Theory of Capillarity. 311 
ever may be the law of the action in these respects, the force 
exerted b y Q upon P must be absolutely the same as the force 
exerted by P upon Q. Now, as we pass downwards from A 
to B, every pair of elements between A and B comes into 
consideration twice. In passing through P we find an in- 
crease of pressure due to the action of Q upon P, but in 
passing through Q we have an equal diminution of pressure 
due to the action of P upon Q. Along the whole path from 
A to B the only elements which can contribute to a final dif- 
ference of pressure are those which He outside, i. e. in the fluid 
above A and below B. By hypothesis the action of the fluid 
above A on the strata traversed in going towards B ceases 
within the limits of the uniform fluid about A] and conse- 
quently the whole difference of pressure due, according to this 
way of treating the matter, to the fluid above A depends only 
upon the properties of A. In like manner the difference due 
to the fluid below B depends only upon the properties of B; 
and we conclude that the whole difference of pressure due to 
the action of the forces along the path AB depends upon the 
properties of the fluids at A and B, and not upon the manner 
in which the transition between the two is made. In par- 
ticular the difference is the same whether we pass direct from 
one to the other, or through an intermediate fluid of any pro- 
perties whatsoever. 
It is evident that the enormous pressure which Laplace's 
theory indicates as prevalent in the interior of liquids cannot 
be submitted to any direct test. Capillary observations can 
neither prove nor disprove it. But it seems to have been 
thought that the relation 
K 13 =K 13 + K 23 (2) 
implies a corresponding relation between the capillary con- 
stants 
Hi3=H 12 + H 2 3; (3) 
and the fact that (3) is inconsistent with observation is sup- 
posed to throw doubts upon (2). Indeed Mr. Riley*, in his 
interesting remarks upon Capillary Phenomena, goes the 
length of asserting that, according to Laplace, K is a function 
of H. It is thus important to show that Laplace's principles, 
even in their most restricted form, are consistent with the vio- 
lation of (3). 
In attempting calculations of this kind we must make some 
assumption as to the forces in operation when more than one 
kind of fluid is concerned. The simplest supposition is that 
* Loc, cit. p. 193. 
