ENERGY AND ITS TRANSFORMATIONS. 



23 



ful work will be, respectively, Ps^ Rs'\ the lost work 

 will be — Rs' , and the 



Rs' 



Efficiency = < i. . . . . (20) 



Comiter-efficieficy, C, is the reciprocal of the effiency ; 

 i.e., 



Ps 



^=w ^2') 



The efficiency and the counter-efficiency of a machine, 

 or of any train of mechanism, are the products of the 

 efficiencies or of the counter-efficiencies of the several 

 elements constituting the train transmitting energy 

 from the point at which it is received to that at which 

 the work is done, i.e., from the driving " to the 

 " working " point. 



Friction is the principal cause, and usually the only 

 cause, of loss of energy and waste of work in machinery. 

 A given amount of energy being expended upon the 

 driving-point in any machine, that amount will, in ac- 

 cordance with the principle of the persistence of energy, 

 be transmitted from piece to piece, from element to 

 element, of the machine or train of mechanism, without 

 diminution, if no permanent distortion takes place and 

 no friction occurs between the several elements of the 

 train, or between those parts and the frame or adjacent 

 objects. Temporary distortion, within the limit of 

 perfect elasticity, causes no waste of energy ; permanent 

 distortion, however, causes a loss of energy equal to 

 the total work performed in producing it. But perma- 

 nent distortion is due to deficiency of strength and de- 

 fective elasticity, and is never permitted in well-designed 



