6 Prof. Clausius on the Determination of the 



cular processes, 



j*f=0. ....... (II) 



It expresses the second fundamental theorem not in the most 

 general way, it is true ; but it is sufficient for our present purpose. 

 From this equation it follows, as already stated, that the dif- 

 ferential expression -„-, so far as it relates to reversible pro- 

 cesses, is the complete differential of a magnitude which, so long 

 as the initial condition of the body is supposed to be given, is 

 fully defined by the actual condition of the body at a given mo- 

 ment, and is independent of the way in which the body came 

 into this condition. If we denote this magnitude by S, and ex- 

 pressly add that we understand by S as well as by U a magni- 

 tude which has a definite value for every condition of the body, 

 we may write the last equation in the following form : 



d -^=dS. . (II «) 



As to the physical meaning of the magnitude S, I have already 

 discussed it in my paper, above referred to, " On the Application 

 of the Principle of the Equivalence of Transformations to Internal 

 Work ; " we have, however, no need to enter upon these consi- 

 derations here, and I have referred to them merely because. I 

 have derived from them the name of the magnitude S. I have 

 formed, namely, from the Greek word rpoTrrj, change, the word 

 Entropy, which expresses the meaning of the magnitude S, in the 

 same way as the word Energy denotes that of the magnitude U. 



The object of the present paper is to deduce, from the funda- 

 mental equations (la) and (II«), other equations which may serve 

 for the determination of energy and entropy, and make the pro- 

 perties and relations of these magnitudes intelligible. 



§3. 



Equation (I a) applies to non-reversible as well as to reversible 

 alterations. But in order to be able to bring this equation into 

 conjunction with equation (II«),we will assume that the alteration 

 to which equation (I a) relates is the same as that to which equa- 

 tion (II a) relates. The thermal element dQ is then the same in 

 both equations, and we may therefore eliminate it from the equa- 

 tions, whereby we obtain 



Td$ = dV+dw (1) 



We will now assume that the condition of the body is defined 

 by any two variables, which we will provisionally denote quite 



