314 Lord Rayleigh on Laplace's 
as due to an uninterrupted mass of infinite extent of density 
pi, and to a spherical mass A of density (p 2 —pi). Since 
the first part can produce no effect at any part of B, we have 
to deal merely with the attraction of the sphere A. 
Laplace has shown that if A were of unit density, its 
action along the line A would he 
a 
where 
K = 2tt( f(r)clr, H = 2tt f r^(r)dr; . . (8) 
Jo J 
while along A B its action would he 
K-?. 
a 
The loss of pressure in going outwards from to A is thus 
(P2-lh)Pi (K+ -); 
and from A to B, 
( P , 
>.)*(*- f). 
Accordingly the whole difference of pressure between and 
Bis 
K(p!-tf)+f(p 2 - Pl ) 2 (9) 
Thus, in addition to the former result that the difference of 
pressure independent of curvature varies as (p\— pf), we see 
that the capillary pressure, proportional to the curvature, 
varies as (p 2 —p l )' 2 . 
The reasoning just given is in fact little more than an ex- 
pansion of that of Young*. If the effect depends only upon 
the difference of densities, it cannot fail to be proportional to 
(p2-pif> 
Writing H 12 = H(p 1 — p 2 ) 2 , we see that there is no reason 
whatever for supposing that the capillary constants of three 
liquids should be subject to the relation 
H 13 =H 12 + H 23 . 
On the contrary, the relation to be expected, if the supposi- 
tions at the basis of the present calculations agree with reality, 
is s/H 13 =*/H 12 +v/H 2 3 (10) 
* Encyc. Brit. 1816. Young's works, vol. i. p. 463. 
