Molecular Constitution of Water. 465 



which agrees with the value found graphically by means of 

 the asymptote. Accordingly, from (5) we have k s ="00033. 

 But S is a mixture of "375 parts of 2 and '625 of 1, and 

 thus 



v='Z75v 2 + '625v 1 ; 

 •vat0° |'= -375^/^0 + -625 VoPi- • • • (11) 



With -00033 as the value of dv/dt at 0°, and the values 

 of px, p 2 , and k lf this gives a negative value for k 2 . This is 

 undoubtedly wrong. One cause of the error may be that we 

 have got too large a value of k± by Thorpe and Riicker's 

 approximate formula ; another cause may be that 1 and 2 do 

 not mix without shrinking, as assumed in establishing (B), 

 a very small change in the neglected shrinkage at different 

 temperatures would modify considerably the meanings of \ 

 and k 2 as they appear in (B), which has been forced into the 

 form of Mendeleeif's empirical equation. Indeed our process 

 of getting (B) into a form the same as (A) tends to make 

 the separation of the true coefficients of expansion difficult. 

 The following method of proceeding for £ x and k 2 seems safer. 

 According to Plucker and Geissler (Pogg. Ann. lxxxvi.) the 

 coefficient of cubical expansion of ice is "000157, and according 

 to Hagen (Wied. Ann. xxxix.) the coefficients of Na and K 

 on melting increase by '3 of their values; so by analogy we 

 shall take the coefficient of liquid trihydrol to be about "0002. 

 With this in (11) and (5) we get 7^ = "00076. I shall adopt 

 '0009 as a reasonable compromise for the value of k 1} retain- 

 ing "0002 as the value of k 2 . This seems small, but as I hope 

 to show that the melting-point of ice is not the true physical 

 melting-point of trihydrol, but its temperature of dissociation, 

 we can take '0002 as the coefficient of trihydrol below its 

 irue melting-point, in solution in dihydrol ; the analogy just 

 used with melting Na and K was intended to provide an 

 allowance for increased molecular freedom in the liquid state, 

 without implying that the melting of ice is a true physical 

 jmelting like that of these metals. 



2. Confirmation from Optical Refraction. 



Before going farther it is important to confirm our con- 

 clusion that water is a mixture of liquids 1 and 2 in propor- 

 tions given by Table I., and at the present stage an optical 

 method is most appropriate. For a mixture of p L parts by 

 weight of a liquid of refractive index hi with p 2 parts of a 



