i8 



THE AXIMAL AS A MACHINE. 



equal to the product of its weight. W, into the height, 



Ji — ■ — , through which it must fall under the action of 



gravity to acquire that velocity, z', with which it is at 

 the instant moving ; i.e., 



E=U=Wh=W~ . . . (14) 



A change of velocity z\ to z'^ causes a variation of 

 actual energy, — E^, and can be effected only by 

 the expenditure of an equal amount of work — 



E,-E,^U= IV^^^=^= IV {k, - h,\ (15) 



This form of energy appears in every moving part of 

 every machine, and its variations often seriously affect 

 the working of mechanism. 



The total actual energ}- of any system is the algebraic 

 sum of the energies, at the instant, of all its parts : i.e., 



e = :ew—] (16) 



and when this energy is all reckoned as acquired or ex- 

 pended at any one point, as at the driving-point, the 

 several parts ha\dng velocities, each times that of the 

 driving-point, which latter velocity is then z\ the total 

 energy becomes 



E = :^W (i;) 



Actual energy is usualh* reckoned relativeh* to the 

 earth : but it must often be reckoned relatively to a 



