towards a Dynamical Theory of Solutions. 41 



Lorenz's value for the D line for vapour of water, hydro!, is 

 0-2068 equivalent to 0*2092 for the F line. Refraction then 

 confirms the result obtained from contraction that the action 

 of alcohol on water may be divided into two processes : first 

 the conversion of trihydrol into dihydrol, and second the 

 conversion of dihydrol into hydrol, whose optical properties 

 are nearly those of vapour and not of water of crystallization, 

 but refraction makes it appear that the two processes over- 

 lap. For the complete investigation of these interesting- 

 problems we require at definite temperatures the most 

 accurate obtainable measurements of density and index of 

 refraction for mixtures of absolute alcohol and water. Let 

 the water in any mixture contain in 1 gramme ac 3 gramme of 

 hydrol, x± of dihydrol, and x b of trihydrol, then we have the 

 equations 



1 = x z -f # 4 + x h 



1 IP =Pl/Pl +P2 fa/PS + Zi/Pi + #5, 'Po) 



r =p iri +p % (x z r z + a,y 4 + x 5 r 5 ) 



l= Jh +p 2 



)>. • (31) 



J 



By special experiments carried towards an infinitely 

 dilute solution of water in alcohol a? 4 and x b may be made 

 negligible so that p z and r 3 may be found, and then the 

 equations give from the experimental data the values of a? 3 , 

 #4, and x 5 for each value of p 1 at each temperature. In some 

 such way, no doubt, the whole of the phenomena will be 

 investigated, so I shall not try to push farther at present 

 with the published data for alcohol and water. 



Treated in the same way the data of Buchkremer for 

 acetic acid and water at 20° C» with the D line of the 

 spectrum yield the table 



lOspj 15077 32125 45686 61948 72223 84504 



10s?V ... 20612-5 20605 29606 20648 20664 20704 20717 



For acetic acid r/ = 0*21675. Here as with alcohol we 

 have first a decrease of r 2 ' with increase of p 1} a graph 

 showing a minimum of value 0*20597 about p 1 ~0'25 and 

 a maximum estimated as 0*2077 for an infinitely dilute 

 solution of water in acetic acid. To compare this limit for 

 the D line with 0*2107 or 0*2110 obtained from alcohol 

 with the F line, we notice that for water the difference in 

 r' for D and F is 0*206125-0*20854= -0*002415, so that 

 0*2077 for the D line with acetic acid means 0*2101 for the 



