264 



THE LEVER AND WHEELWORK. 



tooth 61 of the wheel ; and, after one revolution of the wheel, the leaf 2 of the 

 pinion would be engaged with the tooth 1 of the wheel. Thus, during the first 

 revolution of the wheel, the leaf 1 of the pinion would be successively engaged 

 with the teeth 1, 11, 21, 31, 41, 51, and 61 of the wheel ; at the commence- 

 ment of the second revolution of the wheel the leaf 2 of the pinion would be 

 engaged with the tooth 1 of the wheel ; and, during the second revolution of 

 the wheel, the leaf 1 of the pinion would be successively engaged with the 

 teeth 10, 20, 30, 40, 50, and 60 of^he wheel. In the same manner it may be 

 shown that, in the third revolution pf the wheel, the leaf 1 of the pinion would 

 be successively engaged with the teeth 9, 19, 29, 39, 49, and 59 of the wheel ; 

 during the fourth revolution of the wheel, the leaf 1 of the pinion would be 

 successively engaged with the teeth 8, 18, 28, 38, 48, and 58 of the wheel. 

 By continuing this reasoning it will appear that, during the tenth revolution of 

 the wheel, the leaf 1 of the pinion will be engaged successively with the teeth 

 2, 12, 22, 32, 42, and 52 of the wheel. At the commencement of the eleventh 

 i revolution of the wheel the leaf 1 of the pinion will be engaged with the tooth 

 5 1 of the wheel, as at the beginning of the motion. It is evident, therefore, that, 

 ' during the first ten revolutions of the wheel, each leaf of the pinion has been 

 | successively engaged with every tooth of the wheel, and that during these ten 

 ^. i revolutions the pinion has revolved 61 times. Thus the leaves of the pinion 

 / nave acted 610 times upon the teeth of the wheel, before two teeth can have 

 ** v ' acted twice upon each other. 



The odd tooth which produces this effect is called by millwrights the hunt- 

 ing-cog. 



The most familiar case in which wheelwork is used to produce and regulate 

 motion merely, without any reference to weights to be raised or resistances to 

 be overcome, is that of chronometers. In watch and clock work, the object is 

 to cause a wheel to revolve with a uniform velocity, and at a certain rate. The 

 motion of this wheel is indicated by an index or hand placed upon its axis, and 

 carried round with it. In proportion to the length of the hand, the circle over 

 which its extremity plays is enlarged, and its motion becomes more percepti- 

 ble. This circle is divided, so that very small fractions of a revolution of the 

 hand may be accurately observed. In most chronometers it is required to give 

 motion to two hands, and sometimes to three. These motions proceed at dif- 

 ferent rates, according to the subdivisions of time generally adopted. One 

 wheel revolves in a minute, bearing a hand which plays round a circle divided 

 into sixty equal parts ; the motion of the hand over each part indicating one 

 second, and a complete revolution of the hand being performed in one minute. 

 Another wheel revolves once, while the former revolves sixty times ; conse- 

 quently the hand carried by this wheel revolves once in sixty minutes, or one 

 hour. The circle on winch it plays is, like the former, divided into sixty 

 equal parts, and the motion of the hand over each division is performed in 

 one minute. This is generally called the minute hand, and the former the sec- 

 ond hand. 



A third wheel revolves once, while that which carries the minute hand re- 

 volves twelve times ; consequently this last wheel, which carries the hour hand, 

 revolves at a rate twelve times less than that of the minute hand, and therefore 

 seven hundred and twenty times less than the second hand. We shall now 

 endeavor to explain the manner in which these motions are produced and reg- 

 ulated. Let A, B, C, D, E, fig. 32, represent a train of wheels, and 0, b, c, d, 

 represent their pinions, e being a cylinder on the axis of the wheel E, round 

 which a rope is coiled, sustaining a weight, W. Let the effect of this weight, 

 transmitted through the train of wheels, be opposed by a power, P, acting upon 

 the wheel A, and let this power be supposed to be of such a nature as to cause 



