246 Prof. Clausius ow the Application of the Mechanical 



the temperature abpve the freezing-point, 



T=273 + /. (1) 



In the present memoir T will always have this signification, and 

 for brevity will be called the absolute tempej^ature. It may be 

 here remarked, however, that the conclusions do not essentially 

 depend upon this signification, but remain true even when T is 

 considered as an undetermined function of the temperature. 



Lastly, N denotes the equivalence- value of all the uncompen- 

 sated transformations* involved in a circular process. 



8. If the process is such that it can be reversed in the same 

 manner, then N=0. If, however, one or more changes of con- 

 dition occur in a circular process which are not reversible, then 

 uncompensated transformations necessarily arise, and the mag- 

 nitude N has, consequently, a determinable and necessarily posi- 

 tive value. 



Amongst the operations to which the last remark is applicable, 

 is one which in the following will be often mentioned. When 

 a quantity of gas or vapour expands, and thereby overcomes a 

 pressure equivalent to its total expansive force, it may be again 

 compressed into its former volume by employing the same power, 

 when all the phsenomena which accompanied the expansion will 

 take place in an inverse manner. This is not the case, however, 



* One species of uncompensated transformations requires fui'ther remark . 

 The sources from which the changing matter derives heat must have higher 

 temperatures than itself; and, on the other hand, those from which it de- 

 rives negative quantities of heat, or which deprive it of heat, must have 

 lower temperatures than itself. But whenever heat is interchanged between 

 the changing body and any source whatever, heat passes immediately from 

 the body at a higher to the one at a lower temperature, and thus an 

 uncompensated transformation occurs which is greater the greater the dif- 

 ference between the temperatures. In determining such uncompensated 

 transformations, not only must the changes in the condition of the variable 

 matter be taken into consideration, but also the temperatures of the sources 

 of heat which are employed; and these uncompensated transformations 

 will be included in N or not, according to the signification which is attached 

 to the temperature occurring in equation (II). If thereby the temperature 

 of the source of heat belonging to dQ is understood, the above changes will 

 be included in N. If, however, agreeably to the above definition, and to 

 our intention throughout this memoir, the temperature of the changing 

 matter is imderstood, then the above transformations are excluded from N. 

 One more remark must he added concerning the minus sign prefixed to N, 

 which did not appear in the same equation in my former memoir. This 

 difference arises from the different application of the terms negative and 

 positive with respect to quantities of heat. Before, a quantity of heat 

 received by the changeable body was considered as negative because it was 

 lost by the source of heat; now, however, it is considered as positive. 

 Hereby every element of heat embraced by the integral, and consequently 

 the integral itself, changes its sign ; and hence, to preserve the correctness 

 of the equation, the sign on the other side must be changed. 



