§ 2 OF ARTS AND SCIENCES. 357 



The rough investigation of § i is probably sufficient to 

 show that in vapors, P," in liquids and sohds, P may gen- 

 erally be neglected; so that in vapors Pand P\ in liquids 

 and solids, jP" and P' are very nearly equal and opposite. 

 That is, in liquids and solids, the cohesive pressure plays 

 the same part as does the external pressure in vapors. 



The well-known formula connecting the volume, V^ the 

 pressure, P, and absolute temperature, 2", of a gas, 



— — = constant, 

 or, in the form used largely in the kinetic theory, 



PV = — Mv\ 

 3 



where J/ is the mass and v^ the mean square of the molec- 

 ular velocity, is established upon the assumption that the 

 molecules of a gas are small as compared with the distance 

 between them. If the molecule has any size, that is, if 

 it prevents other molecules from approaching within cer- 

 tain definite limits, the free path (/) will in all cases be 

 shortened by an amount (/') which I propose to call the 

 molecular diameter. The present investigation proceeds 

 on the usual hypothesis that the latter is nearly, at least, 

 constant. 



Since then the free path is shortened in the ratio of/ to 

 / — /', the kinetic pressure will increase, cceteris f>aribus^ 

 in the same ratio, and we shall have for solids and liquids, 



PT = — Mv' 



I 



3 I— I 



The kinetic theor}' asserts that two bodies are at the 

 same temperature when their molecular kinetic energies 

 are equal, that is, when 



mv^ fn^v* 



