MECHANICS. . 81 



139. There are many different curves, accord- 

 ing to which the teeth of wheels might be formed, 

 so as to answer the condition in the last proposi- 

 tion ; but that which seems most convenient, and 

 which has been most generally adopted, is the epi* 

 cycloid. 



Vid. EULER, Nov. Com. Petrop. v. p. 299. and xi. 

 p. 207. One of the curves there proposed, is 

 the evolute of the circle. The same is mentioned,, 

 Encyc. Brit. 



If the circumference of one circle be made to roll along 

 the circumference of another, the curve described by 

 any given point in the first of these circumferences, 

 is an epicycloid. The circle which rolls is called the 

 generating circle^ and that on which it rolls is called 

 the base of the epicycloid. As the former may be 

 supposed to roll either on the outside or the inside of 

 the latter, there are two kinds of epicycloids, distin- 

 guished by the names of Exterior and Interior. 



140. Let it be required, having given the mag- 

 nitude of a wheel and pinion, and the numbers of 

 teeth in each, to determine the figure of those teeth. 

 Let CB (fig. 11.) be the primitive radius of the 

 wheel, and BD the base of the tooth ; bisect BD 

 in E, draw CE, and produce it indefinitely ; and 

 with a generating circle, of which the radius is 

 half the primitive radius of the pinion, describe 

 an arch of an epicycloid on the primitive circum- 



VOL. I. F ferencc 



