ON THE SPECIFIC HEAT OF AQUEOUS SOLUTIONS. 
14 !) 
In the next section these values of n will be compared with those given in 
Table XVII. which are calculated from the specific volumes, with a view to consider 
how far further support is given to the hypothesis as to the variation of the specific 
heat of the free water. 
22. Derivation of the Value of Evj 0 .— Tt remains to deduce the value of E v 0 which 
has been used in preceding sections. This may be obtained, by a process similar to 
that used in the last section for Es s , from the volume data for solutions I., II. and III., 
and with the aid of the values of n deduced from the interpolation formula above 
given, making also a similar assumption as to the change in the specific volume of the 
free water. Let 
v = specific volume of solution, 
v 0 = specific volume of liquid solute, 
w — specific volume of pure water, 
w c = specific volume of combined water. 
iv F — specific volume of uncombined water. 
Then we must have 
(he + Vi)v = E v 0 + new c + ( h—n)ew F , 
and assuming that w c is constant and that w F — w — BP, where B is a constant, and 
introducing this value of w F into the above relation, we get 
(he + E) v— (h—n)eiv = Ey 0 +new c + B (h—n) eP. 
As before using the values of n for solutions I., II. and III., we get three simultaneous 
equations to evaluate the three unknown constants, and obtain 
Er 0 = 25-053, tv c = 0-97551, B = 0-0008536. 
With these values of the constants we may calculate the values of n for the more 
dilute solutions from the expression 
hew + Ev 0 — (he + E) v—he BP 
U ~ (to-Wc- BP)e 
The results are set out in Table XVII. 
Table XVII.—Calculated Values of n for NaCl Solutions at 20° C. 
No. of 
solution. 
h. 
P. 
V. 
BP. 
n. 
I. 
9-7347 
25•000 
0-84119 
0-02134 
3-35 
II. 
13-883 
18-945 
0-87756 
0-01617 
4-26 
III. 
20-758 
13-519 
0-91120 
0-01154 
5-07 
IV. 
29-189 
10•005 
0-93376 
0-00854 
5-45 
y. 
54-442 
5-625 
0-96286 
0-004802 
5-75 
VI. 
109-94 
2-8669 
0-98161 
0-002447 
6-41 
VII. 
220-91 
1-4476 
0-99149 
0-001236 
6-83 
