392 Dr. R. D. Kleeman on Fundamental 



term, for an atom may consist simply of a centre of force. 

 In the present case its volume would be best defined as the 

 volume of the space associated with it through which another 

 molecule never passes. This volume probably depends on 

 the temperature and other conditions of the substance. 



A number of properties of U and u can be deduced from 

 equation (1) on comparing it with the facts. Let us suppose 



that i~ 1 = and (-ttJ =0, or that the force of attraction 



and the internal energy of a molecule in a substance at 

 constant volume are independent of the temperature. This 



reduces equation (1) to m a p——l—r 1 \ — (~j^) +ZT. Ac- 

 cording to this equation the pressure of a substance at constant 

 volume is a linear function of the temperature. But this 

 does not agree with the facts. Hence one or both of the 

 assumptions do not hold. 



Next let us suppose that ( -^ j =0 and ( — j =0, or that 



the attraction of a molecule is independent of its temperature, 

 and its internal energy independent of the vicinity of other 

 molecules. These conditions reduce equation (1) to 



m a \ dv / T m a m a \dv / T 



the intrinsic pressure of the substance *, and 



i> + P n = |2-53xlO- 2 V^t, 



where n denotes the number of molecules crossing per 

 second a plane one cm. 2 in area in one direction in the sub- 

 stance,, and m is the molecular weight relative to hydrogen. 

 Hence we obtain the simple equation 



Z = nwvL-26xlO- 



V© 



connecting Z and n. From the results obtained in previous 

 papers J it appears, however, that the above assumptions are 

 not true, but approximately so. 



Lastly, let us assume that (—-) = and (v ) =0, or 



\dvjT \dvjT 



that the molecules exert no attraction upon one another in 



* Loc. cit. j PhiL Mag. July, 1912, pp. 101-118. 



X Loc, cit. 



