Theorem of the Mechanical Theory of Heat. 409 



supposed, wc may say that the quantity of heat converted into 

 ergon when disgrcgation is increased is exactly the same as the 

 quantity of ergon converted into heat by the corresponding di- 

 minution of disgrcgation. 



It will be evident, from what has been said, that between alte- 

 ration of disgrcgation on the one hand, and conversion of heat 

 into ergon, or vice versa, on the other hand, there exists a causal 

 connexion, which may be expressed in various ways in the form 

 of a definite law. In order to be able to state this law as simply 

 as possible, we will introduce one more special form of ex- 

 pression. 



The process by virtue of which ergon is produced at the ex- 

 pense of heat, or heat is generated at the expense of ergon, has 

 been already spoken of as a transformation, heat being said to be 

 transformed into ergon, or ergon into heat. In like manner w r e 

 may call an alteration of disgrcgation a transformation, the ori- 

 ginal arrangement of the smallest particles of the body being- 

 spoken of as transformed into another arrangement. 



Each of these two kinds of transformation can take place in 

 two opposite ways, which can be distinguished from each other 

 by employing the terms positive and negative. We will, regard 

 an increase of disgregation as a positive, and a diminution of 

 disgrcgation as a negative transformation. And, further, a trans- 

 formation of ergon into heat shall be reckoned as positive, and 

 the transformation of heat into ergon as negative. 



Let us now return to the processes considered above; we 

 then see that when the disgregation of a body is increased (a 

 change which we have agreed to call a positive transformation), 

 a transformation of heat into ergon (which we have agreed to 

 call negative) occurs simultaneously; and in like manner a (ne- 

 gative) diminution of disgregation is accompanied by a (positive) 

 transformation of ergon into heat. Hence we may deduce, as a 

 first conclusion, that in both cases a positive and a negative trans- 

 formation take place at the same time. 



But, in considering transformations, it is needful to attend not 

 only to their sign but also to their magnitude. The disgrega- 

 tion of a body may change to a greater or less extent ; and in the 

 same way a greater or less quantity of heat may be transformed. 

 into ergon, or produced from ergon. Having proper regard to 

 these differences, we may represent the quantitative value of any 

 transformation, when the mode of measuring transformations has 

 been previously determined on, by a definite mathematical magni- 

 tude, which we will call the equivalence-valve of the transformation. 

 The question now arises, in relation to these equivalence-values, 

 whether they are capable of being determined in such a manner 

 that, in the ease of every reversible alteration of a body, the 



