146 
MESSES. W. E. BOUSFIELD AND C. ELSPETH BOUSFIELD 
by eliminating x — Xo we get 
\fs = E(s§ — Li^) + L (p. 
Thus the result of this section involves a linear relationship between (p and 
Furthermore this relation now gives us a new way of obtaining the important 
constant L, which is independent of the necessity of ascertaining s s and v 0 . It now 
turns out that L = dfi/d(p. 
We can get its value at once from the series of values of and (p in Table XIII. 
Deducing it from the values of and <p for the two end solutions at 20° C. we get for 
NaCl, L = 25 '48 ; and similarly for KC1, L = 24'79. 
From the above linear relation between and x it follows that dfi/dx = — L, a 
relation which will be of use later. Hence we get for L three forms of expression :— 
_ ds^ d\Js d\]s 
dw M d(p dx 
20. Relation oj Heat of Dilution to Specific Heat and Contraction .—A certain 
relation comes to light in the course of this enquiry, which it may be well to put on 
record, though no figures are available for testing it practically. Let the heat of 
dilution at temperature t of 1 gr. molecule of the solute from a solution whose specific 
heat is % containing H 2 grammes of water to a solution whose specific heat is s 2 
containing H 2 grammes of water be denoted by q t . To compare q t with q T , the cor¬ 
responding heat of dilution at the higher temperature T, we proceed in the usual 
manner (as in Thomsen, I., 66) on the principle that the heat required to pass from 
separate masses at temperature t to mixed masses at temperature T is independent of 
the order of mixing and heating. Hence we get 
fT rT pT 
(E+H 2 ) s 2 dt—q t = (E + Hj) 5 1 d^ + (H 2 — Hj) s w dt — q T . 
h J t J t 
Now the quantity s which is tabulated in this paper is really 
.§ = | sdt/(T — t), 
and therefore we p - et 
C"5 
^f = (E + H,) Sl + (H a -H 1 ) S „-(E + H 2 ) S2 
= (E + H 1 )s,-H 1 s w -[(E + H 2 )s 2 -H 2 s w ] 
If we take Q as the mean heat of dilution per gramme of added water we have 
QIH.-H,) = q, 
