12 



THE ANIMAL AS A MACHINE, 



and for motion variable only, 



dU= Fds. 



(2) 



For variable forces, 



dU = sdF. 



(3) 



For forces and motion variable. 



dU=d{Fs) 



(4) 



The Unit of Work is the product of the units of its 

 factors force and space, as the foot-pound, the kilo- 

 grammetre, the foot-ton, the gramme-centimetre. 



Useful Work is that which is appHed to the produc- 

 tion of a specified useful effect ; Lost Work is that 

 which is incidentally wasted, in the endeavor to per- 

 form useful work, in overcoming prejudicial resistances, 

 and in doing useless work ; this waste occurs usually 

 and principally in overcoming friction of moving 

 parts. 



Work of Acceleration is work expended in producing 

 increased velocity in a freely moving body. The effort 

 exerted, and the resistance met, is dependent upon the 

 inertia of the mass, and is measured thus: A body 

 moving freely under the action of gravity, i. e., of a 

 force equal to its own weight, acquires, in this latitude, 

 a velocity of 32.2 feet (9.81 metres), nearly, in one 

 second, and the acceleration, or retardation, of any 

 freely-moving body is proportional to the effort applied, 

 as to the resistance met by it. If / is the actual accel- 

 eration, if g measures that produced by gravity, if F is 



