78 THE HUMAN MOTOR 



known that the machine, which had a "vis viva" Jmvf has now a 

 "vis viva " \mv\. The work done is therefore equal to the resistant 

 work and to" the increase of vis viva \ (mv\ mv\). 



The equation is then written : 



T,, =T r +J(wi;; mv\). 



The quantity of energy absorbed in increasing the speed from 

 v l to v 2 is *ra (vi-vi). When the speed becomes uniform there 

 is no more*mertia to be overcome. There is equilibrium between 

 T m and T r , whence : 



1- (mvl mv\) = o, or v a = v l ; 



which is the law of uniform and economical movement, the work 

 done being exactly equal to the resistant work. 



When the power is cut off from the machine, T w becomes 

 zero, and the speed returns to the initial velocity V L ; but the 

 inertia which had absorbed the quantity of energy \m (vl ?), 

 gives it back as momentum and carries on for some time the work 

 of the machine. It is therefore clear that it is inertia which 

 prevents the speed from passing abruptly from one velocity to 

 another, and momentum which prevents a machine stopping 

 instantaneously. 



In practice, the total resistant work Tr includes both the useful 

 work T of the machine and the useless work T z - expended in over- 

 coming the forces of friction. The equation is therefore : 



The irregularities in the motion of some familiar machines are 

 due to the intermittent or ii regular action of the motive force 

 or the resistance (as in the case of pile drivers, hammers, etc.). 

 They are lessened by means of fly wheels and by regulating the 

 admission of steam or combustible gases by the employment of 

 governors. It has been possible to make the action of these 

 regulators or governors extremely sensitive and reliable. In- 

 dustry has almost satisfied all the exigencies of the dynamic 

 equilibrium of machines. 



From the equation 



T w = T K -f T,, 

 can be deduced the relation 



Thus the machine only gives out a part always less than unity 

 of the energy that it receives. That fraction is called its yield, 





