towards a Dynamical Theory of Solutions. 39 



drop out M and denote (n - 1)1 p by r and (n 2 — l)/(n 2 + 2)p 

 by r'. In (6) we put u — r or r' and get 



r=p l r 1 +p 2 r 2 + (p^ +p 2 r 2 )pA +p 1 p 2 p(xjp 2 + tf 2 //°i)- ( 2 $) 



In the simplest kind of mixture A = and r=p- [ r l +p 2 r 2 , 

 so that #i//o 2 + # 2 //c>i = 0, probably because ,r 1 = = ^ 2 . But 

 when A does not vanish, as in the mixtures we are studying, 

 then we see that an important part of r — p^i— p 2 r 2 is directly 

 proportional to the contraction pA on forming unit volume of 

 the mixture. If we denote p>i r i + p% /, % by r c to indicate that 

 it is a value of r calculated by the simple rule of mixtures, 

 we can write (28) thus : 



^^^pb+piltyiasi/pi + xt/pdfr,. . . (29) 



Pulfiich has shown that in such cases (>• — r c )/r c is pro- 

 portional to pA, and Hess has devoted a paper chiefly to the 

 investigation of Pulfrich's formula with mixtures of water 

 with alcohol and acetic acid [Ann. tier Phys. xxvii. p. 589, 

 1908). He finds that on the average with alcohol (r — r c )/r c 

 = 0*977/oA, the coefficient ranging from 0'929 whenjo 1 = 0'2 

 to T04 when p 1 = 0*8. In (29) for alcohol we may say that 

 ^'i/Ps + ^s/^i^O. With acetic acid according to the investi- 

 gation of Buchkremer, quoted by Hess, the mean numerical 

 coefficient is I'll, ranging from 1*04 when jt? 1 = 0'14 to I'M 

 when p { = 0'7. With acetic acid too Xi/p 2 + x 2 /pi is nearly 0. 

 With r the results are similar, the numerical coefficient for 

 alcohol being 0*8852, and for acetic acid 1*0033. Having 

 found in this survey of the broad facts that the term in pip 2 p 

 in (29) cannot at present be detected in a useful manner, we 

 can investigate molecular refraction in a different way if we 

 use the ideas gained in studying contraction. The chief 

 idea is that all the change takes place in the water, none in 

 alcohol or acetic acid. If then we assume that r or **' is 

 unchanged for liquid 1, we can calculate from the data for 

 any mixture the value for r 2 or r 2 for water as the changed 

 liquid 2. I shall use /, having already used it in investi- 

 gating the molecular constitution of water. In 



r T =Pir 1 l +p 2 r 2 ' 



that is (n 2 -l)/(n 2 + 2)p=p l (n 1 2 -l)i(n 1 2 + 2)p i 



+p 2 (nj-l)nn* + 2)p 2 



} 



we know r/, and also r for each value of p^ or n^ and n 



