ON THE SPECIFIC HEAT OF AQUEOUS SOLUTIONS. 
145 
dilutions, whilst the lowering of the mean specific heat of the water is pro¬ 
portional to the mean specific contraction of the water. A glance at Table XVIII., 
which is given in Section 23, will show that this relation brings out the calculated 
results with an accuracy greater than that indicated by the differences set out in 
Table XVI., of Section 18. Another reason for regarding this as the fundamental 
relation is that this result seems to come into line with certain theoretical 
considerations which were developed in a former paper (Bousfield, ‘Roy. Soc. Proc.,’ 
A, vol. 88, 149, 1913). It was shown for a large group of substances in the solid or 
liquid state that the heat of combination of pairs of the substances could be expressed 
by the sum of three components, two of which were constants belonging to the 
respective substances and the third of which was f- $V, SV being the contraction of 
the atomic volumes taking place on combination. Contraction in a solid or liquid 
means a limitation of the vibratory movements which involves a certain loss of kinetic 
energy per unit of mass. In that case it appeared that the heat development due to 
the contraction was proportional to the contraction. Moreover, within the area 
investigated, the ratio was independent of the kind of matter. 
In the case of the specific heat of a solution we now find a lowering of the mean 
specific heat of the water which is proportional to the mean specific contraction of 
the water. The ratio differs from the former ratio in that the specific heat involves 
the additional element of changes of state with temperature, which may differ for 
different solutes. For instance in the case of the series of NaCl solutions at 7° C. 
the graph corresponding to fig. 6 breaks up into two straight lines inclined at a small 
angle to one another and involving two slightly different values of L above and below 
10 per cent, strength. As both portions of the line are straight one can hardly 
attribute this result to experimental errors. It may be that the fundamental hydrate 
of NaCl in solution changes at the lower temperature in the neighbourhood of a 
10 per cent, solution. Any such change of state might affect the ratio L. 
The value for KC1 worked out in the same way by calculating Ec 0 with the aid of 
the known vapour pressures and conductivities in the neighbourhood of 20' C. comes 
out as L = 24'83 as against 2573 for NaCl. Experimental errors in any of the 
numerous data required for the calculation might account for the difference, and the 
area covered by research is not extensive enough for a generalization as to the 
variation of L with different solutes, but the value of L will probably come out 
nearly the same for a series of similar salts. 
It remains to show that the relation As u /Aw u = L necessarily implies (at the same 
time as it interprets) the linear relation between 0 and f to which reference has been 
made in Section 15. 
Since 
A = Es s -L (x-Xo) 
and as can easily be shown 
0 = Eb 0 -( x -Xo) 
