Theorem of the Mechanical Theory of Heat. 417 



Consequently the proposition holds good of the second kind 

 of transformation also, that the negative transformation of heat 

 into ergon cannot occur without a simultaneous positive trans- 

 formation, but that the positive transformation of ergon into 

 heat can take place without a simultaneous negative transforma- 

 tion. 



Finally, we have still to consider the third kind of transforma- 

 tion, or the passage of heat from one temperature to another. 



In order that heat may be transferred from a colder to a hotter 

 body, it is a necessity that a positive transformation should form 

 a part of the same process, as indeed we have seen already, in 

 connexion with cyclical processes, that such a transference of heat 

 involves the transformation of ergon into heat. The inverse trans- 

 ference of heat from a hotter to a colder body, on the contrary, can 

 go on entirely by itself, as it does, for example, when heat passes 

 from a hotter to a colder body by radiation or conduction. 



Hence in this case also, just as in the two previous ones, the 

 negative transformation cannot occur without a positive trans- 

 formation; but the positive transformation can occur without a 

 negative transformation. 



When two transformations are equal in magnitude but of op- 

 posite signs, we agreed above to say that they compensate each 

 other. Accordingly we may enunciate the following theorem 

 in reference to all the three kinds of transformations : — Negative 

 transformations can take place only when they are compensated, 

 but positive transformations can occur even if uncompensated ; or, 

 shorter still, Uncompensated transformations can never be anything 

 but positive. 



This peculiar relation is met with in every change that occurs 

 in nature; for the case of an alteration being completely reversible, 

 so that the sum of all the transformations involved in it is exactly 

 zero, is merely the limiting case of an infinite number of pos- 

 sible cases, just as zero itself is the lower limit of all positive 

 magnitudes. When we consider the universe, keeping this re- 

 lation in mind, we arrive at a very remarkable conclusion. 



One hears it often said that in this world everything is a cir- 

 cuit. While in one place and at one time changes take place in 

 one particular direction, in another place and at another time 

 changes go on in the opposite direction ; so that the same con- 

 ditions constantly recur, and in the long run the state of the 

 world remains unchanged. Consequently, it is said, the world 

 may go on in the same way for ever. 



When the first fundamental theorem of the mechanical theory 

 of heat was established, it may probably have been regarded as 

 an important confirmation of this view. Hitherto, when discus- 

 sing this theorem, we have spoken only of heat and ergon; but 



