of a Mass of Matter. 91 



By disgregation is represented, as stated in § 2, the degree of 

 dispersion of the body. Thus, for example, the disgregation of a 

 body is greater in the liquid state than in the solid, and greater 

 in the aeriform than in the liquid state. Further, if part of a 

 given quantity of matter is solid and the rest liquid, the disgre- 

 gation is greater the greater the proportion of the whole mass 

 that is liquid ; and similarly, if one part is liquid and the re- 

 mainder aeriform, the disgregation is greater the larger the 

 aeriform portion. The disgregation of a body is fully deter- 

 mined when the arrangement of its constituent molecules is 

 given ; but, on the other hand, we cannot say conversely that 

 the arrangement of the constituent molecules is determined when 

 the magnitude of the disgregation is known. It might, for 

 example, happen that the disgregation of a given quantity of 

 matter should be the same when one part was solid and one part 

 aeriform, as when the whole mass was liquid. 



We will now suppose that, with the aid of heat, the body 

 changes its state, and we will provisionally confine ourselves to 

 such changes of state as can occur in a constant and reversible 

 manner, and we will also assume that the body has a uniform 

 temperature throughout. Since the increase of disgregation is 

 the action by means of which heat performs work, it follows that 

 the quantity of work must bear a definite ratio to the quantity 

 by which the disgregation is increased ; we will therefore fix the 

 still arbitrary determination of the magnitude of disgregation so 

 that, at any given temperature, the increase of disgregation shall 

 be proportional to the work which the heat could perform at that 

 temperature. All that further regards the influence of tempe- 

 rature is determined by the foregoing theorem. For if the same 

 alteration of disgregation takes place at different temperatures, 

 the corresponding work must be proportional to the absolute 

 temperature. Accordingly, let Z be the disgregation of the body, 

 and dZ an infinitely small alteration of it, and let dh be the cor- 

 responding infinitely small quantity of work, we can then put 



dL=KTdZ, 

 or 



aZj — T^T* 



where K is a constant dependent on the unit, hitherto left unde- 

 cided upon, according to which Z is to be measured. We will 



choose this unit of measure so that K= -r-, and the equation 



becomes ,, 7 ArfL ... 



«Z = -7jr (2) 



