weak it will be
liable to buckle under the pressure of the escape wheel; this, in turn,
will depend in a great measure on the condition of the spring _h_.
Suppose we have it straight when we put it in position, it will then
have no stress to keep it pressed to the holding, stop or banking screw,
which regulates the lock of the tooth. To obtain this stress we set the
foot _F_ of the detent around to the position indicated by the dotted
lines _r_ and _n_, and we get the proper tension on the detent spring to
effect the lock, or rather of the detent in time to lock the escape
wheel; but the spring _h_, instead of being perfectly straight, is bent
and consequently not in a condition to stand the thrust of the escape
wheel, indicated by the arrows _o p_.


OBTAINING THE BEST CONDITIONS.

Now the true way to obtain the best conditions is to give the spring _h_
a set curvature before we put it in place, and then when the detent is
in the proper position the spring _h_ will have tension enough on it to
bring the jewel _s_ against the stop screw, which regulates the lock,
and still be perfectly straight. This matter is of so much importance
that we will give further explanation. Suppose we bend the detent spring
_h_ so it is curved to the dotted line _t_, Fig. 136, and then the foot
_F_ would assume the position indicated at the dotted line _r_. We next
imagine the foot _F_ to be put in the position shown by the full lines,
the spring _h_ will become straight again and in perfect shape to resist
the thrust of the escape wheel.

Little "ways and methods" like the above have long been known to the
trade, but for some reason are never mentioned in our text books. A
detent spring 2/1000" thick and 80/1000" wide will stand the thrust for
any well-constructed marine chronometer in existence, and yet it will
not require half a pennyweight to deflect it one-fourth of an inch. It
is a good rule to make the length of the detent from the foot _F_ to the
center of the locking jewel pipe _j_ equal to the diameter of the escape
wheel, and the length of the detent spring _h_ two-sevenths of this
distance. The length of the horn _k_ is determined by the graphic plan
and can be taken from the plotted plan. The end, however, should
approach as near to the discharging jewel as possible and not absolutely
touch. The discharging (gold) spring _m_ is attached to the blade _i_ of
the detent with a small screw _l_ cut in a No. 18 hole of a Swiss plate.
While there should be a slight increase in thickness in the detent blade
at _w_, where the gold spring is attached, still it should be no more
than to separate the gold spring _m_ from the detent blade _i_.


IMPORTANT CONSIDERATIONS.

It is important the spring should be absolutely free and not touch the
detent except at its point of attachment at _w_ and to rest against the
end of the horn _k_, and the extreme end of _k_, where the gold spring
rests, should only be what we may term a dull or thick edge. The end of
the horn _k_ (shown at _y_) is best made, for convenience of elegant
construction, square--that is, the part _y_ turns at right angles to
_k_ and is made thicker than _k_ and at the same time deeper; or, to
make a comparison to a clumsy article, _y_ is like the head of a nail,
which is all on one side. Some makers bend the horn _k_ to a curve and
allow the end of the horn to arrest or stop the gold spring; but as it
is important the entire detent should be as light as possible, the
square end best answers this purpose. The banking placed at _j_ should
arrest the detent as thrown back by the spring _h_ at the "point of
percussion." This point of percussion is a certain point in a moving
mass where the greatest effort is produced and would be somewhere near
the point _x_, in a bar _G_ turning on a pivot at _z_, Fig. 138. It will
be evident, on inspection of this figure, if the bar _G_ was turning on
the center _z_ it would not give the hardest impact at the end _v_, as
parts of its force would be expended at the center _z_.

[Illustration: Fig. 138]


DECISIONS ARRIVED AT BY EXPERIENCE.

Experience has decided that the impulse roller should be about half the
diameter of the escape wheel, and experience has also decided that an
escape wheel of fifteen teeth has the greatest number of advantages;
also, that the balance should make 14,400 vibrations in one hour. We
will accept these proportions and conditions as best, from the fact that
they are now almost universally adopted by our best chronometer makers.
Although it would seem as if these proportions should have established
themselves earlier among practical men, we shall in these drawings
confine ourselves to the graphic plan, considering it preferable. In the
practical detail drawing we advise the employment of the scale given,
i.e., delineating an escape wheel 10" in diameter. The drawings which
accompany the description are one-fourth of this size, for the sake of
convenience in copying.

With an escape wheel of fifteen teeth the impulse arc is exactly
twenty-four degrees, and of course the periphery of the impulse roller
must intersect the periphery of the escape wheel for this arc (24°).
The circles _A B_, Fig. 139, represent the peripheries of these two
mobiles, and the problem in hand is to locate and define the position of
the two centers _a c_. These, of course, are not separated, the sum of
the two radii, i.e., 5" + 2½" (in the large drawing), as these
circles intersect, as shown at _d_. Arithmetically considered, the
problem is quite difficult, but graphically, simple enough. After we
have swept the circle _A_ with a radius of 5", we draw the radial line
_a f_, said line extending beyond the circle _A_.


LOCATING THE CENTER OF THE BALANCE STAFF.

Somewhere on this line is located the center of the balance staff, and
it is the problem in hand to locate or establish this center. Now, it is
known the circles which define the peripheries of the escape wheel and
the impulse roller intersect at _e e^2_. We can establish on our
circle _A_ where these intersections take place by laying off twelve
degrees, one-half of the impulse arc on each side of the line of centers
_a f_ on this circle and establishing the points _e e^2_. These points
_e e^2_ being located at the intersection of the circles _A_ and _B_,
must be at the respective distances of 5" and 2½" distance from the
center of the circles _A B_; consequently, if we set our dividers at
2½" and place one leg at _e_ and sweep the short arc _g^2_, and
repeat this process when one leg of the dividers is set at _e^2_, the
intersection of the short arcs _g_ and _g^2_ will locate the center of
our balance staff. We have now our two centers established, whose
peripheries are in the relation of 2 to 1.

To know, in the chronometer which we are supposed to be constructing,
the exact distance apart at which to plant the hole jewels for our two
mobiles, i.e., escape wheel and balance staff, we measure carefully on
our drawing the distance from _a_ to _c_ (the latter we having just
established) and make our statement in the rule of three, as follows: As
(10) the diameter of drawn escape wheel is to our real escape wheel so
is the measured distance on our drawing to the real distance in the
chronometer we are constructing.

It is well to use great care in the large drawing to obtain great
accuracy, and make said large drawing on a sheet of metal. This course
is justified by the degree of perfection to which measuring tools have
arrived in this day. It will be found on measurement of the arc of the
circle _B_, embraced between the intersections _e e^2_, that it is
about forty-eight degrees. How much of this we can utilize in our
escapement will depend very much on the perfection and accuracy of
construction.

[Illustration: Fig. 139]

We show at Fig. 140 three teeth of an escape wheel, together with the
locking jewel _E_ and impulse jewel _D_. Now, while theoretically we
could commence the impulse as soon as the impulse jewel _D_ was inside
of the circle representing the periphery of the escape wheel, still, in
practical construction, we must allow for contingencies. Before it is
safe for the escape wheel to attack the impulse jewel, said jewel must
be safely inside of said escape wheel periphery, in order that the
attacking tooth shall act with certainty and its full effect. A good
deal of thought and study can be bestowed to great advantage on the
"action" of a chronometer escapement. Let us examine the conditions
involved. We show in Fig. 140 the impulse jewel _D_ just passing inside
the circle of the periphery of the escape wheel. Now the attendant
conditions are these: The escape wheel is locked fast and perfectly
dead, and in the effort of unlocking it has to first turn backward
against the effort of the mainspring; the power of force required for
this effort is derived from the balance in which is stored up, so to
speak, power from impulses imparted to the balance by former efforts of
the escape wheel. In actual fact, the balance at the time the unlocking
takes place is moving with nearly its greatest peripheral velocity and,
as stated above, the escape wheel is at rest.

Here comes a very delicate problem as regards setting the unlocking or
discharging jewel. Let us first suppose we set the discharging jewel so
the locking jewel frees its tooth at the exact instant the impulse jewel
is inside the periphery of the escape wheel. As just stated, the escape
wheel is not only dead but actually moving back at the time the release
takes place. Now, it is evident that the escape wheel requires an
appreciable time to move forward and attack the impulse jewel, and
during this appreciable time the impulse jewel has been moving forward
inside of the arc _A A_, which represents the periphery of the escape
wheel. The proper consideration of this problem is of more importance in
chronometer making than we might at first thought have imagined,
consequently, we shall dwell upon it at some length.


HOW TO SET THE DISCHARGING JEWEL.

[Illustration: Fig. 140]

Theoretically, the escape-wheel tooth should encounter the impulse jewel
at the time--instant--both are moving with the same velocity. It is
evident then that there can be no special rule given for this, i.e.,
how to set the discharging jewel so it will free the tooth at exactly
the proper instant, from the fact that one chronometer train may be much
slower in getting to move forward from said train being heavy and clumsy
in construction. Let us make an experiment with a real chronometer in
illustration of our problem. To do so we remove our balance spring and
place the balance in position. If we start the balance revolving in the
direction of the arrow _y_, Fig. 140, it will cause the escapement to be
unlocked and the balance to turn rapidly in one direction and with
increasing velocity until, in fact, the escape wheel has but very little
effect on the impulse jewel; in fact, we could, by applying some outside
source of power--like blowing with a blow pipe on the balance--cause the
impulse jewel to pass in advance of the escape wheel; that is, the
escape-wheel tooth would not be able to catch the impulse jewel during
the entire impulse arc. Let us suppose, now, we set our unlocking or
discharging jewel in advance, that is, so the escapement is really
unlocked a little before the setting parts are in the positions and
relations shown in Fig. 141. Under the new conditions the escape wheel
would commence to move and get sufficient velocity on it to act on the
impulse jewel as soon as it was inside of the periphery of the escape
wheel. If the balance was turned slowly now the tooth of the escape
wheel would not encounter the impulse jewel at all, but fall into the
passing hollow _n_; but if we give the balance a high velocity, the
tooth would again encounter and act upon the jewel in the proper manner.
Experienced adjusters of chronometers can tell by listening if the
escape-wheel tooth attacks the impulse jewel properly, i.e., when both
are moving with similar velocities. The true sound indicating correct
action is only given when the balance has its maximum arc of vibration,
which should be about 1¼ revolutions, or perform an arc of 225
degrees on each excursion.


Fig. 142 is a side view of Fig. 141 seen in the direction of the arrow
_y_. We have mentioned a chariot to which the detent is attached, but we
shall make no attempt to show it in the accompanying drawings, as it
really has no relation to the problem in hand; i.e., explaining the
action of the chronometer escapement, as the chariot relates entirely to
the convenience of setting and adjusting the relation of the second
parts. The size, or better, say, the inside diameter of the pipe at _C_,
Fig. 143, which holds the locking jewel, should be about one-third of a
tooth space, and the jewel made to fit perfectly. Usually, jewelmakers
have a tendency to make this jewel too frail, cutting away the jewel
back of the releasing angle (_n_, Fig. 143) too much.


A GOOD FORM OF LOCKING STONE.

A very practical form for a locking stone is shown in transverse section
at Fig. 143. In construction it is a piece of ruby, or, better, sapphire
cut to coincide to its axis of crystallization, into first a solid
cylinder nicely fitting the pipe _C_ and finished with an
after-grinding, cutting away four-tenths of the cylinder, as shown at
_I_, Fig. 143. Here the line _m_ represents the locking face of the
jewel and the line _o_ the clearance to free the escaping tooth, the
angle at _n_ being about fifty-four degrees. This angle (_n_) should
leave the rounding of the stone intact, that is, the rounding of the
angle should be left and not made after the flat faces _m o_ are ground
and polished. The circular space at _I_ is filled with an aluminum
pin. The sizes shown are of about the right relative proportions; but
we feel it well to repeat the statement made previously, to the effect
that the detent to a chronometer cannot well be made too light.

[Illustration: Fig. 141]

[Illustration: Fig. 142]

[Illustration: Fig. 143]

The so-called gold spring shown at _H_, Figs. 141 and 142, should also
be as light as is consistent with due strength and can be made of the
composite metal used for gold filled goods, as the only real benefit to
be derived from employing gold is to avoid the necessity of applying oil
to any part of the escapement. If such gold metal is employed, after
hammering to obtain the greatest possible elasticity to the spring, the
gold is filed away, except where the spring is acted upon by the
discharging jewel _h_. We have previously mentioned the importance of
avoiding wide, flat contacts between all acting surfaces, like where the
gold spring rests on the horn of the detent at _p_; also where the
detent banks on the banking screw, shown at _G_, Fig. 142. Under this
principle the impact of the face of the discharging jewel with the end
of the gold spring should be confined to as small a surface as is
consistent with what will not produce abrasive action. The gold spring
is shaped as shown at Fig. 142 and loses, in a measure, under the pipe
of the locking jewel, a little more than one-half of the pipe below the
blade of the detent being cut away, as shown in Fig. 143, where the
lines _r r_ show the extent of the part of the pipe which banks against
the banking screw _G_. In this place even, only the curved surface of
the outside of the pipe touches the screw _G_, again avoiding contact of
broad surfaces.

We show the gold spring separate at Fig. 144. A slight torsion or twist
is given to the gold spring to cause it to bend with a true curvature in
the act of allowing the discharging pallet to pass back after unlocking.
If the gold spring is filed and stoned to the right flexure, that is,
the thinnest point properly placed or, say, located, the gold spring
will not continue in contact with the discharging pallet any longer time
or through a greater arc than during the process of unlocking. To make
this statement better understood, let us suppose the weakest part of the
gold spring _H_ is opposite the arrow _y_, Fig. 141, it will readily be
understood the contact of the discharging stone _h_ would continue
longer than if the point of greatest (or easiest) flexure was nearer to
the pipe _C_. If the end _D^2_ of the horn of the detent is as near as
it should be to the discharging stone there need be no fear but the
escapement will be unlocked. The horn _D^2_ of the detent should be
bent until five degrees of angular motion of the balance will unlock the
escape, and the contact of discharging jewel _h_ should be made without
engaging friction. This condition can be determined by observing if the
jewel seems to slide up (toward the pipe _C_) on the gold spring after
contact. Some adjusters set the jewel _J_, Figs. 143 and 141, in such a
way that the tooth rests close to the base; such adjusters claiming this
course has a tendency to avoid cockling or buckling of the detent spring
_E_. Such adjusters also set the impulse jewel slightly oblique, so as
to lean on the opposite angle of the tooth. Our advice is to set both
stones in places corresponding to the axis of the balance staff, and the
escape-wheel mobiles.


THE DETENT SPRING.

[Illustration: Fig. 144]

It will be noticed we have made the detent spring _E_ pretty wide and
extended it well above the blade of the detent. By shaping the detent in
this way nearly all the tendency of the spring _E_ to cockle is
annulled. We would beg to add to what we said in regard to setting
jewels obliquely. We are unable to understand the advantage of
wide-faced stones and deep teeth when we do not take advantage of the
wide surfaces which we assert are important. We guarantee that with a
detent and spring made as we show, there will be no tendency to cockle,
or if there is, it will be too feeble to even display itself. Those who
have had extended experience with chronometers cannot fail to have
noticed a gummy secretion which accumulates on the impulse and
discharging stones of a chronometer, although no oil is ever applied to
them. We imagine this coating is derived from the oil applied to the
pivots, which certainly evaporates, passes into vapor, or the remaining
oil could not become gummy. We would advise, when setting jewels (we
mean the locking, impulse and discharging jewels), to employ no more
shellac than is absolutely necessary, depending chiefly on metallic
contact for security.


DETAILS OF CONSTRUCTION.

We will now say a few words about the number of beats to the hour for a
box or marine chronometer to make to give the best results. Experience
shows that slow but most perfect construction has settled that 14,400,
or four vibrations of the balance to a second, as the proper number, the
weight of balance, including balance proper and movable weights, to be
about 5½ pennyweights, and the compensating curb about 1-2/10" in
diameter. The escape wheel, 55/100" in diameter and recessed so as to be
as light as possible, should have sufficient strength to perform its
functions properly. The thickness or, more properly, the face extent of
the tooth, measured in the direction of the axis of the escape wheel,
should be about 1/20". The recessing should extend half way up the
radial back of the tooth at _t_. The curvature of the back of the teeth
is produced with the same radii as the impulse roller. To locate the
center from which the arc which defines the back of the teeth is swept,
we halve the space between the teeth _A^2_ and _a^4_ and establish
the point _n_, Fig. 141, and with our dividers set to sweep the circle
representing the impulse roller, we sweep an arc passing the point of
the tooth _A^3_ and _u_, thus locating the center _w_. From the center
_k_ of the escape wheel we sweep a complete circle, a portion of which
is represented by the arc _w v_. For delineating other teeth we set one
leg of our dividers to agree with the point of the tooth and the other
leg on the circle _w v_ and produce an arc like _z u_.


ORIGINAL DESIGNING OF THE ESCAPEMENT.

On delineating our chronometer escapement shown at Fig. 141 we have
followed no text-book authority, but have drawn it according to such
requirements as are essential to obtain the best results. An escapement
of any kind is only a machine, and merely requires in its construction a
combination of sound mechanical principles. Neither Saunier nor Britten,
in their works, give instructions for drawing this escapement which will
bear close analysis. It is not our intention, however, to criticise
these authors, except we can present better methods and give correct
systems.


TANGENTIAL LOCKINGS.

It has been a matter of great contention with makers of chronometer and
also lever escapements as to the advantages of "tangential lockings." By
this term is meant a locking the same as is shown at _C_, Fig. 141, and
means a detent planted at right angles to a line radial to the
escape-wheel axis, said radial line passing through the point of the
escape-wheel tooth resting on the locking jewel. In escapements not set
tangential, the detent is pushed forward in the direction of the arrow
_x_ about half a tooth space. Britten, in his "Hand-Book," gives a
drawing of such an escapement. We claim the chief advantage of
tangential locking to lie in the action of the escape-wheel teeth, both
on the impulse stone and also on the locking stone of the detent.
Saunier, in his "Modern Horology," gives the inclination of the front
fan of the escape-wheel teeth as being at an angle of twenty-seven
degrees to a radial line. Britten says twenty degrees, and also employs
a non-tangential locking.

Our drawing is on an angle of twenty-eight degrees, which is as low as
is safe, as we shall proceed to demonstrate. For establishing the angle
of an escape-wheel tooth we draw the line _C d_, from the point of the
escape-wheel tooth resting on the locking stone shown at _C_ at an angle
of twenty-eight degrees to radial line _C k_. We have already discussed
how to locate and plant the center of the balance staff.

We shall not show in this drawing the angular motion of the escape
wheel, but delineate at the radial lines _c e_ and _c f_ of the arc of
the balance during the extent of its implication with the periphery of
the escape wheel, which arc is one of about forty-eight degrees. Of this
angle but forty-three degrees is attempted to be utilized for the
purpose of impulse, five degrees being allowed for the impulse jewel to
pass inside of the arc of periphery of the escape wheel before the
locking jewel releases the tooth of the escape wheel resting upon it. At
this point it is supposed the escape wheel attacks the impulse jewel,
because, as we just explained, the locking jewel has released the tooth
engaging it. Now, if the train had no weight, no inertia to overcome,
the escape wheel tooth _A^2_ would move forward and attack the impulse
pallet instantly; but, in fact, as we have already explained, there will
be an appreciable time elapse before the tooth overtakes the
rapidly-moving impulse jewel. It will, of course, be understood that the
reference letters used herein refer to the illustrations that have
appeared on preceding pages.

If we reason carefully on the matter, we will readily comprehend that we
can move the locking jewel, i.e., set it so the unlocking will take
place in reality before the impulse jewel has passed through the entire
five degrees of arc embraced between the radial lines _c e_ and _c g_,
Fig. 141, and yet have the tooth attack the jewel after the five degrees
of arc. In practice it is safe to set the discharging jewel _h_ so the
release of the held tooth _A^1_ will take place as soon as the tooth
_A^2_ is inside the principal line of the escape wheel. As we
previously explained, the contact between _A^2_ and the impulse jewel
_i_ would not in reality occur until the said jewel _i_ had fully passed
through the arc (five degrees) embraced between the radial lines _c e_
and _c g_.

At this point we will explain why we drew the front fan of the
escape-wheel teeth at the angle of twenty-eight degrees. If the fan of
impulse jewel _i_ is set radial to the axis of the balance, the
engagement of the tooth _A^2_ would be at a disadvantage if it took
place prior to this jewel passing through an arc of five degrees inside
the periphery of the escape wheel. It will be evident on thought that if
an escape-wheel tooth engaged the impulse stone before the five-degrees
angle had passed, the contact would not be on its flat face, but the
tooth would strike the impulse jewel on its outer angle. A continued
inspection will also reveal the fact that in order to have the point of
the tooth engage the flat surface of the impulse pallet the impulse
jewel must coincide with the radial line _c g_. If we seek to remedy
this condition by setting the impulse jewel so the face is not radial,
but inclined backward, we encounter a bad engaging friction, because,
during the first part of the impulse action, the tooth has to slide up
the face of the impulse jewel. All things considered, the best action is
obtained with the impulse jewel set so the acting face is radial to the
balance staff and the engagement takes place between the tooth and the
impulse jewel when both are moving with equal velocities, i.e., when
the balance is performing with an arc (or motion) of 1¼ revolutions
or 225 degrees each way from a point of rest. Under such conditions the
actual contact will not take place before some little time after the
impulse jewel has passed the five-degree arc between the lines _c e_ and
_c g_.


THE DROP AND DRAW CONSIDERED.

Exactly how much drop must be allowed from the time the tooth leaves the
impulse jewel before the locking tooth engages the locking jewel will
depend in a great measure on the perfection of workmanship, but should
in no instance be more than what is absolutely required to make the
escapement safe. The amount of draw given to the locking stone _c_ is
usually about twelve degrees to the radial line _k a_. Much of the
perfection of the chronometer escapement will always depend on the skill
of the escapement adjuster and not on the mechanical perfection of the
parts.

The jewels all have to be set by hand after they are made, and the
distance to which the impulse jewel protrudes beyond the periphery of
the impulse roller is entirely a matter for hand and eye, but should
never exceed 2/1000". After the locking jewel _c_ is set, we can set the
foot _F_ of the detent _D_ forward or back, to perfect and correct the
engagement of the escape-wheel teeth with the impulse roller _B_. If we
set this too far forward, the tooth _A^3_ will encounter the roller
while the tooth _A^2_ will be free.

We would beg to say here there is no escape wheel made which requires
the same extreme accuracy as the chronometer, as the tooth spaces and
the equal radial extent of each tooth should be only limited by our
powers toward perfection. It is usual to give the detent a locking of
about two degrees; that is, it requires about two degrees to open it,
counting the center of fluxion of the detent spring _E_ and five degrees
of balance arc.


FITTING UP OF THE FOOT.

Several attempts have been made by chronometer makers to have the foot
_F_ adjustable; that is, so it could be moved back and forth with a
screw, but we have never known of anything satisfactory being
accomplished in this direction. About the best way of fitting up the
foot _F_ seems to be to provide it with two soft iron steady pins (shown
at _j_) with corresponding holes in the chariot, said holes being
conically enlarged so they (the pins) can be bent and manipulated so the
detent not only stands in the proper position as regards the escape
wheel, but also to give the detent spring _E_ the proper elastic force
to return in time to afford a secure locking to the arresting tooth of
the escape wheel after an impulse has been given.

If these pins _j_ are bent properly by the adjuster, whoever afterwards
cleans the chronometer needs only to gently push the foot _F_ forward so
as to cause the pins _j_ to take the correct positions as determined by
the adjuster and set the screw _l_ up to hold the foot _F_ when all the
other relations are as they should be, except such as we can control by
the screw _G_, which prevents the locking jewel from entering too deeply
into the escape wheel.

In addition to being a complete master of the technical part of his
business, it is also desirable that the up-to-date workman should be
familiar with the subject from a historical point of view. To aid in
such an understanding of the matter we have translated from "L'Almanach
de l'Horologerie et de la Bijouterie" the matter contained in the
following chapter.




CHAPTER IV.

HISTORY OF ESCAPEMENTS.


It could not have been long after man first became cognizant of his
reasoning faculties that he began to take more or less notice of the
flight of time. The motion of the sun by day and of the moon and stars
by night served to warn him of the recurring periods of light and
darkness. By noting the position of these stellar bodies during his
lonely vigils, he soon became proficient in roughly dividing up the
cycle into sections, which he denominated the hours of the day and of
the night. Primitive at first, his methods were simple, his needs few
and his time abundant. Increase in numbers, multiplicity of duties, and
division of occupation began to make it imperative that a more
systematic following of these occupations should be instituted, and with
this end in view he contrived, by means of burning lights or by
restricting the flowing of water or the falling of weights, to subdivide
into convenient intervals and in a tolerably satisfactory manner the
periods of light.

These modest means then were the first steps toward the exact
subdivisions of time which we now enjoy. Unrest, progress, discontent
with things that be, we must acknowledge, have, from the appearance of
the first clock to the present hour, been the powers which have driven
on the inventive genius of watch and clockmakers to designate some new
and more acceptable system for regulating the course of the movement. In
consequence of this restless search after the best, a very considerable
number of escapements have been invented and made up, both for clocks
and watches; only a few, however, of the almost numberless systems have
survived the test of time and been adopted in the manufacture of the
timepiece as we know it now. Indeed, many such inventions never passed
the experimental stage, and yet it would be very interesting to the
professional horologist, the apprentice and even the layman to become
more intimately acquainted with the vast variety of inventions made upon
this domain since the inception of horological science. Undoubtedly, a
complete collection of all the escapements invented would constitute a
most instructive work for the progressive watchmaker, and while we are
waiting for a competent author to take such an exhaustive work upon his
hands, we shall endeavor to open the way and trust that a number of
voluntary collaborators will come forward and assist us to the extent of
their ability in filling up the chinks.


PROBLEMS TO BE SOLVED.

The problem to be solved by means of the escapement has always been to
govern, within limits precise and perfectly regular, if it be possible,
the flow of the motive force; that means the procession of the
wheel-work and, as a consequence, of the hands thereto attached. At
first blush it seems as if a continually-moving governor, such as is in
use on steam engines, for example, ought to fulfil the conditions, and
attempts have accordingly been made upon this line with results which
have proven entirely unsatisfactory.

Having thoroughly sifted the many varieties at hand, it has been finally
determined that the only means known to provide the most regular flow of
power consists in intermittently interrupting the procession of the
wheel-work, and thereby gaining a periodically uniform movement.
Whatever may be the system or kind of escapement employed, the
functioning of the mechanism is characterized by the suspension, at
regular intervals, of the rotation of the last wheel of the train and in
transmitting to a regulator, be it a balance or a pendulum, the power
sent into that wheel.


ESCAPEMENT THE MOST ESSENTIAL PART.

Of all the parts of the timepiece the escapement is then the most
essential; it is the part which assures regularity in the running of the
watch or clock, and that part of parts that endows the piece with real
value. The most perfect escapement would be that one which should
perform its duty with the least influence upon the time of oscillation
or vibration of the regulating organ. The stoppage of the train by the
escapement is brought about in different ways, which may be gathered
under three heads or categories. In the two which we shall mention
first, the stop is effected directly upon the axis of the regulator, or
against a piece which forms a part of that axis; the tooth of the escape
wheel at the moment of its disengagement remains supported upon or
against that stop.

In the first escapement invented and, indeed, in some actually employed
to-day for certain kinds of timekeepers, we notice during the locking a
retrograde movement of the escape wheel; to this kind of movement has
been given the name of _recoil escapement_. It was recognized by the
fraternity that this recoil was prejudicial to the regularity of the
running of the mechanism and, after the invention of the pendulum and
the spiral, inventive makers succeeded in replacing this sort of
escapement with one which we now call the _dead-beat escapement_. In
this latter the wheel, stopped by the axis of the regulator, remains
immovable up to the instant of its disengagement or unlocking.

In the third category have been collected all those forms of escapement
wherein the escape wheel is locked by an intermediate piece, independent
of the regulating organ. This latter performs its vibrations of
oscillation quite without interference, and it is only in contact with
the train during the very brief moment of impulse which is needful to
keep the regulating organ in motion. This category constitutes what is
known as the _detached escapement_ class.

Of the _recoil escapement_ the principal types are: the _verge
escapement_ or _crown-wheel escapement_ for both watches and clocks, and
the _recoil anchor escapement_ for clocks. The _cylinder_ and _duplex
escapements_ for watches and the _Graham anchor escapement_ for clocks
are styles of the _dead-beat escapement_ most often employed. Among the
_detached escapements_ we have the _lever_ and _detent_ or _chronometer
escapements_ for watches; for clocks there is no fixed type of detached
lever and it finds no application to-day.


THE VERGE ESCAPEMENT.

The _verge escapement_, called also the _crown-wheel escapement_, is by
far the simplest and presents the least difficulty in construction. We
regret that the world does not know either the name of its originator
nor the date at which the invention made its first appearance, but it
seems to have followed very closely upon the birth of mechanical
horology.

Up to 1750 it was employed to the exclusion of almost all the others. In
1850 a very large part of the ordinary commercial watches were still
fitted with the verge escapement, and it is still used under the form of
_recoil anchor_ in clocks, eighty years after the invention of the
cylinder escapement, or in 1802. Ferdinand Berthoud, in his "History of
the Measurement of Time," says of the balance-wheel escapement: "Since
the epoch of its invention an infinite variety of escapements have been
constructed, but the one which is employed in ordinary watches for
every-day use is still the best." In referring to our illustrations, we
beg first to call attention to the plates marked Figs. 145 and 146.
This plate gives us two views of a verge escapement; that is, a balance
wheel and a verge formed by its two opposite pallets. The views are
intentionally presented in this manner to show that the verge _V_ may be
disposed either horizontally, as in Fig. 146, or vertically, as in Fig.
145.

[Illustration: Figs. 145 and 146]

[Illustration: Fig. 147]

Let us imagine that our drawing is in motion, then will the tooth _d_,
of the crown wheel _R_, be pushing against the pallet _P_, and just upon
the point of slipping by or escaping, while the opposite tooth _e_ is
just about to impinge upon the advancing pallet _P'_. This it does, and
will at first, through the impulse received from the tooth _d_ be forced
back by the momentum of the pallet, that is, suffer a recoil; but on the
return journey of the pallet _P'_, the tooth _e_ will then add its
impulse to the receding pallet. The tooth _e_ having thus accomplished
its mission, will now slip by and the tooth _c_ will come in lock with
the pallet _P_ and, after the manner just described for _e_, continue
the escapement. Usually these escape wheels are provided with teeth to
the number of 11, 13 or 15, and always uneven. A great advantage
possessed by this form of escapement is that it does not require any
oil, and it may be made to work even under very inferior construction.


OLDEST ARRANGEMENT OF A CROWN-WHEEL ESCAPEMENT.

[Illustration: Fig. 148]

Plate 147 shows us the oldest known arrangement of a crown-wheel
escapement in a clock. _R_ is the crown wheel or balance wheel acting
upon the pallets _P_ and _P'_, which form part of the verge _V_. This
verge is suspended as lightly as possible upon a pliable cord _C_ and
carries at its upper end two arms, _B_ and _B_, called adjusters,
forming the balance. Two small weights _D D_, adapted to movement along
the rules or adjusters serve to regulate the duration of a vibration. In
Fig. 148 we have the arrangement adopted in small timepieces and
watches: _B_ represents the regulator in the form of a circular balance,
but not yet furnished with a spiral regulating spring; _c_ is the last
wheel of the train and called the _fourth wheel_, it being that number
distant from the great wheel. As will be seen, the verge provided with
its pallets is vertically placed, as in the preceding plate.

[Illustration: Fig. 149]

Here it will quickly be seen that regarded from the standpoint of
regularity of motion, this arrangement can be productive of but meager
results. Subjected as it is to the influence of the slightest variation
in the motive power and of the least jar or shaking, a balance wheel
escapement improvided with a regulator containing within itself a
regulating force, could not possibly give forth anything else than an
unsteady movement. However, mechanical clocks fitted with this
escapement offer indisputable advantages over the ancient clepsydra; in
spite of their imperfections they rendered important services,
especially after the striking movement had been added. For more than
three centuries both this crude escapement and the cruder regulator were
suffered to continue in this state without a thought of improvement;
even in 1600, when Galileo discovered the law governing the oscillation
of the pendulum, they did not suspect how important this discovery was
for the science of time measurement.


GALILEO'S EXPERIMENTS.

[Illustration: Fig. 150]

Galileo, himself, in spite of his genius for investigation, was so
engrossed in his researches that he could not seem to disengage the
simple pendulum from the compound pendulums to which he devoted his
attention; besides, he attributed to the oscillation an absolute
generality of isochronism, which they did not possess; nor did he know
how to apply his famous discovery to the measurement of time. In fact,
it was not till after more than half a century had elapsed, in 1657, to
be exact, that the celebrated Dutch mathematician and astronomer,
Huygens, published his memoirs in which he made known to the world the
degree of perfection which would accrue to clocks if the pendulum were
adopted to regulate their movement.

[Illustration: Fig. 151]

An attempt was indeed made to snatch from Huygens and confer upon
Galileo the glory of having first applied the pendulum to a clock, but
this attempt not having been made until some time after the publication
of "Huygens' Memoirs," it was impossible to place any faith in the
contention. If Galileo had indeed solved the beautiful problem, both in
the conception and the fact, the honor of the discovery was lost to him
by the laziness and negligence of his pupil, Viviani, upon whom he had
placed such high hopes. One thing is certain, that the right of priority
of the discovery and the recognition of the entire world has been
incontestably bestowed upon Huygens. The escapement which Galileo is
supposed to have conceived and to which he applied the pendulum, is
shown in Fig. 149. The wheel _R_ is supplied with teeth, which lock
against the piece _D_ attached to a lever pivoted at _a_, and also with
pins calculated to impart impulses to the pendulum through the pallet
_P_. The arm _L_ serves to disengage or unlock the wheel by lifting the
lever _D_ upon the return oscillation of the pendulum.

[Illustration: Fig. 152]

[Illustration: Fig. 153]

A careful study of Fig. 150 will discover a simple transposition which
it became necessary to make in the clocks, for the effectual adaptation
of the pendulum to their regulation. The verge _V_ was set up
horizontally and the pendulum _B_, suspended freely from a flexible
cord, received the impulses through the intermediation of the forked arm
_F_, which formed a part of the verge. At first this forked arm was not
thought of, for the pendulum itself formed a part of the verge. A
far-reaching step had been taken, but it soon became apparent that
perfection was still a long way off. The crown-wheel escapement forcibly
incited the pendulum to wider oscillations; these oscillations not being
as Galileo had believed, of unvaried durations, but they varied sensibly
with the intensity of the motive power.


THE ATTAINMENT OF ISOCHRONISM BY HUYGENS.

Huygens rendered his pendulum _isochronous_; that is, compelled it to
make its oscillations of equal duration, whatever might be the arc
described, by suspending the pendulum between two metallic curves _c
c'_, each one formed by an arc of a cycloid and against which the
suspending cord must lie upon each forward or backward oscillation. We
show this device in Fig. 151. In great oscillations, and by that we mean
oscillations under a greater impulse, the pendulum would thus be
shortened and the shortening would correct the time of the oscillation.
However, the application of an exact cycloidal arc was a matter of no
little difficulty, if not an impossibility in practice, and practical
men began to grope about in search of an escapement which would permit
the use of shorter arcs of oscillation. At London the horologist, G.
Clement, solved the problem in 1675 with his rack escapement and recoil
anchor. In the interval other means were invented, especially the
addition of a second pendulum to correct the irregularities of the
first. Such an escapement is pictured in Fig. 152. The verge is again
vertical and carries near its upper end two arms _D D_, which are each
connected by a cord with a pendulum. The two pendulums oscillate
constantly in the inverse sense the one to the other.

[Illustration: Fig. 154]

[Illustration: Fig. 155]


ANOTHER TWO-PENDULUM ESCAPEMENT.

We show another escapement with two pendulums in Fig. 153. These are
fixed directly upon two axes, each one carrying a pallet _P P'_ and a
segment of a toothed wheel _D D_, which produces the effect of
solidarity between them. The two pendulums oscillate inversely one to
the other, and one after the other receives an impulse. This escapement
was constructed by Jean Baptiste Dutertre, of Paris.

Fig. 154 shows another disposition of a double pendulum. While the
pendulum here is double, it has but one bob; it receives the impulse by
means of a double fork _F_. _C C_ represents the cycloidal curves and
are placed with a view of correcting the inequality in the duration of
the oscillations. In watches the circular balances did not afford any
better results than the regulating rods or rules of the clocks, and the
pendulum, of course, was out of the question altogether; it therefore
became imperative to invent some other regulating system.

[Illustration: Fig. 156]

[Illustration: Fig. 157]

It occured to the Abbé d'Hautefeuille to form a sort of resilient
mechanism by attaching one end of a hog's bristle to the plate and the
other to the balance near the axis. Though imperfect in results, this
was nevertheless a brilliant idea, and it was but a short step to
replace the bristle with a straight and very flexible spring, which
later was supplanted by one coiled up like a serpent; but in spite of
this advancement, the watches did not keep much better time. Harrison,
the celebrated English horologist, had recourse to two artifices, of
which the one consisted in giving to the pallets of the escapement such
a curvature that the balance could be led back with a velocity
corresponding to the extension of the oscillation; the second consisted
of an accessory piece, the resultant action of which was analogous to
that of the cycloidal curves in connection with the pendulum.


CORRECTING IRREGULARITIES IN THE VERGE ESCAPEMENT.

Huygens attempted to correct these irregularities in the verge
escapement in watches by amplifying the arc of oscillation of the
balance itself. He constructed for that purpose a pirouette escapement
shown in Fig. 155, in which a toothed wheel _A_ adjusted upon the verge
_V_ serves as an intermediary between that and the balance _B_, upon the
axis of which was fixed a pinion _D_. By this method he obtained
extended arcs of vibration, but the vibrations were, as a consequence,
very slow, and they still remained subject to all the irregularities
arising from the variation in the motive power as well as from shocks. A
little later, but about the same epoch, a certain Dr. Hook, of the Royal
Society of London, contrived another arrangement by means of which he
succeeded, so it appeared to him at least, in greatly diminishing the
influence of shock upon the escapement; but many other, perhaps greater,
inconveniences caused his invention to be speedily rejected. We shall
give our readers an idea of what Dr. Hook's escapement was like.

[Illustration: Fig. 158]

[Illustration: Fig. 159]

On looking at Fig. 156 we see the escape wheel _R_, which was flat and
in the form of a ratchet; it was provided with two balances. _B B_
engaging each other in teeth, each one carrying a pallet _P P'_ upon its
axis; the axes of the three wheels being parallel. Now, in our drawing,
the tooth _a_ of the escape wheel exerts its lift upon the pallet _P'_;
when this tooth escapes the tooth _b_ will fall upon the pallet _P'_ on
the opposite side, a recoil will be produced upon the action of the two
united balances, then the tooth _b_ will give its impulse in the
contrary direction. Considerable analogy exists between this form of
escapement and that shown in Fig. 153 and intended for clocks. This was
the busy era in the watchmaker's line. All the great heads were
pondering upon the subject and everyone was on the _qui vive_ for the
newest thing in the art.

In 1674 Huygens brought out the first watch having a regulating spring
in the form of a spiral; the merit of this invention was disputed by the
English savant, Dr. Hook, who pretended, as did Galileo, in the
application of the pendulum, to have priority in the idea. Huygens, who
had discovered and corrected the irregularities in the oscillations of
the pendulum, did not think of those of the balance with the spiral
spring. And it was not until the close of the year 1750 that Pierre Le
Roy and Ferdinand Berthoud studied the conditions of isochronism
pertaining to the spiral.


AN INVENTION THAT CREATED MUCH ENTHUSIASM.

However that may be, this magnificent invention, like the adaptation of
the pendulum, was welcomed with general enthusiasm throughout the
scientific world: without spiral and without pendulum, no other
escapement but the recoil escapement was possible; a new highway was
thus opened to the searchers. The water clocks (clepsydrę) and the hour
glasses disappeared completely, and the timepieces which had till then
only marked the hours, having been perfected up to the point of keeping
more exact time, were graced with the addition of another hand to tell
off the minutes.

[Illustration: Fig. 160]

[Illustration: Fig. 161]

It was not until 1695 that the first _dead-beat escapement_ appeared
upon the scene; during the interval of over twenty years all thought had
been directed toward the one goal, viz.: the perfecting of the _verge
escapement_; but practice demonstrated that no other arrangement of the
parts was superior to the original idea. For the benefit of our readers
we shall give a few of these attempts at betterment, and you may see for
yourselves wherein the trials failed.

Fig. 157 represents a _verge escapement_ with a ratchet wheel, the
pallets _P P'_ being carried upon separate axes. The two axes are
rigidly connected, the one to the other, by means of the arms _o o'_.
One of the axes carries besides the fork _F_, which transmits the
impulse to the pendulum _B_. In the front view, at the right of the
plate, for the sake of clearness the fork and the pendulum are not
shown, but one may easily see the jointure of the arms _o o'_ and their
mode of operation.

Another very peculiar arrangement of the _verge escapement_ we show at
Fig. 158. In this there are two wheels, one, _R'_, a small one in the
form of a ratchet; the other, _R_, somewhat larger, called the balance
wheel, but being supplied with straight and slender teeth. The verge _V_
carrying the two pallets is pivoted in the vertical diameter of the
larger wheel. The front view shows the _modus operandi_ of this
combination, which is practically the same as the others. The tooth _a_
of the large wheel exerts its force upon the pallet _P_, and the tooth
_b_ of the ratchet will encounter the pallet _P'_. This pallet, after
suffering its recoil, will receive the impulse communicated by the tooth
_b_. This escapement surely could not have given much satisfaction, for
it offers no advantage over the others, besides it is of very difficult
construction.

[Illustration: Fig. 162]

[Illustration: Fig. 163]


INGENIOUS ATTEMPTS AT SOLUTION OF A DIFFICULT PROBLEM.

Much ingenuity to a worthy end, but of little practical value, is
displayed in these various attempts at the solution of a very difficult
problem. In Fig. 159 we have a mechanism combining two escape wheels
engaging each other in gear; of the two wheels, _R R'_, one alone is
driven directly by the train, the other being turned in the opposite
direction by its comrade. Both are furnished with pins _c c'_, which act
alternately upon the pallets _P P'_ disposed in the same plane upon the
verge _V_ and pivoted between the wheels. Our drawing represents the
escapement at the moment when the pin _C'_ delivers its impulse, and
this having been accomplished, the locking takes place upon the pin _C_
of the other wheel upon the pallet _P'_. Another system of two escape
wheels is shown in Fig. 160, but in this case the two wheels _R R_ are
driven in a like direction by the last wheel _A_ of the train. The
operation of the escapement is the same as in Fig. 159.

[Illustration: Fig. 164]

[Illustration: Fig. 165]

In Fig. 161 we have a departure from the road ordinarily pursued. Here
we see an escapement combining two levers, invented by the Chevalier de
Béthune and applied by M. Thiout, master-horologist, at Paris in 1727.
_P P'_ are the two levers or pallets separately pivoted. Upon the axis
_V_, of the lever _P_, is fixed a fork which communicates the motion to
the pendulum. The two levers are intimately connected by the two arms _B
B'_, of which the former carries an adjusting screw, a well-conceived
addition for regulating the opening between the pallets. The
counter-weight _C_ compels constant contact between the arms _B B'_. The
function is always the same, the recoil and the impulsion operate upon
the two pallets simultaneously. This escapement enjoyed a certain degree
of success, having been employed by a number of horologists who modified
it in various ways.


VARIOUS MODIFICATIONS

Some of these modifications we shall show. For the first example, then,
let Fig. 162 illustrate. In this arrangement the fork is carried upon
the axis of the pallet _P'_, which effectually does away with the
counter-weight _C_, as shown. Somewhat more complicated, but of the same
intrinsic nature, is the arrangement displayed in Fig. 163. We should
not imagine that it enjoyed a very extensive application. Here the two
levers are completely independent of each other; they act upon the piece
_B B_ upon the axis _V_ of the fork. The counter-weights _C C'_ maintain
the arms carrying the rollers _D D'_ in contact with the piece _B B'_
which thus receives the impulse from the wheel _R_. Two adjusting screws
serve to place the escapement upon the center. By degrees these
fantastic constructions were abandoned to make way for the anchor recoil
escapement, which was invented, as we have said, in 1675, by G. Clement,
a horologist, of London. In Fig. 164 we have the disposition of the
parts as first arranged by this artist. Here the pallets are replaced by
the inclines _A_ and _B_ of the anchor, which is pivoted at _V_ upon an
axis to which is fixed also the fork. The tooth _a_ escapes from the
incline or lever _A_, and the tooth _b_ immediately rests upon the lever
_B_; by the action of the pendulum the escape wheel suffers a recoil as
in the pallet escapement, and on the return of the pendulum the tooth
_c_ gives out its impulse in the contrary direction. With this new
system it became possible to increase the weight of the bob and at the
same time lessen the effective motor power. The travel of the pendulum,
or arc of oscillation, being reduced in a marked degree, an accuracy of
rate was obtained far superior to that of the crown-wheel escapement.
However, this new application of the recoil escapement was not adopted
in France until 1695.

[Illustration: Fig. 166]

[Illustration: Fig. 167]

The travel of the pendulum, though greatly reduced, still surpassed in
breadth the arc in which it is isochronous, and repeated efforts were
made to give such shape to the levers as would compel its oscillation
within the arc of equal time; a motion which is, as was recognized even
at that epoch, the prime requisite to a precise rating. Thus, in 1720,
Julien Leroy occupied himself working out the proper shapes for the
inclines to produce this desired isochronism. Searching along the same
path, Ferd. Berthoud constructed an escapement represented by the Fig.
165. In it we see the same inclines _A B_ of the former construction,
but the locking is effected against the slides _C_ and _D_, the curved
faces of which produce isochronous oscillations of the pendulum. The
tooth _b_ imparts its lift and the tooth _c_ will lock against the face
_C_; after having passed through its recoil motion this tooth _c_ will
butt against the incline _A_ and work out its lift or impulse upon it.


THE GABLE ESCAPEMENT.

[Illustration: Fig. 168]

[Illustration: Fig. 169]

The _gable escapement_, shown in Fig. 166, allows the use of a heavier
pendulum, at the same time the anchor embraces within its jaws a greater
number of the escape-wheel teeth; an arrangement after this manner leads
to the conclusion that with these long levers of the anchor the friction
will be considerably increased and the recoil faces will, as a
consequence, be quickly worn away. Without doubt, this was invented to
permit of opening and closing the contact points of the anchor more
easily. Under the name of the _English recoil anchor_ there came into
use an escapement with a _reduced gable_, which embraced fewer teeth
between the pallets or inclines; we give a representation of this in
Fig. 167. This system seems to have been moderately successful. The
anchor recoil escapement in use in Germany to-day is demonstrated in
Fig. 168; this arrangement is also found in the American clocks. As we
see, the anchor is composed of a single piece of curved steel bent to
the desired curves. Clocks provided with this escapement keep reasonably
good time; the resistance of the recoils compensate in a measure for the
want of isochronism in the oscillations of the pendulum. Ordinary clocks
require considerably more power to drive them than finer clocks and, as
a consequence, their ticking is very noisy. Several means have been
employed to dampen this noise, one of which we show in Fig. 169.

[Illustration: Fig. 170]

Here the anchor is composed of two pieces, _A B_, screwed upon a plate
_H_ pivoting at _V_. In their arrangement the two pieces represent, as
to distance and curvature, the counterpart of Fig. 168. At the moment of
impact their extreme ends recoil or spring back from the shock of the
escape teeth, but the resiliency of the metal is calculated to be strong
enough to return them immediately to the contact studs _e e_.

As a termination to this chapter, we shall mention the use made at the
present day of the recoil lever escapement in repeating watches. We give
a diagram of this construction in Fig. 170. The lever here is intended
to restrain and regulate the motion of the small striking work. It is
pivoted at _V_ and is capable of a very rapid oscillatory motion, the
arc of which may, however, be fixed by the stud or stop _D_, which
limits the swing of the fly _C_. This fly is of one piece with the lever
and, together with the stud _D_, determines the angular motion of the
lever. If the angle be large that means the path of the fly be long,
then the striking train will move slowly; but if the teeth of the escape
wheel _R_ can just pass by without causing the lever to describe a
supplementary or extended arc, the striking work will run off rapidly.




CHAPTER V.

PUTTING IN A NEW CYLINDER.


Putting in a new cylinder is something most watchmakers fancy they can
do, and do well; but still it is a job very few workmen can do and
fulfill all the requirements a job of this kind demands under the
ever-varying conditions and circumstances presented in repairs of this
kind. It is well to explain somewhat at this point: Suppose we have five
watches taken in with broken cylinders. Out of this number probably two
could be pivoted to advantage and make the watches as good as ever. As
to the pivoting of a cylinder, we will deal with this later on. The
first thing to do is to make an examination of the cylinder, not only to
see if it is broken, but also to determine if pivoting is going to bring
it out all right. Let us imagine that some workman has, at some previous
time, put in a new cylinder, and instead of putting in one of the proper
size he has put one in too large or too small. Now, in either case he
would have to remove a portion of the escape-wheel tooth, that is,
shorten the tooth: because, if the cylinder was too large it would not
go in between the teeth, and consequently the teeth would have to be cut
or stoned away. If the cylinder was too small, again the teeth would
have to be cut away to allow them to enter the cylinder. All workmen
have traditions, rules some call them, that they go by in relation to
the right way to dress a cylinder tooth; some insisting that the toe or
point of the tooth is the only place which should be tampered with.
Other workmen insist that the heel of the tooth is the proper place.
Now, with all due consideration, we would say that in ninety-nine cases
out of a hundred the proper thing to do is to let the escape-wheel teeth
entirely alone. As we can understand, after a moment's thought, that it
is impossible to have the teeth of the escape wheel too long and have
the watch run at all; hence, the idea of stoning a cylinder escape-wheel
tooth should not be tolerated.


ESCAPE-WHEEL TEETH _vs._ CYLINDER.

It will not do, however, to accept, and take it for granted that the
escape-wheel teeth are all right, because in many instances they have
been stoned away and made too short; but if we accept this condition as
being the case, that is, that the escape-wheel teeth are too short, what
is the workman going to do about it? The owner of the watch will not pay
for a new escape wheel as well as a new cylinder. The situation can be
summed up about in this way, that we will have to make the best we can
out of a bad job, and pick out and fit a cylinder on a compromise idea.

In regard to picking out a new cylinder, it may not do to select one of
the same size as the old one, from the fact that the old one may not
have been of the proper size for the escape wheel, because, even in new,
cheap watches, the workmen who "run in" the escapement knew very well
the cylinder and escape wheel were not adapted for each other, but they
were the best he had. Chapter II, on the cylinder escapement, will
enable our readers to master the subject and hence be better able to
judge of allowances to be made in order to permit imperfect material to
be used.

In illustration, let us imagine that we have to put in a new cylinder,
and we have none of precisely the proper size, but we have them both a
mere trifle too large and too small, and the question is which to use.
Our advice is to use the smaller one if it does not require the
escape-wheel teeth to be "dressed," that is, made smaller. Why we make
this choice is based on the fact that the smaller cylinder shell gives
less friction, and the loss from "drop"--that is, side play between the
escape-wheel teeth and the cylinder--will be the same in both instances
except to change the lost motion from inside to outside drop.

In devising a system to be applied to selecting a new cylinder, we meet
the same troubles encountered throughout all watchmakers' repair work,
and chief among these are good and convenient measuring tools. But even
with perfect measuring tools we would have to exercise good judgment, as
just explained. In Chapter II we gave a rule for determining the outside
diameter of a cylinder from the diameter of the escape wheel; but such
rules and tables will, in nine instances out of ten, have to be modified
by attendant circumstances--as, for instance, the thickness of the shell
of the cylinder, which should be one-tenth of the outer diameter of the
shell, but the shell is usually thicker. A tolerably safe practical rule
and one also depending very much on the workman's good judgment is, when
the escape-wheel teeth have been shortened, to select a cylinder giving
ample clearance inside the shell to the tooth, but by no means large
enough to fill the space between the teeth. After studying carefully
the instructions just given we think the workman will have no difficulty
in selecting a cylinder of the right diameter.


MEASURING THE HEIGHTS.

The next thing is to get the proper heights. This is much more easily
arrived at: the main measurement being to have the teeth of the escape
wheel clear the upper face of the lower plug. In order to talk
intelligently we will make a drawing of a cylinder and agree on the
proper names for the several parts to be used in this chapter. Such
drawing is shown at Fig. 171. The names are: The hollow cylinder, made
up of the parts _A A' A'' A'''_, called the shell--_A_ is the great
shell, _A'_ the half shell, _A''_ the banking slot, and _A'''_ the small
shell. The brass part _D_ is called the collet and consists of three
parts--the hairspring seat _D_, the balance seat _D'_ and the shoulder
_D''_, against which the balance is riveted.

[Illustration: Fig. 171]

The first measurement for fitting a new cylinder is to determine the
height of the lower plug face, which corresponds to the line _x x_,
Fig. 171. The height of this face is such as to permit the escape wheel
to pass freely over it. In selecting a new cylinder it is well to choose
one which is as wide at the banking slot _A''_ as is consistent with
safety. The width of the banking slot is represented by the dotted lines
_x u_. The dotted line _v_ represents the length to which the lower
pivot _y_ is to be cut.

[Illustration: Fig. 172]

[Illustration: Fig. 173]

There are several little tools on the market used for making the
necessary measurements, but we will describe a very simple one which can
readily be made. To do so, take about a No. 5 sewing needle and, after
annealing, cut a screw thread on it, as shown at Fig, 172, where _E_
represents the needle and _t t_ the screw cut upon it. After the screw
is cut, the needle is again hardened and tempered to a spring temper and
a long, thin pivot turned upon it. The needle is now shaped as shown at
Fig. 173. The pivot at _s_ should be small enough to go easily through
the smallest hole jewel to be found in cylinder watches, and should be
about 1/16" long. The part at _r_ should be about 3/16" long and only
reduced in size enough to fully remove the screw threads shown at _t_.

[Illustration: Fig. 174]

[Illustration: Fig. 175]

[Illustration: Fig. 176]

[Illustration: Fig. 177]

We next provide a sleeve or guard for our gage. To do this we take a
piece of hard brass bushing wire about ½" long and, placing it in a
wire chuck, center and drill it nearly the entire length, leaving, say,
1/10" at one end to be carried through with a small drill. We show at
_F_, Fig. 174, a magnified longitudinal section of such a sleeve. The
piece _F_ is drilled from the end _l_ up to the line _q_ with a drill of
such a size that a female screw can be cut in it to fit the screw on the
needle, and _F_ is tapped out to fit such a screw from _l_ up to the
dotted line _p_. The sleeve _F_ is run on the screw _t_ and now appears
as shown at Fig. 175, with the addition of a handle shown at _G G'_. It
is evident that we can allow the pivot _s_ to protrude from the sleeve
_F_ any portion of its length, and regulate such protrusion by the screw
_t_. To employ this tool for getting the proper length to which to cut
the pivot _y_, Fig. 171, we remove the lower cap jewel to the cylinder
pivot and, holding, the movement in the left hand, pass the pivot _s_,
Fig. 175, up through the hole jewel, regulate the length by turning the
sleeve _F_ until the arm of the escape wheel _I_, Fig. 176, will just
turn free over it. Now the length of the pivot _s_, which protrudes
beyond the sleeve _F_, coincides with the length to which we must cut
the pivot _y_, Fig. 171. To hold a cylinder for reducing the length of
the pivot _y_, we hold said pivot in a pair of thin-edged cutting
pliers, as shown at Fig. 177, where _N N'_ represent the jaws of a pair
of cutting pliers and _y_ the pivot to be cut. The measurement is made
by putting the pivot _s_ between the jaws _N N'_ as they hold the pivot.
The cutting is done by simply filing back the pivot until of the right
length.


TURNING THE PIVOTS.

We have now the pivot _y_ of the proper length, and what remains to be
done is to turn it to the right size. We do not think it advisable to
try to use a split chuck, although we have seen workmen drive the shell
_A A'''_ out of the collet _D_ and then turn up the pivots _y z_ in said
wire chuck. To our judgment there is but one chuck for turning pivots,
and this is the cement chuck provided with all American lathes. Many
workmen object to a cement chuck, but we think no man should lay claim
to the name of watchmaker until he masters the mystery of the cement
chuck. It is not such a very difficult matter, and the skill once
acquired would not be parted with cheaply. One thing has served to put
the wax or cement chuck into disfavor, and that is the abominable stuff
sold by some material houses for lathe cement. The original cement, made
and patented by James Bottum for his cement chuck, was made up of a
rather complicated mixture; but all the substances really demanded in
such cement are ultramarine blue and a good quality of shellac. These
ingredients are compounded in the proportion of 8 parts of shellac and 1
part of ultramarine--all by weight.


HOW TO USE A CEMENT CHUCK.

The shellac is melted in an iron vessel, and the ultramarine added and
stirred to incorporate the parts. Care should be observed not to burn
the shellac. While warm, the melted mass is poured on to a cold slab of
iron or stone, and while plastic made into sticks about ½" in
diameter.

[Illustration: Fig. 178]

[Illustration: Fig. 179]

We show at Fig. 178 a side view of the outer end of a cement chuck with
a cylinder in position. We commence to turn the lower pivot of a
cylinder, allowing the pivot _z_ to rest at the apex of the hollow cone
_a_, as shown. There is something of a trick in turning such a hollow
cone and leaving no "tit" or protuberance in the center, but it is
important it should be done. A little practice will soon enable one to
master the job. A graver for this purpose should be cut to rather an
oblique point, as shown at _L_, Fig. 179. The slope of the sides to the
recess _a_, Fig. 178, should be to about forty-five degrees, making the
angle at _a_ about ninety degrees. The only way to insure perfect
accuracy of centering of a cylinder in a cement chuck is center by the
shell, which is done by cutting a piece of pegwood to a wedge shape and
letting it rest on the T-rest; then hold the edge of the pegwood to the
cylinder as the lathe revolves and the cement soft and plastic. A
cylinder so centered will be absolutely true. The outline curve at _c_,
Fig. 178, represents the surface of the cement.

The next operation is turning the pivot to the proper size to fit the
jewel. This is usually done by trial, that is, trying the pivot into the
hole in the jewel. A quicker way is to gage the hole jewel and then turn
the pivot to the right size, as measured by micrometer calipers. In some
cylinder watches the end stone stands at some distance from the outer
surface of the hole jewel; consequently, if the measurement for the
length of the pivot is taken by the tool shown at Fig. 175, the pivot
will apparently be too short. When the lower end stone is removed we
should take note if any allowance is to be made for such extra space.
The trouble which would ensue from not providing for such extra end
shake would be that the lower edge of the half shell, shown at _e_, Fig.
171, would strike the projection on which the "stalk" of the tooth is
planted. After the lower pivot is turned to fit the jewel the cylinder
is to be removed from the cement chuck and the upper part turned. The
measurements to be looked to now are, first, the entire length of the
cylinder, which is understood to be the entire distance between the
inner faces of the two end stones, and corresponds to the distance
between the lines _v d_, Fig. 171. This measurement can be got by
removing both end stones and taking the distance with a Boley gage or a
douzieme caliper.


A CONVENIENT TOOL FOR LENGTH MEASUREMENT.

[Illustration: Fig. 180]

A pair of common pinion calipers slightly modified makes as good a pair
of calipers for length measurement as one can desire. This instrument is
made by inserting a small screw in one of the blades--the head on the
inner side, as shown at _f_, Fig. 180. The idea of the tool is, the
screw head _f_ rests in the sink of the cap jewel or end stone, while
the other blade rests on the cock over the balance. After the adjusting
screw to the caliper is set, the spring of the blades allows of their
removal. The top pivot _z_ of the cylinder is next cut to the proper
length, as indicated by the space between the screwhead _f_ and the
other blade of the pinion caliper. The upper pinion _z_ is held in the
jaws of the cutting pliers, as shown in Fig. 177, the same as the lower
one was held, until the proper length between the lines _d v_, Fig. 171,
is secured, after which the cylinder is put back into the cement chuck,
as shown at Fig. 178, except this time the top portion of the cylinder
is allowed to protrude so that we can turn the top pivot and the balance
collet _D_, Fig. 171.

The sizes we have now to look to is to fit the pivot _z_ to the top
hole jewel in the cock, also the hairspring seat _D_ and balance seat
_D'_. These are turned to diameters, and are the most readily secured by
the use of the micrometer calipers to be had of any large watchmakers'
tool and supply house. In addition to the diameters named, we must get
the proper height for the balance, which is represented by the dotted
line _b_. The measurement for this can usually be obtained from the old
cylinder by simply comparing it with the new one as it rests in the
cement chuck. The true tool for such measurements is a height gage. We
have made no mention of finishing and polishing the pivots, as these
points are generally well understood by the trade.


REMOVING THE LATHE CEMENT.

One point perhaps we might well say a few words on, and this is in
regard to removing the lathe cement. Such cement is usually removed by
boiling in a copper dish with alcohol. But there are several objections
to the practice. In the first place, it wastes a good deal of alcohol,
and also leaves the work stained. We can accomplish this operation
quicker, and save alcohol, by putting the cylinder with the wax on it in
a very small homeopathic bottle and corking it tight. The bottle is then
boiled in water, and in a few seconds the shellac is dissolved away. The
balance to most cylinder watches is of red brass, and in some instances
of low karat gold; in either case the balance should be repolished. To
do this dip in a strong solution of cyanide of potassium dissolved in
water; one-fourth ounce of cyanide in half pint of water is about the
proper strength. Dip and rinse, then polish with a chamois buff and
rouge.

[Illustration: Fig. 181]

In staking on the balance, care should be observed to set the banking
pin in the rim so it will come right; this is usually secured by setting
said pin so it stands opposite to the opening in the half shell. The
seat of the balance on the collet _D_ should be undercut so that there
is only an edge to rivet down on the balance. This will be better
understood by inspecting Fig. 181, where we show a vertical section of
the collet _D_ and cylinder _A_. At _g g_ is shown the undercut edge of
the balance seat, which is folded over as the balance is rivetted fast.

About all that remains now to be done is to true up the balance and
bring it to poise. The practice frequently adopted to poise a plain
balance is to file it with a half-round file on the inside, in order not
to show any detraction when looking at the outer edge of the rim. A
better and quicker plan is to place the balance in a split chuck, and
with a diamond or round-pointed tool scoop out a little piece of metal
as the balance revolves. In doing this, the spindle of the lathe is
turned by the hand grasping the pulley between the finger and thumb. The
so-called diamond and round-pointed tools are shown at _o o'_, Fig. 182.
The idea of this plan of reducing the weight of a balance is, one of the
tools _o_ is rested on the T-rest and pressed forward until a chip is
started and allowed to enter until sufficient metal is engaged, then, by
swinging down on the handle of the tool, the chip is taken out.

[Illustration: Fig. 182]

[Illustration: Fig. 183]

In placing a balance in a step chuck, the banking pin is caused to enter
one of the three slots in the chuck, so as not to be bent down on to the
rim of the balance. It is seldom the depth between the cylinder and
escape wheel will need be changed after putting in a new cylinder; if
such is the case, however, move the chariot--we mean the cock attached
to the lower plate. Do not attempt to change the depth by manipulating
the balance cock. Fig. 183 shows, at _h h_, the form of chip taken out
by the tool _o o'_, Fig. 182.




INDEX


  A

  Acid frosting, 46

  "Action" drawings, 90

  Action of a chronometer escapement, 142

  Acting surface of entrance lip, 127

  Actions of cylinder escapement, 112

  Adhesion of parallel surfaces, 94

  Adjustable pallets, 98

  Adjusting screw for drawing instruments, 21

  Analysis of principles involved in detent, 137

  Analysis of the action of a lever escapement, 86

  Angle-measuring device, 68

  Angular extent of shell of cylinder, 122

  Angular motion, drawing an escapement to show, 91
    How measured, 69
    Of escape wheel, 37

  Antagonistic influences, 133

  Arc of degrees, 9

  Atmospheric disturbances, 74

  Attainment of isochronism, 159


  B

  Balance, how it controls timekeeping, 73
    Weight and inertia of, 133

  Balance spring, inventor of, 132

  Banking slot of cylinder, 112

  Bankings, effect of opening too wide, 63

  Bar compasses, 21

  Barometric pressure, 74

  Basis for close measurements, 96


  C

  Cement chuck, how to use, 173

  Chronometer detent, importance of light construction, 136

  Chronometer escapement, 131, 155
    Four principal parts of, 134

  Circular pallets, 27

  Club-tooth escapement, 30, 34

  Club-tooth lever escapement with circular pallets and
    tangential lockings, 83

  Crown-wheel escapement, 155

  Cylinder, drawing a, 120
    Outer diameter of, 116
    Putting in a new, 169

  Cylinder escapement, 155
    Date of invention, etc., 111
    Forms and proportions of several parts of, 111
    Names of various parts, 112

  Cylinder lips, proper shape of, 124


  D

  Dead-beat escapement, 131, 135
    Only one true, 112

  Depth, between cylinder and escape wheel, 129
    Effect of changing, 176

  Designing a double roller, 77

  Detached escapement, 155

  Detent, functions of the, 137

  Detent escapement, 131, 155
    Faults in, 132

  Detent spring dimensions, 138

  Detent springs, width of, 147

  Discharging jewel, setting the, 142

  Discharging roller, 136

  Dividers, 9
    Making, 10

  Double pendulum, 160

  Double-roller escapement, 75

  Draw defined, 85

  Drawing-board, 11

  Drawing instruments, 9

  Drawings, advantage of large, 29

  Drop and draw, 150

  Duplex escapement, 131, 155


  E

  Elasticity of spring, 133

  Engaging friction, 81

  English recoil anchor, 167

  Entrance lip of cylinder escapement, 125

  Escapement angles, measuring, 101

  Escapement error, study of, 64

  Escapement matching tool, 106

  Escapement model, 40
    Balance, 42
    Balance staff, 44
    Bridges, 41, 42
    Escape wheel, 43
    Extra balance cock, 45
    "Frosting", 46
    Hairspring, 42
    Jewel for, 43
    Lower plate, 41
    Main plate, 41
    Movement for, 41
    Pallet staff, 42
    Pillars, 43
    Regulator, 46
    Uses of, 44
    Wood base for, 41

  Escapements compared, 103

  Escapement of Dutertre, 160

  Escape-wheel action, 30

  Escape-wheel, delineating an, 11

  Escape-wheel teeth vs. cylinder, 169

  Escape-wheel tooth in action, delineating an, 126

  Exit pallet, 26

  Experiments of Galileo, 158

  Experiments with a chronometer, 142

  Extent of angular impulse, 118


  F

  "Fall" defined, 106

  Faults in the detent escapement, 132

  Fixed rules, of little value to student, 137

  Flexure of gold spring, 146

  Foot, fitting up the, 151

  Fork, testing the, 71

  Fork action, 30
    Theory of, 59

  Fork and roller action, 54

  Formulas for delineating cylinder escapement, 115

  Frictions, 24

  Frictional escapement, 131, 132

  Frictional surfaces, 63

  Fusee, 131


  G

  Gable escapement, 167

  Gage, a new, 172

  Graham anchor escapement, 155

  Gold spring, 146

  Guard point, 79
    Material for, 79

  Gummy secretion on impulse and discharging stones, 147


  H

  Heights in cylinders, how obtained, 171

  Hole jewels, distance apart, 140


  I

  Imaginary faults in cylinders, 129

  Impulse angle, 118

  Impulse arc, extent of, 134

  Impulse jewel set oblique, 147

  Impulse planes, locating outer angle of, 39

  Impulse roller, 136

  Incline of teeth, 122

  Inertia of balance, 133

  Inventions of
    Berthoud, 163
    Béthune, 165
    Clement, 166
    Dr. Hook, 162
    Harrison, 161
    Hautefeuille, 161
    Huygens, 158
    Leroy, 163
    Thiout, 165


  J

  Jewel pin, determining size, 58
    Cementing in, 67
    Settings, 66

  Jewel-pin setters, 67


  L

  Lathe cement, 173
    Removing, 175

  Lever, proper length of, 61

  Lever fork, horn of, 61
    prongs of, 60

  Lift, real and apparent, 112

  Lifting angle, 114

  Lock, amount of, 28
    Defined, 85

  Lock and drop testing, 69

  Locking jewel, moving the, 149

  Locking stone, good form of, 144

  Lower plate, circular opening in, 56


  M

  Marine chronometer, number of beats to hour, 148

  Mathematics, 95

  Measuring tools, 171

  Metal drawings, advantages of, 140

  Motion, how obtained, 16

  Movement holder, 110


  N

  Neutral lockings, 84


  O

  Original designing, 148


  P

  Pallet action, locating the, 90

  Pallet-and-fork action, 12, 13, 17, 18

  Pallet stones, how to set, 104

  Pallets, adjusting to match the fork, 65

  Paper for drawing, 11

  Parts, relations of the, 32

  Passing hollow, 62

  Perfected lever escapement, 87

  Pivots, turning, 172

  Point of percussion, 139

  Points for drawing instruments, 20

  Polishing materials, 52

  Power leaks, 16

  Power lost in lever escapement, 87

  Practical problems in the lever escapement, 98


  R

  Radial extent of outside of cylinder, 125

  Ratchet-tooth escape wheel, 12

  Recoil anchor escapement, 155

  Recoil escapement, 154

  Reduced gable escapement, 167

  Retrograde motion, 36

  Roller action, why 30 degrees, 55
    Of double roller, 78

  Roller diameter, determining the, 55

  Ruling pen, 9


  S

  Safety action, 56

  Scale of inches, 9

  Screws, making extra large, 45

  Screwheads, fancy, 45

  Selecting new cylinder, 170

  Shaping, advantages gained in, 116

  Sheet steel, cutting, 48

  Short fork, 100

  Sound as indicator of correct action, 144

  Spring, elasticity of, 133

  Staking on a balance, 175

  Steel, polishing, 49
    Tempering, 49

  Study drawings, 124

  Systems of measurements, 114


  T

  Tangential lockings, 80, 148

  Test gage for angular movement, 65

  Theoretical action of double roller, 76

  Timekeeping, controlled by balance, 73

  Tool for length measurement, 174

  Tools, measuring, 171

  Triangle, 18

  T-square, 9


  U

  Unlocking action, 56

  Unlocking roller, 136


  V

  Verge escapement, 131, 155


  W

  Weight and inertia of balance, 133

  Working model of cylinder escapement, 123



     *     *     *     *     *     *



THE WATCH ADJUSTER'S MANUAL

[Illustration]

A Complete and Practical Guide for Watchmakers in Adjusting Watches and
Chronometers for Isochronism, Position, Heat and Cold.


BY CHARLES EDGAR FRITTS (EXCELSIOR),

Author of "Practical Hints on Watch Repairing," "Practical Treatise on
Balance Spring," "Electricity and Magnetism for Watchmakers," etc., etc.

This well-known work is now recognized as the standard authority on the
adjustments and kindred subjects, both here and in England. It contains
an exhaustive consideration of the various theories proposed, the
mechanical principles on which the adjustments are based, and the
different methods followed in actual practice, giving all that is
publicly known in the trade, with a large amount of entirely new
practical matter not to be found elsewhere, obtained from the best
manufacturers and workmen, as well as from the author's own studies and
experiences.

Sent postpaid to any part of the world on receipt of $2.50 (10s. 5d.)

  THE KEYSTONE (SOLE AGENT),
  19TH AND BROWN STREETS, PHILADELPHIA, U.S.A.

         *       *       *       *       *

THE ART OF ENGRAVING

[Illustration]

A Complete Treatise on the Engraver's Art, with Special Reference to
Letter and Monogram Engraving. Specially Compiled as a Standard
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This work is the only thoroughly reliable and exhaustive treatise
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The most notable feature of the new treatise is the instructive
character of the illustrations. There are over 200 original
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Bound in Silk Cloth--208 Pages and 216 Illustrations.

Sent postpaid to any part of the world on receipt of price, $1.50 (6s.
3d.)

  PUBLISHED BY THE KEYSTONE,
  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
  19TH & BROWN STS., PHILADELPHIA, U.S.A.

         *       *       *       *       *

THE KEYSTONE PORTFOLIO OF MONOGRAMS

[Illustration: C.B.R.]

[Illustration: A.O.U.W]

[Illustration: I.R.C.]

[Illustration: G.H.I.]

This portfolio contains 121 combination designs. These designs were
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The portfolio is a bench requirement that no jeweler can afford to be
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  Price,
  50 Cents (2s.)

  PUBLISHED BY THE KEYSTONE,
  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
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         *       *       *       *       *

THE OPTICIAN'S MANUAL

VOL. I.

BY C.H. BROWN, M.D.

Graduate University of Pennsylvania; Professor of Optics and Refraction;
formerly Physician in Philadelphia Hospital; Member of Philadelphia
County, Pennsylvania State and American Medical Societies.

[Illustration]

The Optician's Manual, Vol. I., has proved to be the most popular work
on practical refraction ever published. The knowledge it contains has
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optical knowledge, as the titles of its ten chapters show:

  Chapter    I.--Introductory Remarks.
  Chapter   II.--The Eye Anatomically.
  Chapter  III.--The Eye Optically; or, The Physiology of Vision.
  Chapter   IV.--Optics.
  Chapter    V.--Lenses.
  Chapter   VI.--Numbering of Lenses.
  Chapter  VII.--The Use and Value of Glasses.
  Chapter VIII.--Outfit Required.
  Chapter   IX.--Method of Examination.
  Chapter    X.--Presbyopia.

The Optician's Manual, Vol. I., is complete in itself, and has been the
entire optical education of many successful opticians. For student and
teacher it is the best treatise of its kind, being simple in style,
accurate in statement and comprehensive in its treatment of refractive
procedure and problems. It merits the place of honor beside Vol. II. in
every optical library.

Bound in Cloth--422 pages--colored plates and Illustrations.

Sent postpaid on receipt of $2.00 (8s. 4d.)

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         *       *       *       *       *

THE OPTICIAN'S MANUAL

VOL. II.

BY C.H. BROWN, M.D.

Graduate University of Pennsylvania; Professor of Optics and Refraction;
formerly Physician in Philadelphia Hospital; Member of Philadelphia
County, Pennsylvania State and American Medical Societies.

[Illustration]

The Optician's Manual, Vol. II., is a direct continuation of The
Optician's Manual, Vol. I., being a much more advanced and comprehensive
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  Myopia.
  Hypermetropia.
  Astigmatism.
  Muscular Anomalies.

It contains the most authoritative and complete researches up to date on
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This book fills the last great want in higher refractive optics, and the
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Bound in Cloth--408 pages--with illustrations.

Sent postpaid on receipt of $2.00 (8s. 4d.)

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         *       *       *       *       *

SKIASCOPY AND THE USE OF THE RETINOSCOPE

[Illustration]

A Treatise on the Shadow Test in its Practical Application to the Work
of Refraction, with an Explanation in Detail of the Optical Principles
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Bound in cloth; contains 231 pages and 73 illustrations and colored
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Sent postpaid to any part of the world on receipt of $1.00 (4s. 2d.)

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         *       *       *       *       *

PHYSIOLOGIC OPTICS

Ocular Dioptrics--Functions of the Retina--Ocular Movements and
Binocular Vision

BY DR. M. TSCHERNING

Adjunct-Director of the Laboratory of Ophthalmology at the Sorbonne,
Paris

AUTHORIZED TRANSLATION

BY CARL WEILAND, M.D.

Former Chief of Clinic in the Eye Department of the Jefferson College
Hospital, Philadelphia, Pa.

This is the crowning work on physiologic optics, and will mark a new era
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The chapters on Ophthalmometry, Ophthalmoscopy, Accommodation,
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entire book contains so much that is new, practical and necessary that
no refractionist can afford to be without it.

Bound in Cloth. 380 Pages, 212 Illustrations.

Price, $3.50 (14s. 7d.)

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         *       *       *       *       *

OPHTHALMIC LENSES

Dioptric Formulę for Combined Cylindrical Lenses, The Prism-Dioptry and
Other Original Papers

BY CHARLES F. PRENTICE, M.E.

A new and revised edition of all the original papers of this noted
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This book of over 200 pages contains the following papers:

  Ophthalmic Lenses.
  Dioptric Formulę for Combined Cylindrical Lenses.
  The Prism-Dioptry.
  A Metric System of Numbering and Measuring Prisms.
    The Relation of the Prism-Dioptry to the Meter Angle.
    The Relation of the Prism-Dioptry to the Lens-Dioptry.
  The Perfected Prismometer.
  The Prismometric Scale.
  On the Practical Execution of Ophthalmic Prescriptions involving Prisms.
  A Problem in Cemented Bi-Focal Lenses, Solved by the Prism-Dioptry.
  Why Strong Contra-Generic Lenses of Equal Power Fail to Neutralize
    Each Other.
  The Advantages of the Sphero-Toric Lens.
  The Iris, as Diaphragm and Photostat.
  The Typoscope.
  The Correction of Depleted Dynamic Refraction (Presbyopia).

_Press Notices on the Original Edition:_


OPHTHALMIC LENSES.

"The work stands alone, in its present form, a compendium of the various
laws of physics relative to this subject that are so difficult of access
in scattered treatises."--_New England Medical Gazette._

"It is the most complete and best illustrated book on this special
subject ever published."--_Horological Review_, New York.

"Of all the simple treatises on the properties of lenses that we have
seen, this is incomparably the best.... The teacher of the average
medical student will hail this little work as a great boon."--_Archives
of Ophthalmology, edited by H. Knapp, M.D._

DIOPTRIC FORMULĘ FOR COMBINED CYLINDRICAL LENSES.

"This little brochure solves the problem of combined cylinders in all
its aspects, and in a manner simple enough for the comprehension of the
average student of ophthalmology. The author is to be congratulated upon
the success that has crowned his labors, for nowhere is there to be
found so simple and yet so complete an explanation as is contained in
these pages."--_Archives of Ophthalmology, edited by H. Knapp, M.D._

"This exhaustive work of Mr. Prentice is a solution of one of the most
difficult problems in ophthalmological optics. Thanks are due to Mr.
Prentice for the excellent manner in which he has elucidated a subject
which has not hitherto been satisfactorily explained."--_The Ophthalmic
Review_, London.

The book contains 110 Original Diagrams. Bound in cloth.

Price, $1.50 (6s. 3d.)

  PUBLISHED BY THE KEYSTONE,
  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
  19TH & BROWN STS., PHILADELPHIA, U.S.A.

         *       *       *       *       *

OPTOMETRIC RECORD BOOK


A record book, wherein to record optometric examinations, is an
indispensable adjunct of an optician's outfit.

The Keystone Optometric Record Book was specially prepared for this
purpose. It excels all others in being not only a record book, but an
invaluable guide in examination.

The book contains two hundred record forms with printed headings,
suggesting, in the proper order, the course of examination that should
be pursued to obtain most accurate results.

Each book has an index, which enables the optician to refer instantly to
the case of any particular patient.

The Keystone Record Book diminishes the time and labor required for
examinations, obviates possible oversights from carelessness and assures
a systematic and thorough examination of the eye, as well as furnishes a
permanent record of all examinations.

Sent postpaid on receipt of $1.00 (4s. 2d.)

  PUBLISHED BY THE KEYSTONE,
  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
  19TH & BROWN STS., PHILADELPHIA, U.S.A.

         *       *       *       *       *

THE KEYSTONE BOOK OF MONOGRAMS

This book contains 2400 designs and over 6000 different combinations of
two and three letters.

Is an essential to every jeweler's outfit. It is not only necessary for
the jeweler's own use and guidance, but also to enable customers to
indicate exactly what they want, thus saving time and possible
dissatisfaction.

The Monograms are purposely left in outline, in order to show clearly
how the letters are intertwined or woven together. This permits such
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shading, ornamentation and artistic finish as the jeweler may wish to
add.

This comprehensive compilation of Monograms is especially available as a
reference book in busy seasons. Its use saves time, thought and labor,
and ensures quick and satisfactory work.

Monograms are the fad of the time, and there's money for the jeweler in
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All the various styles of letters are illustrated.

Price, $1.00 (4s. 2d.)

  PUBLISHED BY THE KEYSTONE,
  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
  19TH & BROWN STS., PHILADELPHIA, U.S.A.

         *       *       *       *       *

THE KEYSTONE RECORD BOOK OF WATCH REPAIRS

This book is 9 × 11 inches, has 120 pages, and space for recording
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in cloth with leather back and corners.

Price, $1.00 (4s. 2d.), prepaid.

No other record book on the market is so complete, and all cost more.

  PUBLISHED BY THE KEYSTONE,
  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
  19TH & BROWN STS., PHILADELPHIA, U.S.A.

         *       *       *       *       *

  THE KEYSTONE
  BOOK OF GUARANTEES OF WATCH REPAIRS

  This book contains two hundred printed guarantees, and is
  handsomely bound. Each guarantee is 3¼ × 7½ inches, and
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  $1.00 (4s. 2d.), prepaid,

  which is one-third less than the price charged by others for a
  similar book.

  PUBLISHED BY THE KEYSTONE,
  THE ORGAN OF THE JEWELRY AND OPTICAL TRADES,
  19TH & BROWN STS., PHILADELPHIA, U.S.A.



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