634 Mr. W. Sutherland on the 



a collision. Thus on the average the attracting power of 

 molecules containing n symmetrically arranged doublets 

 each is only n 2 /n = n times that due to a single doublet. Ju 

 this way the remarkable equation (A) may be explained. 

 The attraction of such molecules depends on the number of 

 equivalents in each in a way that points suggestively to the 

 doublet origin of molecular attraction. 



The most important point now is to determine the definite 

 connexion between the electric properties of doublets and the 

 experimental parameters of molecular attraction. If we 

 write Clausius's equation of the Virial as adapted for the 

 kinetic theory of N molecules in a volume v w r e have 



3pv/2 = Nmw 2 /2 + J . itlRr, 



where the last term, which is the virial of the internal central 

 forces R (different from Maxwell's R for magnets), includes 

 the virial of the preponderating attractive force as well as 

 that of the repulsive forces coining into play during mole- 

 cular collisions. These latter give a virial proportional to 

 the kinetic energy, so that the last equation may be cast in 

 the form 



pv = BTvf(v)+v<j>{v) 9 (2) 



where vcj)(v) represents two-thirds of the virial of the attrac- 

 tive forces, and R is now the usual gas constant. Now ac- 

 cording to the law of attraction 3Am' 2 /r 4 , or better 3a 2 /r A , 

 I have shown (xxxv.) that if the N molecules form a sphere 

 of radius R (still another signification for R, but the context 

 prevents confusion), and if b is a length of the order of the 

 distance between neighbour molecules, 



=6«T 2 £{ i{R_J)31og ^-i( R - 6 ) 3 



-fR'(K-&) + flog^}, . {3) 



where p is the density of the substance formed by the !N" 

 molecules. 



But according to what we have stipulated about the origin 

 of our preponderating attraction and the range of molecular 

 force we can evaluate | . ^22Rr in a far simpler manner. Let 

 esi and es 2 be the electric moments of any two doublets, 

 where e is the numerical value of the charge # or b and s x 

 and s 2 are the distances between ft and b in the doublets, 

 then, if r denote the- average distance apart of two neighbours 



