of a Mass of Matter. 207 



circumstances have to be taken into consideration as have 

 already been discussed in § 5. If a body changes its disgre- 

 gation in a reversible manner, the change is accompanied by a 

 transformation of heat into work, or of work into heat, and we 

 can determine the equivalent values of the two kinds of trans- 

 formations by comparing together the transformations which 

 take place simultaneously. 



Let us first assume that a constant alteration of arrangement 

 takes place at different temperatures ; the quantity of heat which 

 is thereby converted into work, or is produced from work, is then 

 different in the different cases, and is, in fact, according to the 

 above law, proportional to the absolute temperature. If, now, we 

 regard as equivalent the transformations which correspond to one 

 and the same alteration of arrangement, it results that, for the 

 determination of the equivalent values of these transformations, 

 we must divide the several quantities by the absolute tempera- 

 tares respectively corresponding to them. The production of the 

 quantity of heat Q from work must, therefore, if it takes place 

 at the temperature T, have the equivalent value 



7p const. ; 



and if we here take the constant, which can be assumed at will, 

 as equal to unity, we obtain the expression given in § 1. 



We will assume, in the second place, that various alterations 

 of arrangement occur at a constant temperature, these alterations 

 being accompanied by increase of disgregation ; and if we adopt 

 as a principle that increments of disgregation wherein the same 

 quantity of heat is converted into work shall be regarded as equi- 

 valent to each other, and that their equivalent value shall be equal, 

 when taken absolutely, to that of the simultaneously occurring 

 transformation from heat into work, but that they shall have the 

 opposite sign, we thus acquire a starting-point for the determi- 

 nation of the equivalent values of alterations of disgregation. 



By combining these two rules, we can determine also the 

 equivalent value of an alteration of disgregation occurring at 

 various temperatures, and we thus obtain the expression given 

 in § 5. Let, for instance, dh be an element of the work per- 

 formed during an alteration of disgregation, in effecting which 

 the quantity of heat AdL is consumed, and let the equivalent 

 value of the alteration of disgregation be denoted by Z — Z , we 

 then have 



Z-Z 



J T~* 



Finally, as to the process cited above as the second kind of 

 transformation — namely, the passage of heat between bodies of 



