of a Mass of Matter. 83 



is undergoing modification absorbing heat from the one body and 

 giving it out again to the other. In this case the bodies between 

 which the transference of heat takes place are to be viewed merely 

 as heat- reservoirs, of which we are not concerned to know any- 

 thing except the temperatures. If the temperatures of the two 

 bodies differ, heat passes, either from a warmer to a colder body, 

 or from a colder to a warmer body, according to the direction in 

 which the transference of heat takes place. Such a passage of 

 heat may also be designated, for the sake of uniformity, as a 

 transformation, inasmuch as it may be said that heat of one tem- 

 perature is transformed into heat of another temperature. 



The two kinds of transformations that have been mentioned 

 are related in such a way that one presupposes the other, and 

 that they can mutually replace each' other. If we call transfor- 

 mations which can replace each other equivalent, and seek the 

 mathematical expressions which determine the amount of the 

 transformations in such a manner that equivalent transforma- 

 tions become equal in magnitude, we arrive at the following ex- 

 pression : — If the quantity of heat Q of the temperature t is pro- 

 duced from work, the equivalent value of this transformation is 



T , 



and if the quantity of heat Q passes from a body whose tempera- 

 ture is tj into another whose temperature is t 2 , the equivalent value 

 of this transformation is 



Q \T S T,)' 



where T is a function of the temperature which is independent 

 of the kind of process by means of which the transformation is 

 effected, and Tj and T 2 denote the values of this function which 

 correspond to the temperatures t x and / 2 . I have shown by 

 separate considerations that T is in all probability nothing more 

 than the absolute temperature. 



These two expressions further enable us to recognize the posi- 

 tive or negative sense of the transformations. In the first, Q is 

 taken as positive when work is transformed into heat, and as 

 negative when heat is transformed into work. In the second, 

 we may always take Q as positive, since the opposite senses of 

 the transformations are indicated by the possibility of the differ- 

 ence;^ — fp being either positive or negative. It will thus be 



seen that the passage of heat from a higher to a lower tempera- 

 ture is to be looked upon as a positive transformation, and its 



G 2 



