i the teeth are small this ratio very nearly 

 of wheel A 



of wheel /T 



. Wheels are in some cases turned ly means of straps 

 passing over t a inferences. In such cases the minute 



Iterances of the surfaces prevent the sliding of the straps, 

 mutual action takes place such as to n-n-l.-r the calcu- 

 i exactly analogous to that in the Proposition. 

 For the calculation of the best forms for the teeth, the 

 reader is referred to a Paper -i' Mr Airy's, in the Comb. 

 2Vww. Vol. i: 



158. The fourth Mechanical Power is the Pully. There 

 are several species of pullies : we shall mm: . in order. 



illy is a small wheel moveable about its axis: 

 ug passes over part of its circumference. If the a\ 



pully is only to i n of 



the string passing over it : if however the axis be moveable, 



as will be presently seen, a mechanical advantage may 



IK- :;ninr.l. 



incs assumed as axiomatic that if a perfectly 



>le string passes over a smooth surface the tension of the 



sun- thr "luhout ; we shall see, howev. 



the Chnj .nga that this result admits of 



dem . In the present Chapter we shall only require 



a part of the general proposition. \Y. shall suppose the {-al- 

 lies to be circular, and assume that the tensions of th 

 portions of any string which are separated by a portion in 

 contact with a pully are equal. An I this may be shewn to 

 be necessarily tru-- it we merely admit that the string is 



.cent to t -ases to be in 



contact with the pul' since the pully is smoot: 



.ions of all the forces which it exerts on the string must 

 pass t centre of tht ;>/ -o if we tak 



nts with respect to this \ .c forces which act on 



the string we see that the string cannot be in equilibrium 

 unless the tensions of the two portions are equaL 



