Energy and Entropy of a Body. 5 



quantity of heat absorbed during an infinitely small change of 

 the body's condition. dW further expresses the external work 

 simultaneously performed by the body, and d\J the alteration 

 which is thereby produced in the magnitude, denoted in the title 

 of this paper by the word Energy. When I introduced the 

 magnitude U into the theory of heat for the first time*, I gave 

 it no, particular name, but contented myself with defining its 

 signification by a definition which amounted to saying that this 

 magnitude was the sum of the actual heat gained by a body and 

 of that consumed in internal work, starting from any given initial 

 condition. Since, however, W. Thomson, who subsequently in- 

 troduced this same magnitude into his equations, has proposed 

 for it the convenient name of Energy, I have adopted this ex- 

 pression. 



The peculiarity of the magnitude U, whereby it is distin- 

 guished from the other variable quantities occurring in the above 

 equation, is this, that the initial condition of the body being sup- 

 posed given, it is completely defined by the actual condition of 

 the body at any time, without reference to the way in which the 

 body arrived at that condition, whereas the magnitudes W and Q 

 depend not only on the actual condition of the body, but also on 

 the manner of its transition to that condition from its initial state. 



A slight simplification can still be introduced into the above 

 equation. In one of the Additions to be found in my ' Collec- 

 tion of Memoirs/ I have proposed to speak of mechanical work, 

 when it is expressed not in the usual measure, but in heat- 

 measure (that is, when we adopt for it as unit the quantity of 

 work corresponding to a unit of heat) by the name of Work+. 

 Accordingly, since W denotes the external work expressed in 

 mechanical units, the product AW denotes the external work 

 expressed in thermal units. We will express this by a particular 



letter, thus, A w 



' ' w = AW. 



The above equation then runs, 



dQ=dV + dw (la) 



§2. 



The second fundamental equation with which we have to do 

 here is the one already mentioned as applying to reversible cir- 



* PoggendorfFs Annalen, vol. lxxix. p. 384, March 1850 ; Abhandlungen- 

 sammlung, part 1, p. 32. 



t* [The German word is "Werk" in contradistinction to "Arbeit." 

 The latter word having been rendered throughout by work, in accordance 

 with prevailing English usage, it is not easy to reproduce without circum- 

 locution the distinction intended in the original between Arbeit and Werk. 

 — Transl.] 



