28 



THE ANIMAL AS A MACHINE. 



forms. But every such change must be effected by a 

 perfectly definite and exact quantivalence. 



Assuming this ratio of values of customary units 

 reduced to a system of equivalents, it becomes at once 

 practicable to measure all these energies in the same 

 units ; as, for example, when Joule measures either 

 heat or mechanical energy, taking / = 778 foot-pounds, 

 as the equivalent of a British thermal unit, oyJ= about 

 427 kilogrammetres, as the equivalent of one calorie or 

 metric thermal unit ; the thermal unit being defined as 

 the quantity of heat or energy-equivalent demanded to 

 raise the temperature of unit weight of water one 

 degree from the temperature of maximum density. 



Taking either kind of unit in thus measuring, we 

 shall have the initial stock of the one kind of energy 

 altered by the quantity which, in the same units, 

 measures the aggregate several quantities of energy 

 resulting from the change ; and 



where E, T, U, F, etc., are the symbols representing 

 the several energies, initial and other. 



If 7" measure heat-energy, and Uhe taken as poten- 

 tial energy of the molecular kind, V the potential 

 energy of an elastic fluid varying in volume, W the 

 work of some mechanism or a dynamic process, the 

 total variation of the initial energy E, will be equal 

 to the total of all the new energies and the new work, 

 in proportions which become known as soon as the 

 dE 



partial coefficients etc., are determined. 



