Electric Origin of Molecular Attraction. 635 



which have their axes so directed as to attract one another 

 with the maximum force at that distance, we may consider 

 the total attraction in which these two take part at a given 

 instant to be expressed on our magnetic analogy by 6e 2 s 1 s 2 /r i , 

 all other forces in which these two are involved cancelling 

 one another. Thus, as in the theory of the viscosity of gases 

 and molecular force (xxxvi.), we replace the almost intract- 

 able medley of nature by a simple representative pair of 

 molecules. The part contributed to the first summation in 

 the internal virial by this pair is 3e 2 5 i . < ? 2 /2r 3 , which stands for 

 -^2Rr, and then 



i.±22Rr=3N*V 2 /2r\ 



In a homogeneous substance Si=s 2 =s, and we may 

 write ? >3 = r/iSr, obtaining for the virial of the attractions 

 3NW/2«. 



The expression (3) may be written 



6a 2 7r(W/v 2 ) (4ttR 3 /3)/(5/R) = 67r/(6/R)a 2 N 2 /r, 



making it evident that a is proportional to es. The simplest 

 way of comparing the results of the two methods of calcu- 

 lating the virial of the attractive forces, namely that which 

 treats the attractions as operating between each molecule and 

 all the rest within a sphere of radius R, and that which 

 treats them as on the average acting only between imme- 

 diate neighbours taken in pairs, is to calculate numerical 

 values for f(b/R) when R/& = 2, 10, and 100, namely 0*60, 

 2-69, and 7*78, which give (3) the three values (0*94, 4'2, 

 and 12*2) a 2 N 2 /v. By increasing R from 26 to 1006, that is 

 by increasing the number of molecules included in the first 

 summation of 22 from 8 to 100,000, the value of the internal 

 virial of the attractions is increased only 13-fold. This 

 illustrates how the effect of molecular attraction depends 

 mostly on the mutual actions of immediate neighbours, as we 

 indicated in discussing the range of molecular force. 



In the papers referred to, the internal virial term v<j>(v) 

 in (2) is proved for the element gases to take the form —l/v, 

 while for compounds at small enough values of v it also 

 takes the form —l/2v 3 passing at larger values of v through 

 a very interesting transition to be discussed in section 5. 

 In these communications values o£ I have been found for 

 many substances, though mostly given indirectly by the 

 tabulation of M 2 /, where M is the molecular mass referred to 

 that of the hydrogen atom as 1, and I is given for unit mass 

 of the substance in terms of 10 12 dynes as unit of force. 

 Then, since I is (2/3) 6tt/(6/R) NV or NW, and if N refers 



