THE LEVER AND WHEELWORK. 265 



the weight W to descend with a uniform velocity, and at any proposed rate. 

 The wheel E carries on its circumference eighty-four teeth. The wheel D 

 carries eighty teeth ; the wheel C is also furnished with eighty teeth, and the 



Fig. 32. 



wheel B with seventy-five. The pinions d and c are each furnished with 

 twelve leaves, and the pinions b and a with ten. 



If the power at P be so regulated as to allow the wheel A to revolve once 

 in a minute, with a uniform velocity, a hand attached to the axis of this wheel 

 will serve as the second hand. The pinion a, carrying ten teeth, must revolve ( 

 seven times and a half to produce one revolution of B, consequently fifteen f 

 revolutions of the wheel A will produce two revolutions of the wheel B ; the 

 wheel B therefore revolves twice in fifteen minutes. The pinion b must re- 

 volve eight times to produce one revolution of the wheel C, and therefore the 

 wheel C must revolve once in four quarters of an hour, or in one hour. If a 

 hand be attached to the axis of this wheel, it will have the motion necessary 

 for the minute hand. The pinion c must revolve six and two thirds times to 

 produce one revolution of the wheel D, and therefore this wheel must revolve 

 once in six and two thirds hours. The pinion d revolves seven times for one 

 revolution of the wheel E, and therefore the wheel E will revolve once in 

 forty-six and two thirds hours. 



On the axis of the wheel C a second pinion may be placed, furnished with 

 seven leaves, which may lead a wheel of eighty-four teeth, so that this wheel 

 shall turn once during twelve turns of the wheel C. If a hand be fixed upon 

 the axis, this hand will revolve once for twelve revolutions of the minute hand 

 fixed upon the axis of the wheel C ; that is, it will revolve once in twelve 

 hours. If it play upon a dial divided into twelve equal parts, it will move over 

 each part in an hour, and will serve the purpose of the hour hand of the chro- 

 nometer. 



We have here supposed that the second hand, the minute hand, and the hour 

 hand, move on separate dials. This, however, is not necessary. The axis of 

 the hour hand is commonly a tube, enclosing within it that of the minute hand, 

 so that the same dial serves for both. The second hand, however, is generally 

 furnished with a separate dial. 



We shall now explain the manner in which a power is applied to the wheel 

 A, so as to regulate and equalize the effect of the weight W. Suppose the 

 wheel A furnished with thirty teeth, as in fig. 33 ; if nothing check the mo- 

 tion, the weight W would descend with an accelerated velocity, and would 

 communicate an accelerated motion to the wheel A. This effect, however, is 

 interrupted by the following contrivance : L M is a pendulum vibrating on 

 the centre L, and so regulated that the time of its oscillation is one second. 

 The pallets I and K are connected with the pendulum, so as to oscillate with 

 it. In the position of the pendulum represented in the figure, the pallet I stops 

 the motion of the wheel A, and entirely suspends the action of the weight W, 



