100 WHEEL-WORK. 



d revolves once, the wheel and pinion c will revolve as 

 many times as the number of leaves borne by c is con- 

 tained times in the number of teeth borne by /. In like 

 manner, while the wheel c revolves once, the wheel and 

 pinion b will revolve as many times as the number of leaves 

 borne by b is contained times in the number of teeth 

 borne by c. By combination of these results, we see that 

 while d revolves once, # will have as many revolutions as 

 the product of the number of leaves is contained times in 

 the product of the number of teeth. From this it follows 

 that the ratio between the continued product of the cir- 

 cumference (diameter or radius) of d into the number of 

 leaves on the several pinions and the continued product of 

 the corresponding dimension of Z> into the number of teeth 

 on the several wheels will be the ratio between the dis- 

 tances or velocities of W and P, and therefore the ratio 

 between the intensities of balancing weights or forces. 



In short, the continued product of the power, the cir- 

 cumference of a and the number of teeth on c and / 

 equals the continued product of the weight, the circum- 

 ference of d and the number of leaves on the pinions c 

 and I. 



188. Example. Suppose the circumferences of a 

 and d to be 60 mm. and 15 mm. respectively ; that I has 9 

 leaves ; c has 36 teeth and 13 leaves ; / has 40 teeth. 

 Then will 



P x 60 x 36 x 40 = W x 15 x 13 x 9. 



189. Ways of Connecting Wheels. Wheels 

 may be connected in three ways : 



(1.) By the friction of their circumferences. 

 (2.) By bands or belts. 



