184 TOOTH I'D V 



two of the other (as r< |)i H the 



figure); t: I KM <>f th<-m In- inni.-.l P.uii.l ly any n 



the Otlicr will be turned mund also. This is the si; 

 pair of tootl Is. 



: . To find the relation of the power and i 

 Toothed Wheels. 



: A and B be the fixed centres of the toothed wheels 



Q 



on the circumferences of which the teeth arc arranged ; C the 

 point of contact of two teeth ; QCQ a normal t 

 in contact at C. Suppose an axle is fixed on the whirl 7>, 

 and the weight W suspended from it at E l>y a cord : 

 suppose the power P acts by an arm AD\ draw Au, .1>1> prr- 

 JM -ndicular to QCQ. Let the mutual pressure at C be Q. 

 Then, since the wheel A is in equilibrium about the iixrd 

 .1, the sum of the moments about A equals zero; there- 

 fore 



P.AD-Q.Aa-0. 



Also since the wheel 7? is in equilibrium about J5, the sum of 

 the moments about B equals zero ; therefore 



Q.&-W.BE-0. 



ii by eliminating Q from these two cq nations, 



L- P 0_^a / 



W~ (r \\'~ Alt' 



moment of P _ . 

 moment ot \V~ 



