OSMOTIC PRESSURES DERIVED FROM VAPOUR-PRESSURE MEASUREMENTS. 
313 
From this it follows, since c l + c 2 — 1, that 
W — .S'jC, + .S.jC.j .. . (l) 
and 
c, dsjdc 2 = c 2 0.s- 2 /0e,.(2) 
The form of (1) at first suggests that Sj and s 2 are the specific volumes in the 
solution of the two components. This is not necessarily so. For calling the true 
specific volumes .sfi and s 2 , then we have w = Si 1 c 1 + s 2 1 c 2 , which on differentiating gives 
Si 1 = w — c 2 
dwfdc 2 + c 2 (c : 
0S ] 1 /0C 2 — C 2 05 2 */0Cj), 
and 
s 2 = w — c : 
dw/cCi —c l (c x 
0S‘i 1 /0C 2 — Co 0.9 2 1 /0C 1 ), 
thus 
.sfi = s 1 and s. 
= s.j only if 
c 1 dsi/dc 2 — c 2 0.s - 2 Y0 
1* 
There does not appear to be any adequate ground for supposing this condition 
is in general satisfied. If it is not, we have sfi = ^ -f hc 2 and s 2 — s 2 — kc 1 where 
Jc = (p dsi/dc 2 —c 2 0s 2 1 /0c 1 ) is in general a function of the pressure and concentration. 
Returning now to the calculation of Sj. Some of the densities given in Landholt 
and Bornstein for cane sugar solutions having been verified experimentally, the 
remainder of their table was taken as correct; the densities of the a-methyl glucoside 
solutions were determined by us and the mean values are tabulated in Table VII. 
Table VII.—Cane Sugar. 
Weight 
«i 
at 
concentration. 
0 ° c. 
30° C. 
34-00 
0-99768 
1-00287 
56-50 
0-99515 
1-00103 
81-20 
0-98157 
0-99873 
112-0 
0-98690 
0-99554 
141-0 
0-98321 
0-99176 
183-0 
0-97842 
0-98653 
217-5 
0-97399 
0-97360 
243-0 
0-97117 
0-98176 
a-Methyl Glucoside. 
Weight 
Densities at 
at 
concentration. 
o 
o 
p 
30° C. 
d 
O 
O 
30° C. 
25-0 
_ 
_ 
_ 
_ 
35-0 
1-09319 
1-08399 
0-99810 
1-00260 
45-0 
1-11341 
1-10308 
0-99709 
1-00186 
55-0 
1-13149 
1-12017 
0-99597 
1-00087 
64-0 
1-14619 
1•13407 
0-99491 
0-99996 
75-0 
1-16243 
1-14942 
0-99354 
0-99881 
90-0 
1-18195 
1-16788 
0-99166 
0-99721 
105-0 
1-19896 
1-18399 
0-98974 
0-99507 
2 T 2 
