properly so called, is that part of the movement which strikes the hours, &c., on a bell; in contradistinction to that part of the movement of a clock or watch which is designed to measure and exhibit the time on a dial-plate, and which is termed Watch-work.

I. Of the Clock part. The wheels composing this part are: The great or first wheel H, which is moved by the weight or spring at the barrel G; in fifteen or thirty-hour clocks, this has usually pins, and is called the pin-wheel; in eight-day pieces, the second wheel I is commonly the pin-wheel, or striking wheel, which is moved by the former. Next the striking wheel is the detent-wheel, or hoop-wheel K, having a hoop almost round it, wherein is a vacancy at which the clock locks. The next is the third or fourth wheel, according to its distance from the first, called the warning-wheel L. The last is the flying pinion Q, with a fly or fan, to gather air, and to bridle the rapidity of the clock's motion. To these must be added the pinion of report, which drives round the locking-wheel, called also the count wheel; ordinarily with eleven notches in it, unequally distant, to make the clock strike the hours.

Besides the wheels, to the clock part belongs the ratchet or ratch; a kind of wheel with twelve large fangs, running concentrical to the dial-wheel, and serving to lift up the detents every hour, and make the clock strike: the detents or stops, which being lifted up and let fall, lock and unlock the clock in striking the hammer, as S, which strikes the bell R; the hammer-tails, as T, by which the striking pins draw back the hammers; latches, whereby the work is lifted up and unlocked; and lifting-pieces, as P, which lift up and unlock the detents.

The method of calculating the numbers of a piece of clock-work having something in it very entertaining, and at the same time very easy and useful, we shall give our readers the rules relating thereto: 1. Regard here needs only be had to the counting-wheel, striking-wheel, and detent-wheel, which move round in this proportion: the count-wheel commonly goes round once in 12 or 24 hours; the detent-wheel moves round every stroke the clock strikes, or sometimes but once in two strokes: wherefore it follows, that, 2. As many pins as are in the pin-wheel, so many turns hath the detent-wheel in one turn of the pin-wheel; or, which is the same, the pins of the pin-wheel are the quotients of that wheel divided by the pinion of the detent-wheel. But if the detent-wheel moves but once round in two strokes of the clock, then the said quotient is but half the number of pins. 3. As many turns of the pin-wheel as are required to perform the strokes of 12 hours (which are 78), so many turns must the pinion of report have to turn round the count-wheel once; or thus the quotient of 78, divided by the number of striking-pins, shall be the quotient for the pinion of report and the count wheel; and this is in case the pinion of report be fixed to the arbor of the pin-wheel, which is commonly done.

An example will make all plain: The locking-wheel being 48, the pinion of report 8, the pin-wheel 78, the striking pins are 13, and so of the rest. Note also, that \( \frac{78}{8} = 9.75 \) (6 divided by 13 gives 6, the quotient of the pinion of report. As for the warning-wheel and fly-wheel, it matters little what numbers they have; their use being only to bridle the rapidity of the motion of the other wheels.

The following rules will be of great service in this calculation.

1. To find how many strokes a clock strikes in one turn of the fusee or barrel: As the turns of the great wheel or fusee are to the days of the clock's continuance; so is the number of strokes in 24 hours, viz. 156, to the strokes of one turn of the fusee.

2. To find how many days a clock will go: As the strokes in 24 hours are to those in one turn of the fusee; so are the turns of the fusee to the days of the clock's going.

3. To find the number of turns of the fusee or barrel: As the strokes in one turn of the fusee are to those of 24 hours; so is the clock's continuance to the turns of the fusee or great wheel.

4. To find the number of leaves in the pinion of report on the axis of the great wheel: As the number of strokes in the clock's continuance is to the turns of the fusee; so are the strokes in 12 hours, viz. 78, to the quotient of the pinion of report fixed on the arbor of the great wheel.

5. To find the strokes in the clock's continuance: As 12 is to 78; so are the hours of the clock's continuance to the number of strokes in that time.

By means of the following table, clocks and watches may be so regulated as to measure true equal time.

The stars make 366 revolutions from any point of the compass to the same point again in 365 days and one minute; and therefore they gain a 365th of a revolution every 24 hours of mean solar time, near enough for regulating any clock or watch.

This acceleration is at the rate of 3 min. 55 sec. 53 thirds, 59 fourths in 24 hours; or in the nearest round numbers, 3 minutes, 56 seconds; by which quantity of time every star comes round sooner than it did on the day before.

Therefore if you mark the precise moment shown by a clock or watch when any star vanishes behind a chimney, or any other object, as seen through a small hole in a thin plate of metal, fixed in a window-shutter; and do this for several nights successively (as suppose twenty); if, at the end of that time, the star vanishes as much sooner than it did the first night, by the clock, as answers to the time denoted in the table for so many days, the clock goes true; otherwise not.

If the difference between the clock and star be less than the table shows, the clock goes too fast; if greater, it goes too slow; and must be regulated accordingly, by letting down or raising up the ball of the pendulum, by little and little, by turning the screw-nut under the ball, till you find it keeps true equal time.

Thus supposing the star should disappear behind a chimney, any night when it is XII. by the clock; and that, on the 20th night afterward, the same star should disappear when the time is 41 minutes 22 seconds past X., by the clock; which being subtracted from 12 hours o min. o sec. leaves remaining 1 hour 18 minutes 40 seconds for the time the star is then faster than the clock: look in the table, and against 20, in the left hand column, you will find the acceleration of the star to be 1 hour 18 min. 40 sec., agreeing exactly with what the difference ought to be between the clock and star; which shows that the clock measures true equal time, and agrees with the mean solar time, as it ought to do.

II. Of the Watch part of a clock or watch. This is that part of the movement which is designed to measure and exhibit the time on a dial-plate; in contradiction to that part which contributes to the striking of the hour, &c.

The several members of the watch part are, 1. The balance, consisting of the rim, which is its circular part; and the verge, which is its spindle; to which belong two pallets or leaves, that play in the teeth of the crown-wheel. 2. The potence, or pottance, which is the strong fluid in pocket watches, whereon the lower pivot of the verge plays, and in the middle of which one pivot of the balance wheel plays; the bottom of the pottance is called the foot, the middle part the nose, and the upper part the shoulder. 3. The cock, which is the piece covering the balance. 4. The regulator, or pendulum spring, which is the small spring, in the new pocket-watches, underneath the balance. 5. The pendulum (fig. 13.); whose parts are, the verge x, pallets s, s, cocks y, y, the rod, the fork, z, the flat 2, the bob or great ball 3, and the corrector or regulator, 4, being a contrivance of Dr. Derham for bringing the pendulum to its nice vibrations. 6. The wheels, which are the crown-wheel F in pocket-pieces, and swing-wheel in pendulums; serving to drive the balance or pendulum. 7. The contrate-wheel E, which is that next the crown-wheel, &c. and whose teeth and hoop lie contrary to those of other wheels; whence the name. 8. The great, or first wheel C; which is that the fusee B, &c. immediately drives, by means of the chain or string of the spring-box or barrel A; after which are the second wheel D, third wheel, &c. Lastly, between the frame and dial-plate, is the pinion of report, which is that fixed on the arbor of the great wheel; and serves to drive the dial-wheel, as that serves to carry the hand.

For the illustration of this part of the work which lies concealed, let ABC (fig. 14.) represent the uppermost side of the frame-plate, as it appears when detached from the dial-plate: the middle of this plate is perforated with a hole, receiving that end of the arbor of the centre wheel which carries the minute hand; near the plate is fixed the pinion of report a b of 10 teeth; this drives a wheel c d of 40 teeth; this wheel carries a pinion e f of 12 teeth; and this again drives a wheel g h with 36 teeth.

As in the body of the watch the wheels everywhere divide the pinions; here, on the contrary, the pinions divide the wheels, and by that means diminish the motion, which is here necessary; for the hour hand, which is carried on a socket fixed on the wheel g h, is required to move but once round, while the pinion a b moves twelve times round. For this purpose the motion of the wheel c d is \( \frac{1}{4} \) of the pinion a b. Again, while the wheel c d, or the pinion e f, goes once round, it turns the wheel g h but \( \frac{1}{4} \) part round; consequently the motion of g h is but \( \frac{1}{4} \) of \( \frac{1}{4} \) of the motion of a b; but \( \frac{1}{4} \) of \( \frac{1}{4} \) is \( \frac{1}{16} \); i.e. the hour-wheel g h moves once round in the time that the pinion of report, on the arbor of the centre of the minute wheel, makes 12 revolutions, as required. Hence the structure of that part of a clock or watch which shows the time may be easily understood.

The cylinder A (fig. 13.) put into motion by a weight or inclosed spring moves the fusee B, and the great wheel C, to which it is fixed by the line or cord that goes round each, and answers to the chain of a watch.

The method of calculation is easily understood by the sequel of this article; for, suppose the great wheel C goes round once in 12 hours, then if it be a royal pendulum clock, vibrating seconds, we have \( 60 \times 60 \times 12 = 43200 \) seconds or beats in one turn of the great wheel. But because there are 60 swings or seconds in one minute, and the seconds are shown by an index on the end of the arbor of the swing-wheel, which in those clocks is in an horizontal position; therefore it is necessary that the swing-wheel F should have 30 teeth; hence \( \frac{43200}{60} = 720 \), the number to be broken into quotients for finding the number of teeth for the other wheels and pinions.

In spring-clocks, the disposition of the wheels in the watch part is such as is here represented in the figure, where the crown-wheel F is in an horizontal position; the seconds not being shown there by an index, as is done in the large pendulum clocks. Whence in these clocks the wheels are disposed in a different manner, as represented in fig. 15, where C is the great wheel, Fig. 16, and D the centre or minute wheel, as before; but the contrate wheel E is placed on one side, and F the swing-wheel is placed with its centre in the same perpendicular line GH with the minute-wheel, and with its plane perpendicular to the horizon, as are all the others. Thus the minute and hour hands turn on the end of the arbor of the minute wheel at a, and the second hand on the arbor of the swing-wheel at b.

Theory and calculation of the Watch-part, as laid down by Clock by the Rev. Dr Derham.—1. The same motion, it is evident, may be performed either by one wheel and one pinion, or many wheels and many pinions; provided the number of turns of all the wheels bear the proportion to all the pinions which that one wheel bears to its pinion: or, which is the same thing, if the number produced by multiplying all the wheels together be to the number produced by multiplying all the pinions together, as that one wheel to that one pinion. Thus, suppose you had occasion for a wheel of 1440 teeth, and a pinion of 28 leaves; you make it into three wheels of 36, 8, and 5, and three pinions of 4, 7, and 1. For the three wheels, 36, 8, and 5, multiplied together, give 1440 for the wheels, and the three pinions, 4, 7, and 1, multiplied together, give 28 for the pinions. Add, that it matters not in what order the wheels and pinions are set, or which pinion runs in which wheel; only for convenience sake, the biggest numbers are commonly put to drive the rest.

2. Two wheels and pinions of different numbers may perform the same motion. Thus, a wheel of 36 drives a pinion of four; the same as a wheel of 45 a pinion of 5; or a wheel of 90 a pinion of 10; the turns of each being 9.

3. If, in breaking the train into parcels, any of the quotients should not be liked; or if any other two numbers, to be multiplied together, are desired to be varied, it may be done by this rule. Divide the two numbers by any other two numbers which will measure them; multiply the quotients by the alternate divisors; the product of these two last numbers found will be equal to the product of the two numbers first given. Thus, if you would vary 46 times 8, divide these by any two numbers which will evenly measure them: so, 36 by 4 gives 9; and 8 by 1 gives 8; now, by the rule, 9 times 1 is 9, and 8 times 4 is 32; so that for 36+8, you have 32+9; each equal to 288. If you divide 36 by 6, and 8 by 2, and multiply as before, you have 24+12=36+8=288.

4. If a wheel and pinion fall out with crofs numbers, too big to be cut in wheels, and yet not to be altered by these rules; in seeking for the pinion of report, find two numbers of the same, or a near proportion, by this rule; as either of the two given numbers is to the other, so is 36 to a fourth. Divide that fourth number, as also 360, by 4, 5, 6, 8, 9, 10, 12, 15, (each of which numbers exactly measures 360), or by any of those numbers that bring a quotient nearest to an integer. As suppose you had 147 for the wheel, and 170 for the pinion; which are too great to be cut into small wheels, and yet cannot be reduced into lefs, as having no other common measure but unity; say, as 170 : 147 :: 360 : 311. Or, as 147 : 170 :: 360 : 416. Divide the fourth number and 360 by one of the foregoing numbers; as 311 and 360 by 6, it gives 52 and 60; divide them by 8, you have 39 and 45; and if you divide 360 and 416 by 8, you have 45 and 52 exactly. Wherefore, instead of the two numbers 147 and 170, you may take 52 and 60, or 39 and 45, or 45 and 52, &c.

5. To come to practice in calculating a piece of watch-work: First pitch on the train or beats of the balance in an hour; as, whether a swift one of about 20,000 beats (the usual train of a common 30 hour pocket-watch), or a slower of about 16,000 (the train of the new pendulum pocket-watches), or any other train. Next, resolve on the number of turns the fusee is intended to have, and the number of hours the piece is to go: suppose e. gr. 12 turns, and to go 30 hours, or 192 hours (i.e. 8 days), &c. Proceed now to find the beats of the balance or pendulum in one turn of the fusee; thus in numbers, 12 : 16 :: 20,000 : 26666. Wherefore 26666 are the beats in one turn of the fusee or great wheel, and are equal to the quotients of all the wheels unto the balance multiplied together. Now this number is to be broken into a convenient parcel of quotients; which is to be done thus: first, halve the number of beats, viz. 26666, and you have 13333; then pitch on the number of the crown-wheel, suppose 17: divide 13333 by 17, and you have 784 for the quotient (or turns) of the rest of the wheels and pinions; which, being too big for one or two quotients, may be best broken into three. Choose therefore three numbers; which, when multiplied all together continually, will come nearest 784: as suppose 10, 9, and 9, multiplied continually, give 810, which is somewhat too much; therefore try again other numbers, 11, 9, 8: these, drawn one into another continually, produce 792; which is as near as can be, and is a convenient quotient. Having thus contrived the piece from the great wheel to the balance, but the numbers not falling out exactly, as you first proposed, correct the work thus: first multiply 792, the product of all the quotients pitched upon, by 17 (the notches of the crown-wheel); the product is 13464, which is half the number of beats in one turn of the fusee: Then find the true number of beats in an hour. Thus, 16 : 12 :: 13464 : 10098 which is half the beats in an hour. Then find what quotient is to be laid upon the pinion of report (by the rule given under that word). Thus, 16 : 12 :: 12 : 9. The quotient of the pinion of report. Having thus found your quotients, it is easy to determine what numbers the wheels shall have, for choosing what numbers the pinions shall have, and multiplying the pinions by their quotients, the product is the number for the wheels. Thus the number of the pinion of report is 4, and its quotient is 9; therefore the number for the dial-wheel must be 4×9, or 36: so the next pinion being 5, its quotient 11, therefore the greater wheel must be 5×11=55; and so of the rest.

Such is the method of calculating the numbers of a 16 hour watch. Which watch may be made to go longer by lessening the train, and altering the pinion of report. Suppose you could conveniently slacken the train to 16000; then say, As 4 : 16000 or 8000 : 13464 :: 12 : 20; so that this watch will go 20 hours. Then, for the pinion of report, say (by the rule given under that word), as 20 : 12 :: 12 : 7. So that 7 is the quotient of the pinion of report. And as to the numbers, the operation is the same as before, only the dial-wheel is but 28; for its quotient is altered to 7. If you would give numbers to a watch of about 10,000 beats in an hour, to have 12 turns of the fusee, to go 170 hours, and 17 notches in the crown-wheel; the work Clock.

is the same, in a manner, as in the last example: and consequently thus: as $12 : 170 :: 10000 : 141666$, which fourth number is the beats in one turn of the fusee; its half, 70833, being divided by 17, gives 4167 for the quotient; and because this number is too big for three quotients, therefore choose four, as 10, 8, 8, 6 $\frac{1}{3}$; whose product into 17 makes 71808, nearly equal to half the true beats in one turn of the fusee. Then say, as $170 : 12 :: 71808 : 5069$, which is half the true train of your watch. And again, $170 : 12 :: 12144 : 305$, the denominator of which expresses the pinion of report, and the numerator is the number of the dial-wheel. But these numbers being too big to be cut in small wheels, they must be varied by the fourth rule above. Thus:

As $144 : 170 :: 360 : 425$; Or $170 : 144 :: 360 : 305$.

Then dividing 360, and either of these two fourth proportional (as directed by the rule), suppose by 15; you will have

$\begin{array}{c} 6) \quad 60 \quad (10 \\ 6) \quad 48 \quad (8 \quad \frac{3}{8} \text{ or } \frac{3}{4} \\ 5) \quad 40 \quad (8 \\ 5) \quad 33 \quad (6\frac{1}{3} \end{array}$

Such is the calculation of ordinary watches, to show the hour of the day: in such as show minutes, and seconds, the process is thus:

1. Having resolved on the beats in an hour, by dividing the designed train by 60, find the beats in a minute; and accordingly, find proper numbers for the crown-wheel and quotients, so as the minute-wheel shall go round once in an hour, and the second wheel once in a minute.

Suppose, you shall choose a pendulum of seven inches, which vibrates 142 strokes in a minute, and 8520 in an hour. Half these sums are 71, and 4260. Now, the first work is to break this 71 into a good proportion, which will fall into one quotient, and the crown-wheel. Let the crown-wheel have 15 notches; then 71, divided by 15, gives nearly 5; so a crown-wheel of 15, and a wheel and pinion whose quotient is 5, will go round in a minute to carry a hand to show seconds. For a hand to go round in an hour to show minutes, because there are 60 minutes in an hour, it is but breaking 60 into good quotients (suppose 10 and 6, or 8 and 7$\frac{1}{2}$, &c.) and it is done. Thus, 4260 is broken as near as possible into proper numbers. But since it does not fall out exactly into the above mentioned numbers, you must correct (as before directed), and find the true number of beats in an hour, by multiplying 15 by 5, which makes 75; and 75 by 60 makes 4500, which is half the true train. Then find the beats in one turn of the fusee; thus, $16 : 192 :: 4500 : 54000$; which last is half the beats in one turn of the fusee. This 54000 being divided by 4500 (the true numbers already pitched on), the quotient will be 12; which, not being too big for a single quotient, needs not be divided further: and the work will stand as in the margin. As to the hour-hand, the great wheel, which performs only one revolution in 12 turns of the minute-wheel, will show the hour; or it may be done by the minute-wheel.

It is requisite for those who make nice astronomical observations, to have watches that make some exact number of beats per second, without any fraction; but we seldom find a watch that does. As four beats per second would be a very convenient number, we shall here give the train for such a watch, which would (like most others) go 30 hours, but is to be wound up once in 24 hours.

The fusee and first wheel to go round in four hours. This wheel has 48 teeth, and it turns a pinion of 12 leaves, on whose axis is the second wheel, which goes round in one hour, and carries the minute-hand. This wheel has 60 teeth, and turns a pinion of 15 leaves; on whose axis is the third wheel of 63 teeth, turning a pinion of 6 leaves; on whose axis is the fourth (or contrate) wheel, turning round in a minute, and carrying the small hand that shows the seconds, on a small circle on the dial-plate, divided into 60 parts: this contrate wheel has 48 teeth, and turns a pinion of 6 leaves; on whose axis is the crown or balance-wheel of 15 teeth, which makes 30 beats in each revolution.

The crown-wheel goes 480 times round in an hour, and 30 times 480 make 14400, the number of beats in an hour. But one hour contains 3600 seconds; and 14400 divided by 3600 quotes 4, the required number of beats in a second.

The fusee must have 7$\frac{1}{2}$ turns, to let the chain go so many times round it. Then, as 1 turn is to 4 hours, so is 7$\frac{1}{2}$ turns to 30 hours, the time the watch would go after it is wound up.

See further the articles Movement, Turn, &c. And for the history and particular construction of Watches, properly so called, see the article Watch.