292 E. G. Spaiilding 



Now the use which can be made of this equation is twofold, 

 namely, theoretical and practical, with both bearing most inti- 

 mately on our special problem. The theoretical will be considered 

 first; it has to do with the generalization of the equation as ex- 

 pressed above. Here Q is the quantity of heat absorbed by the 

 system when the change takes place in it under reversible condi- 

 tions. But not only since heat is energy, but also since it is often 

 impossible to measure this quantity of heat directly, there can be 

 substituted for it, as equivalent to it according to the First Law, its 

 value as obtained from equation [2] by putting, where J = o, Q 

 in place of E; we thus get 



/F+(C/,-t/.) = r^ [5] 



But, furthermore, just as Q = E (energy), so is T an intensity in 

 equations [3], [4], and [5], and as these equations have been derived 

 by considering reversible cyclical heat processes, so it is possible 

 to derive analogous equations by considering reversible cyclical 

 processes in which quantities other than, yet analogous to, Q and 

 T are concerned. This could be done, for example, by considering 

 electrical or mechanical changes.'' 



Thus, with U and W as before, if we let A = any other energy- 

 form than heat, it is possible to get the equation, analogous to [3] 



r= A 



•c^^-) 



in which /^ and I^ stand for any initial and final intensity, and like- 

 wise, analogous to [4], 



dW=A''-l [7] 



Accordingly, the possibility of such a procedure makes it quite 

 evident that it is entirely permissible to make equation [5] of the 

 most general form simply by replacing T', Q having been elimi- 

 nated, by / as standing for any intensity whatsoever; thus we get, 



W+ {U._-U,)==li^ [8] 



^Cf. Mach, Principien der Warmelehre, pp. 328-346. 



