9 14 
HOROLOGY. 
are reprefented in fuch a manner, that we may eafily per¬ 
ceive at firft fight how the motion is communicated from 
the barrel to the balance. The fame letters in fig. 78, de-. 
note the fame parts. 
In fig. 84, are reprefented the wheels under the dial- 
plate, by which the hands are moved. The pinion a is 
adjulted to the force of the prolonged pivot of the wheel 
D in fig. 80, and is called a cannon pinion. This wheel re¬ 
volves in an hour. The end of the axis of the pinion a, 
upon which the minute-hand is fixed, is fquare the pi¬ 
nion c, fig. 84., is fixed upon the wheel b, which is carried 
by the pinion a. Fig. 85, is a wheel fixed upon a barrel, 
into the cavity of which the part above the pinion a en¬ 
ters, and upon which-it turns freely. This wheel works 
in the pinion c, revolves in 12 hours, and carries along 
with it the hour-hand. 
. Such, in brief, is the meehanifin of a watch 5 and we 
need not farther enlarge on the action of the leveral parts, 
that, talk having been performed under the general head 
Machines with Toothed Wheels,- and the fubdivifions, 
Balance, Wheel-work, and Scapement, in this article. 
From what has been laid under the laft-mentioned fubdi- 
vifion, it will be readily perceived, that the common, re¬ 
coiling fcapement of the old clocks ftill holds its place in 
the ordinary pocket-watches, and anfwers all the common 
piirpofes of a watch very well. A well-finilhed watch, 
with a recoiling fcapement, will keep time within a mi¬ 
nute in the day. This is enough for the ordinary affairs 
of iife. But fuch watches are lubjeft to great variation in 
their rate of going by any change in the power of the 
wheels. This is evident} for, if the watch be held back, 
or preffed forward, by the key applied to the fufee-fquare, 
we hear the beating greatly retarded or accelerated. The 
maintaining power, in the beft of fuch watches, is never 
lefs than one-fifth of the regulating power of the fpring. 
For, if we take off the balance-fpring, and allow the ba¬ 
lance to vibrate by the impulfe of the wheels alone, we 
iball find the minute-hand to go forward from 25 to 30 
minutes per hour. Suppofe it 30. Then, lince the wheels 
aft through equal fpaces with or without a fpring, the 
forces are as the fquares of the acquired velocities. The 
velocity in this cafe is double ; therefore the accelerating 
force is quadruple, and the force of the fpring is three 
times that of the wheels. If the hand goes forward 25 
minutes, the fotce of the wheels is about one-fif th of that 
of the fpringkglfhis great prportion is neceffary, as already 
ebferved, that the watch may go as foon as pnltopped. 
We have but little to fay on this fcapement; its prin¬ 
ciple and manner of aftion, and its good and bad quali¬ 
ties, being the fame with thofe of the fimilar fcapement 
for clocks, upon which we have fufficiently enlarged. It 
is evident that, the maintaining power being applied in 
the moll direft manner, and during the whole of the vi¬ 
bration, it will have the greatefl: pofiible influence to 
move the balance. A given main-fpring and train will 
l;eep in motion a heavier balance by means of this fcape- 
raent than by any other. But, on the other hand, and 
for the fame reafon, the balance has lefs dominion over 
the wheel-work, and its vibrations are more affefted by 
any irregularities of the wheel-work. Moreover, the chief 
aftion of the wheel being at the very extremities of the 
vibrations, and being, very abrupt, the variations in its 
force are moft hurtful-to the ifochronifm of the vibrations. 
Although this fcapement is extremely Ample, it is fuf- 
ceptible of more degrees of goodnefs or imperfeftion than, 
almoft any other, by the variation of the few particulars 
of its conftruftion. We-fhajl therefore briefly defcribe 
that conftruftion which long experience has fanftioned as 
approaching near to the bell performance that can be ob¬ 
tained from the common fcapement. Fig. 86 reprefents 
it in what are thought its beft proportions, as it appears 
when looking ftraight down on the end of the balance- 
arbor. C is the centre of the balance and verge. C A 
and C B are the two pallets; C A being the upper pallet, 
or the one next to the balance, and CB being the lower 
one. F and D are two teeth of the balance-wheel, mov¬ 
ing from left to right; and E, G, are two teeth on the 
lower part of the circumference, moving from right to left. 
The tooth T is reprefented as juft efcaped from the point 
of C A, and the lower tooth E as juft come in contaft 
with the lower pallet. The fcapement fhould not, how¬ 
ever, be quite fo dole, becaufe an inequality on the teeth 
might prevent D from efcaping at all. For, if E touch 
the pallet CB before D has quitted CA, all will (land 
ftill. This fault will be correfted by withdrawing the 
wheel a little from the verge, or by fliortening the pallets. 
The proportions are as follow. The diftance between 
the front of the teeth (that is, of G, F, E, D) and the axis 
C of the balance, is one-fifth of F A, the diftance between 
the points of the teeth. The length, CA, CB, of the 
pallets, is three-fifths of the fame diftance. The pallets 
make an angle AC B of 95 degrees, and the front DPI or 
FK of the teeth make an angle of 25 0 with the axis of 
the crown-wheel. The hoping fide of the tooth mull be 
of an epicycloidal form, 1'uited to the relative motion of 
the tooth and pallet. From thefe proportions it appears 
that the pallet A can throw out, by the aftion of the tooth 
D, till it reaches a, 120 degrees from CL, the line of the 
crown-wheel axis. For it can throw out till the pallet B 
ftrikes againlt the front of E, which is inclined 25° to 
C'L; to this add BCA=95°, and we have LC a — 120. 
In like manner B will throw out as far on the other fide, or 
to b. From 240 0 , the fum of thefe angles, take the angle 
of the pallets 95 0 , and there remains 145 0 for the greatefl: 
vibration which the balance can make without linking 
tlie front of the teeth. This extent of vibration fuppofes 
the teeth to terminate in points, and the afting furfaces 
of the pallets to be planes direfted to the very axis of the 
verge. But the points of the teeth moft be rounded off a 
little for ftrength, and to diminilh friftion on the face of 
the pallets. This diminilhes the angle of fcapement very 
considerably, by Ihortening the teeth. Moreover,'we mult 
by no means allow the point of the pallet to bank or 
ftxike on the forelide of a tooth. This would greatly de¬ 
range the vibration by the violence and abruptnel's of the' 
check which the wheel would give to the pallet. This 
circumftance makes it improper to continue the vibrations 
much beyond the angle of fcapement. One-third of a 
circle, or 12 0 , is therefore reckoned a very proper vibra¬ 
tion for a fcapement made in thefe proportions. The 
impuife of the-wheels, or the angle of fcapement, may be 
increafed by making the face of the pallets a little con¬ 
cave, (preferring the fame angle at the centre.) The vi¬ 
bration may alfo be widened by pulhing the wheel nearer 
to the verge. This would alfo dirniniih the recoil. In¬ 
deed this may be entirely removed by bringing the.front 
of the wheel up to C, and making the face of the pallet 
not a radius, but parallel to a radius,-and behind it, i. e. 
by placing the pallet CA 1’q that its afting face may be 
where its back is juft now. In this cafe, the tooth D 
would drop on it at the centre, and lie there at reft, 
while the balance completes its vibration. But this would 
make the banking (as the ftroke is called) on the teeth al¬ 
moft unavoidable. In fhort, after varying every circum¬ 
ftance in every pofiible manner, the beft makers have fet r 
tied on a fcapement very nearly fuch as we have defcribed. 
Precife rules can Icarceiy be given ; becaufe the law, by 
which the force acting on the pallets varies in its intercity, 
deviates fo widely from the aftion of the balance-fpring, 
efpecially near the limit? of the excurfions. 
Of the other icapements in occalional ale we have fuf¬ 
ficiently fpoken under that head ; but we may oblerve in 
general, that the execution of a proper fcapement for 
watches is a far more delicate and difficult problem than 
for a clock, on account of the fmall fize, which requires 
much more accurate workmanlbip, becaufe-the error of 
the hundreth part of an inch has as great a proportion to 
the dimenfions of the regulator as an inch in a common, 
houfe-clock. It is much more difficult on another ac¬ 
count. We have no means of accumulating fuch a do¬ 
minion 
