Theorem of the Mechanical Theory of Heat. 407 



that the quantities of heat and ergon which are mutually con- 

 vertible, and which can therefore replace each other, are expressed 

 by the same numbers. Another convenience is that quantities 

 of heat and ergon can be added together or subtracted from one 

 another without any previous reduction having to be performed 

 upon either the one or the other. 



We will consequently in the following discussion always speak 

 of ergon instead of work, and will accordingly call the first fun- 

 damental theorem the Theorem of the Equivalence of Heat and 

 Ergon. 



When once this theorem had been propounded and been con- 

 firmed by experiment, it very quickly became generally known ; 

 and we may often find that people who have only a superficial 

 acquaintance with the mechanical theory of heat suppose that it 

 is the sole foundation of this theory. Such a view of it is indi- 

 cated, for example, by the name which the mechanical theory of 

 heat often goes by in France, namely, la theorie de V equivalent 

 mecanique de la chaleurl There is, however, a second theorem, 

 not included in the first, but one which requires to be separately 

 proved, and which is of as much importance as the other, inas- 

 much as both theorems together constitute the complete founda- 

 tion of the mechanical theory of heat. 



The fact that this second theorem is less known than the first, 

 and, especially in popular expositions of the mechanical theory of 

 heat, is sometimes passed over in complete silence, is chiefly 

 due to its being much more difficult to understand than the first 

 theorem, since in expounding it we are obliged to discuss con- 

 ceptions which are then introduced for the first time, and to in- 

 stitute quantitative comparisons between processes which have 

 not previously been considered as mathematical magnitudes. I 

 believe, however, that when once the necessary mode of viewing 

 the subject has become familiar, the second fundamental theorem 

 will appear just as simple and natural as the first. 



I will now try to set before you the processes with which we 

 are here concerned, in such a manner that the new kind of com- 

 parison may present itself spontaneously as a necessary conse- 

 quence, and that thus the second fundamental theorem may be 

 clearly seen to be established as well as the first. 



If we examine the conditions under which heat can be trans- 

 formed into ergon, and, conversely, ergon into heat, we find, in 

 the first place, that the commonest and simplest process is the 

 following. The heat which exists in material bodies tends to 

 alter their condition. It tends to expand them, to render solid 

 bodies liquid and gaseous, and, as we may likewise add, to resolve 



2E2 



