490 Mr. W. Sutherland on Molecular Force 



substances at their melting-points, and with those obtained 

 according to the Kinetic Theory of Solids ; there remains 

 now to discuss the meaning of a peculiar empirical relation 

 given in " The Laws of Molecular Force " (Phil. Mag. 5 sei\ 

 xxxv. p. 277), namely, that if iv is the molecular mass of 

 water, and p the molecular mass of a substance dissolved in it 

 to form a solution containing n molecules of p to 1 of w, 

 then the solution may be regarded as a substance of molecular 

 mass m = (w-\-np)/(l-\-n), these molecules m attracting one 

 another according to the law 3Xm 2 /^ 4 , so that X can be cal- 

 culated from the surface-tension of the solution according to 

 the equation 



Then it was asserted that W in 3Wio 2 /r 4 for the attraction 

 of two molecules of water, and A in 3Ap 2 /V 4 for the attraction 

 of two molecules of the dissolved substance, are connected 

 with X by the peculiar relation 



X-\~W- l + nA~ l )/(l+n), 



so that A -1 can be calculated from the observed surface- 

 tension of the solution. As they stand, these equations can 

 be got to represent the connexion between surface-tension 

 and concentration in solutions fairly well, and by slight modi- 

 fication can be got to represent the relation accurately ; but 

 from the previous part of this paper it can be seen that 

 they can only do so in an accidental empirical manner, for 

 X -1 -f (X -1 — W~ 1 )/n, which in our empirical relation is 

 assumed to be A -1 , can be expressed in a form which shows 

 it to be a function of p and A, approximately linear in each ; 

 it so happened that for a number of organic compounds this 

 function was approximately equal to A -1 , and was therefore 

 identified as such, but with the values found in this paper for 

 (M// 2 ) J , which is proportional to A*M, it appears that for the 

 inorganic compounds the function cannot be said to be equal 

 to A -1 , unless in a very roughly approximate manner. Thus 

 all that was said in sections 15 and 16 of a The Laws of 

 Molecular Force," on the supposition that what was denoted 

 by A -1 was really A~S must be withdrawn to be replaced by 

 the results of the present paper. The relation which was 

 proved in the former paper to hold between the surface- 

 tensions and compressibilities of solutions can be brought out 

 more clearly when we abandon the empirical relation and 

 proceed according to dynamical principles. We have to 

 establish a relation between the compressibility fi and /, 



La 



