towards a Dynamical Theory of Solutions. 51 



is 0*8 and of trihydrol 0*6, so that the change of trihydrol 

 into dihydrol causes on that account a decrease of specific 

 heat. But the rate of change of the remaining trihydrol may 

 be affected and the heat of solution of the mixed trihydrol 

 and dihydrol may also be changed. Thus, notwithstanding 

 the one known cause of a reduction of specific heat when a 

 little alcohol is added to water, the total result is an increase, 

 which in the limit when p L is small amounts to 0*640/?! 

 neglecting 0*005. From the data of Winkelmann at 0° 0. 

 1 have obtained the equations 



c —piCi —p 2 c 2 



=0'78p 1 p 2 from p. 2 = 1 to 0*8 



=0 m 78p 1 p 2 — (0'8— P2)piP2 fro™ 7>2 = 0'8 to 0*5 



= 0-33^92 + 0-5(p 2 - 0'2) Pl p. 2 from p 2 =0'5 to 0*2 



=0-33^2 fi'o:n p 2 =0'2 to 



y m 



Thus {c—piCi—p 2 c^)lp2 i when p 2 is nearly 1, has the 

 limiting value 0*640/?! nearly at 60° C. and 0'78pi at 0°, 

 while when p 2 is small the value is 0*458 at 60° C. and 

 0*33 at 0°. The opposite changes with temperature at these 

 two limits are further evidence that there are two main 

 reactions of alcohol on water. The data of Dupre and Page 

 at about 17° C. make the large limit a little larger and 

 the smaller limit smaller than the values just given from 

 Winkelmann's, but they confirm the result that the change 

 with temperature at the two limits takes place in opposite 

 directions. As the experiments of Winkelmann are of later 

 date and carried out as a check on those of Dupre and Page, 

 it is necessary to take as disproved the remarkable conclusion 

 of Dupre and Page that the heat evolved on mixing is pro- 

 portional to the change of specific heat. But as the values 

 found for the heat evolved agree well in the two sets of 

 experiments, these can be investigated on an assured basis. 

 The following table gives Wmkelmann's values for H, the 

 heat evolved in forming 1 gramme of mixture at 0° C, and 

 also H/j5j^ 2 '• — 



IOOjd, 10 20 30 40 50 60 70 80 SO 



10 H 64 107 120 110 91 71 52 33 18 



H/PyP.2 71 67 57 46 36 30 25 21 20 



It appears that H//?]^ 2 tends towards a limit near 70 when 

 p% is 1, and towards a limit about 20 when p 2 is small, its 

 values for intermediate cases being expressible by simple 

 linear forms. The difference between the two limits is great 

 enough to confirm the idea that they belong to two different 



E2 



