§ 2 OF ARTS AND SCIENCES. 359 



that is, the continued product of the coefficients of vo- 

 himinal elasticity and expansion with the absolute tem- 

 perature is equal to the kinetic pressure. 



This theorem applies only to liquids or solids in which 

 no molecular rearrangement is brought about by heat or 

 pressure, and which consequently agree, like gases, in 

 obeying the same general laws of expansion. An exami- 

 nation of the tables will show that most liquids fall under 

 this categor}^ The most important exception is water, 

 which we shall see, from many considerations, is not to be 

 treated as a pure liquid, even at moderately high tempera- 

 tures. In such liquids, /' may be treated as a variable, and 

 there is no connection between the real and apparent 

 compressibility and expansion. 



The theorem is, in other respects, perfectly general, and 

 gives, for gases (in which eT ^=. \ by the Law of Charles), 

 P' ^^ E^ as it should be. The importance of the theorem, 

 in determining readily the free path of a molecule and the 

 measure of cohesion for liquids and solids, has apparently 

 been overlooked. The application to liquids is restricted 

 only by the paucity of those whose elasticity has been de- 

 termined, and its extension only by our ignorance of the 

 real nature of the law which governs molecular cohesion. 



Let us therefore assume that the force between any two 

 molecules in the line joining them varies as the x\\\ power 

 of their distance, inversely; then the component of this at- 

 traction in any direction will also vary as the x\k). power 

 inversely; and if we conceive of a perfectly homogeneous 

 and uniform expansion in which every line is increased 

 in a certain ratio, called the ratio of linear expansion, so 

 that the angles subtended by a particle are in no case 

 altered, nor the direction of any line fixed in it, then the 

 component of the attraction of every particle for every 

 other, resolved in any one direction, will also vary as the .rth 

 power of the linear expansion, inversely, no matter how the 



