464 . Mr. W. Sutherland on the 



shall denote by 2. This in its solid form as ice has a density 

 •91662, and if it conld expand without dissociation would 

 probably expand like a melting metal by about 3 or 4 per 

 cent., so that the density of our second pure ingredient as a 

 liquid at ought to be about *88. If, then, this is mixed 

 with the pure ingredient 1 having density 1*08942 to produce 

 without shrinkage our standard mixture S of density 1 (nearly) 

 at 0, it is easy to calculate what part p% of it by weight has to 

 be mixed with p L = 1 — -p 2 of 1 by the equation 



l=p,/-88 + (l-p,)/l'089, .... (8) 



.*. at 0, jt? 2 =*375 



and at t, p a =-375(l/2 + q), (9> 



because water at temperature t contains 1/2 + q parts of S in 

 one part of water, and therefore it contains '375 (1/2+q) 

 parts of 2 in one part of water, q being 1/2 almost at 0°. 

 In the following table are given the fraction p 2 of in- 

 gredient 2 (trihydrol) in one part of water at different tem- 

 peratures, the values of q according to (7) being also in- 

 cluded. 



Table I. 



t.. 



. 0° 



20° 



40° 



60° 



80° 



100° 



120° 



140° 



198° 



q.. 



. -5 



•357 



•256 



•181 



•123 



•087 



•040 



•010 



-061 



1000 p 2 .. 



. 375 



321 



284 



255 



234 



217 



203 



191 



165 



Iii using the formulas to calculate values for 198° we are 

 extrapolating beyond their proper range, and must take such 

 values as first approximations only. It is evident from these 

 numbers that at the critical temperature of water, which is 

 about 368° C, water must consist of nearly pure ingredient 1 

 which we shall prove in section 4 to be dihydrol. Now 

 Thorpe and Riicker have furnished a convenient approximate 

 relation between the coefficient of expansion of a liquid and. 

 its critical temperature (Journ. Chem. Soc. xliv.), namely, 



v _ 1-99TV-T 



^~l-99T c -273' • • • • ^ 1U A 



where v and v t are volumes at 0° and t C, while T c is the 

 absolute critical temperature, which for dihydrol is 641. Thus,, 

 then, for this liquid we have 



-Sl = -900=1 -100^, .-. ^ = '001, 



