yo Clock-work. [Book I. 



the wheels and the radii of the nuts. The firft pro- 

 duct will be 512; and the fecond 8, in which cafe the 

 power Q^ought to be to the weight P, as 8 is to 512, 

 or as i is to 64. Hence it follows, that to preferve 

 ' an equilibrium, whatever is the diameter of the wheels 

 and of the nuts, the power is to the refiftance as the 

 product of the radii of the nuts is to the product of the 

 radii of the wheels. 



It appears then that this form of machines is ca- 

 pable of giving a great advantage to the force or 

 power over the refiftance ; but this advantage is necei- 

 v ceffarily acquired at the expence of time or velocity; 

 when the machine paries from a ftate of reft to that 

 of motion. For there is always as much left in time 

 as there is gained in force, and fo reciprocally. 



There is often occafion, efpecially in clock-work, 

 that the number of the revolutions of the wheels and 

 that of the nuts fhould beajpa certain proportion. 

 This is performed by giving a convenient number of 

 teeth or cogs to the wheels and nuts : as for example, 

 if it was required that a wheel fhould make only one 

 revolution while a nut fhould make four, there muft 

 be four times as many teeth in the wheel as there are 

 cogs in the nut. Suppofe ABCD (fig. 2.) to be 

 four wheels, the firft of which A, catches the nut b 

 fixed to the fecond B ; this catches the nut c fixed to 

 the third wheel C ; this third catches the nut 4 fixed 

 to the fourth D j laftly, this fourth wheel catches the 

 laft nut e ; now to obtain the proportion between the 

 number of revolutions of the firft wheel A, and the 

 number of revolutions of the laft nut e, multiply the 

 number of teeth of the wheel A, by the number of 

 teeth of the wheel B > this firft product by the num- 

 ber of teeth in the wheel C, and the fecond product 

 8 by 



