Theorem of the Mechanical Theory of Heat* 413 



another quantity of heat is transferred from a hotter to a colder 

 body. 



If the cyclical process had been gone through in the inverse 

 order, the final result would have been that ergon would have 

 been transformed into heat, and that at the same time an ad- 

 ditional quantity of heat would have been transferred from 

 a colder to a hotter body. 



It will be thus seen that, even in a cyclical process, the trans- 

 formation of heat into ergon, or of ergon into heat, is not an iso- 

 lated occurrence, but is connected with another change, namely 

 the transference of heat from a hotter to a colder body, or from 

 a colder to a hotter body; and hence it is natural to regard this 

 transference of heat as a compensation for the transformation 

 which it accompanies. 



In order that we may employ a form of expression correspond- 

 ing to that adopted in considering the previous case, we will speak 

 of the passage of heat from a body of one temperature into a 

 body of another temperature as being likewise a transformation, 

 inasmuch as heat of one temperature is in fact thereby trans- 

 formed into heat of another temperature ; and, further, we will 

 call the passage from a higher to a lower temperature a positive 

 transformation, and that from a lower to a higher temperature a 

 negative transformation. We may then express the result at 

 which we have arrived in reference to the cyclical process as fol- 

 lows : — In such a process a positive and a negative transformation 

 occur simultaneously, namely the negative transformation of 

 heat into ergon, and the positive transformation of heat of higher 

 into heat of lower temperature, or the positive transformation of 

 ergon into heat, and the negative transformation of heat of lower 

 into heat of higher temperature. 



Examining the matter more closely, we find that the equiva- 

 lence-value of the transference of heat can be determined in such 

 a way that the two transformations, which occur simultaneously 

 in every reversible cyclical process, are not only of opposite signs, 

 but are always of equal absolute values, so that in the algebraic 

 sum they exactly counterbalance each other. It is very easy to 

 assign the equivalence-value, determined in accordance with 

 these conditions, of the passage of heat from one temperature to 

 another ; it is in fact the value that would be obtained as the 

 resultant value of the double transformation if the heat were to 

 be transformed into ergon at the one temperature, and reproduced 

 from ergon at the other temperature. 



If we now consider conjointly the three kinds of transforma- 

 tion that we have been discussing, namely the alteration of dis- 

 gregation, the transformation of heat into ergon, or vice versa , 

 and, lastly, the transference of heat, we can establish a theorem 



