DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
497 
the difference between (o'/p for the solution, and the same quantity for the salt, and 
therefore probably diminish the quantity of salt in the solution ; for it seems natural 
to expect that, the more salt we have dissolved in the solution, the more nearly will 
the properties of the solution approximate to those of the salt. Any additional 
energy which increases as solution goes on makes cl (</V 2 ) /dq positive, and therefore 
tends to stop the solution. 
To calculate the magnitude of the effect due to capillarity, let us suppose that the 
mixture of salt and solution is in the form of a spray of spherical drops of radius a. 
The additional term in q'V 3 due to the surface-tension will be 
47ra 3 T, 
where T is the surface-tension. We have then, from (37), 
but 
so that 
and therefore 
, , d 1 ,dvj’\ 
+ w q ~ + v -Y 7 
dq p dq 
_ „ da , . 0 dT 
87mT — + 47ra 2 — ; 
dq dq 
w f k= 
dq 
1 
P 
I d 
a 
3 
0S 
+ / / 
ivq 
_d i 
d</ p 
d 1 
+ ?'A- t + ; 
i,' P 
a 
£ + A fi 
<J p/ dq 
(39) 
We can determine experimentally the value of all the quantities on the right-hand 
side of this equation, and, if we know the quantity in brackets on the left-hand side 
as a function of p, we can at once determine the change in the density of the solution. 
We can express this in a way which more readily admits of comparison with experi¬ 
ment. Suppose that the existence of the surface-tension causes as much salt to be 
absorbed at 6 as would be absorbed if there were no surface-tension at 6 + 8 d\ then, 
by comparing equations (37) and (39), we see that 
but the denominator is the increase of potential energy when unit mass of the salt 
dissolves. We can measure this by the cooling. Let it be denoted by X ; then 
2/1 1 , ,d_l\ 
ci\p a 1 dq' p) 
T + 
ci 
dT 
dq' 
3 s 
(41) 
MDCCCLXXXVII.-A. 
