of a Mass of Matter. 85 



rature, among the immediate consequences of which is the prin- 

 ciple of the equivalence of transformations in its more complete 

 form, and which at the same time involves other important con- 

 clusions. This law I will at once quote, and will endeavour to 

 make its meaning clear bv the addition of a few comments. As 

 for the reasons for supposing it to be true, such as do not at 

 once appear from its internal probability will gradually become 

 apparent in the course of this paper. It is as follows : — 



In all cases in which the heat contained in a body does mecha- 

 nical work by overcoming a resistance, the magnitude of the resist- 

 ance which it is capable of overcoming is proportional to the abso- 

 lute temperature. 



In order to understand the significance of this law, we require 

 to consider more closely the processes by which heat can perform 

 mechanical work. These processes alwavs admit of beins; reduced 

 to the alteration in some way or another of the arrangement of 

 the constituent molecules of a body. For instance, bodies are 

 expanded by heat, their molecules being thus separated from 

 each other : in this case the mutual attractions of the molecules 

 on the one hand, and on the other external opposing forces, in 

 so far as any such are in operation, have to be overcome. Again, 

 the state of aggregation of bodies is altered by heat, solid bodies 

 being rendered liquid, and both solid and liquid bodies being 

 rendered aeriform : here likewise internal forces, and in general 

 external forces also, have to be overcome. Another case which 

 I will also mention, because it differs so widely from the fore- 

 going, and therefore shows how various are the modes of action 

 which belong to the class we are considering, is the transference 

 of electricity from one body to the uther, constituting the thermo- 

 electric current, which takes place by the action of heat on two 

 heterogeneous bodies in contact. 



In the cases first mentioned, the arrangement of the molecules 

 is altered. Since, even while a body remains in the same state 

 of aggregation, its molecules do not retain fixed unvarying posi- 

 tions, but are constantly in a state of more or less extended 

 motion, we may, when speaking of the arrangement of the mole- 

 cules at any particular time, understand either the arrangement 

 which would result from the molecules being fixed in the actual 

 positions they occupy at the instant in question, or we may sup- 

 pose such an arrangement that each molecule occupies its mean 

 position. Now the effect of heat always tends to loosen the 

 connexion between the molecules, and so to increase their mean 

 distances from one another. In order to be able to represent 

 this mathematically, we will express the degree in which the 

 molecules of a body are dispersed, by introducing a new magni- 

 tude, which we will call the disgregation of the body, and by help 



