278 Dynamics. 



the resistance of friction, and the resistance arising from the in- 

 ertia of all the parts of the machinery ; for a certain portion of 

 the moving power is necessarily wasted in overcoming these 

 obstacles to motion. 



The impelled point of a machine is that point at which the 

 moving power is applied, or rather that point at which the mov- 

 ing force is supposed to act, when this moving force is the result- 

 ant of various powers differently applied. The working point of 

 a machine is that point at which the resistance is overcome, or 

 that point at which the resultant of all the resisting forces is sup- 

 posed to act. 



The work performed, or the effect of a machine, is equal to 

 the resistance multiplied by the velocity of the working point. 



The moment of impulse is equal to the moving force mul- 

 tiplied by the velocity of the impelled point. 



396. In proceeding to investigate general expressions for the 

 ratio of the velocities of the impelled and working points of ma- 

 chines, when their performance is a maximum, let 



D = the radius of the wheel to which the power is applied ; 

 or, which is the same thing, the velocity of the impelled 

 point of the machine ; 



d = the radius of the axle to which the resistance is applied, 

 or the velocity of the working point of the machine ; 



p = the moving force applied at the impelled point; 



r = the resistance arising solely from the work to be per- 

 formed ; 



m = the inertia of the moving power/?, or the quantity of mat- 

 ter to which that power must communicate the velocity of 

 the impelled point ; 



n = the inertia of the resistance, or the quantity of matter 

 to be moved with the velocity of the working point be- 

 fore any work can be performed ; 



/ = the quantity of matter, which, if placed at the working 

 point, would create the same resistance as friction ; 



