530 



Mr. W. Sutherland on a 



where a is a length of the order of e, and R is a length of the 

 order of the linear dimensions of the body. 



%rcj)(r) — 12Kimrp log R/a. 



On account of the small n ess of a, log R/a is approximately 

 the same for all ordinary bodies, and then %r<j>(r) for a given 

 body is always proportional to the density, and for different 

 bodies its value depends on that of a parameter A, which has 

 a definite value for each body. Apart from all specification 

 of the law of molecular force, if the potential energy and the 

 virial of a number of molecules are proportional to the den- 

 sity of their distribution, and can be represented by such 

 forms as Bp, where B is constant for each substance, the same 

 conclusions will hold as those I am about to draw from the 

 law of the inverse fourth power. My previous arguments in 

 favour of the inverse fourth power law amounted to this, that 

 that is the only simple natural law, like the law of gravitation, 

 that will make the potential energy of a number of molecules 

 and their virial both closely proportional to the density of 

 distribution, as experiment shows they must be. 



With the„ above value of Xr<f>(r) and with p=m/e s , we have 



2 e d ( D _3AmV]ogRAo 

 le'{e-E) e Q j 



k = 



'dSdele'ie-E) 



2e 



r 2D 



D 



e\e-^f 



+ 



18Am-VlogR/q\ 

 e 1 5 



But in the absence of external stress (4) becomes 



D 



oAm 2 7r log R/rt 



e 2 (e-E) 



and hence 



_ 2 e f 4D D •)' 



(6) 



2. Testing of the Equations on the supposition that the 

 Molecules are unalterable. — Suppose that E is constant, then 

 if b is the mean coefficient of linear expansion between 

 zero and 6 which corresponds to kinetic energy D, then 

 (e — ~Ej)/e=bO, and if c is the mean specific heat between zero 

 and 0, then L) = Jmc0, where J is the mechanical equivalent 

 of heat, if we suppose that all the energy of the molecules 

 exists in their vibrations as wholes; if not, then we must 

 write D = hJcm0, where h is a fraction probably not differing 

 much from unity. Thus we have 



2 , Jem 



3 ' 3bm/p 



(<-A> 



(7) 



