ON THE SPECIFIC HEAT OF AQUEOUS SOLUTIONS. 
143 
19. Change in the Mean Specific Heat of the Water. —There appeared good reason 
to suppose that the specific heat of the liquid solute might be treated as practically 
constant for all dilutions, and that the change in the mean specific heat of the 
water itself was that which was fundamentally related to the contraction. This 
hypothesis was tested in the following manner :—- 
Let 
s M = the mean specific heat of the total water both free and combined, 
s s = the specific heat of the liquid solute, taken as constant for all isothermal 
dilutions. 
Then we have 
s (E + H) = Es s + Hs M , 
or 
s M = s + E (s—s s )/H. 
Hence for the lowering of the mean specific heat of the water we have 
A<S'jj — S-\ y S E (<$* sfijd. 
Now if As M is proportional to AxJH, we must have As M = LA xJH where L is a 
constant, and therefore 
L Ax,, = (s w —s) H— Es + Es s , 
or since 
\js = E.s- — II As 
we must have 
L Axo = — V^ + Esg. 
Hence if we plot the values of upon the values ol Ax 0 we must get a straight line 
if the suggested' relation holds. 
In Table XV. are set out for NaCl solutions at 20° C. the values of A Xo and the 
values of calculated from the experimental data, and in fig. 6 the values of are 
shown plotted upon the values of Ax 0 - 
Table XV.—NaCl Solutions at 20° C. 
No. of 
solution. 
A Xo-. 
I. 
4-04 
II. 
4-82 
III. 
5'66 
IV. 
6-23 
V. 
6-93 
VI. 
7-60 
VII. 
8-00 
’A- 
38 
17 
4 
18 
34 
51 
62 
06 
27 
59 
30 
46 
61 
84 
VOL. CCXVLLI.-A. 
U 
