402 



J. W. Gihbs on a Reprefientattoti by Surfaces 



can be diminished, nsing for that purpose, according to tlie condi- 

 tions, only the force derived from the body itself. The conditions 



of V and passing through the point A, which represents the initial state of the body. 

 MN is the section of the surface of dissipated 

 energy. Qe and Q?7 are sections of the planes 

 ;? = and £ = 0, and therefore parallel to the 

 axes of e and rj respectively. AD and AE are 

 the energy and entropy of the body in its ini- 

 tial state, AB and AC, its available energy and 

 its capacity for entropy respectively. It will 

 be observed that when" either the available 

 energy or the capacity for entropy of the body 

 is 0, the other has the same value. '% Except in 

 this case, either quantity may be varied without 

 affecting the other. For, on account of the 

 curvature of the surface of dissipated energy, 

 it is evidently possible to change the position of 

 the point representing the initial state of the 

 body so as to vary its distance from tlie surface 

 measured parallel to one axis witliout varying that measured parallel to the other. 



As the different senses in which the word entropy has been used by different writ- 

 ers is liable to cause misunderstanding, it may not be out of place to add a few words 

 on the terminology of this subject. If Professor Clausius had defined entropy so that 

 its value should be determined by the equation 



7" 

 instead of his equation (Mechanische Warmetheorie, Abhand. ix, § li; Pogg. Ann., 

 July, 1865) dQ 



where S denotes the entropy and 7' tlie temperature of a body and dQ the element of 

 heat imparted to it, that whicli is here called capacity for entropy would naturally be 

 called available entropy, a term the more convenient on account of its analogy with the 

 term available energy. Such a difference in the definition of entropy would involve no 

 difference in the form of the thermod3'namic surface, nor in any of our geometrical 

 constructions, if only we suppose the direction in which entropy is measured to be 

 reversed. It would only make it necessary to substitute — r/ for ;; m our equations, 

 and to make the corresponding change in the verbal enunciation of propositions. Pro- 

 fessor Tait has proposed to use the word entropy " in the opposite sense to that in 

 which Clausius has employed it," (Thermodynamics, i^ 48. See also § 178), which 

 appears to mean that he would determine its value by the first of the above equations. 

 He nevertheless appears suljsequently to use the word to denote available energy 

 (§ 182, '2d theorem). Professor Maxwell uses the word entropy as synonymous with 

 available energy, with the erroneous statement tliat Clausius uses the word to denote 

 the part of the energy which is not available, (Tiieory of Heat, pp. 186 and 188). The 

 term entropy, however, as used by Clausius does not denote a quantity of the same 

 kind (i. e., one which can be measured by the same unit) as energy, as is evident from 

 his equation, cited above, in which Q (heat) denotes a quantity measured by the unit 



