564 
Proceedings of the Royal Society 
But if E be very small the second term is of more importance 
than the first. The following are rough approximations only : — 
K 
r 
P 
in. 
K 
Po 
O-OOOl 
•75 
2-3 
0-00001 
•3 
35 
0-000001 
•1 
1000 
0-0000001 
•03 
33,000. 
1 whose radius is 
•00001 
inch, which 
smallest that can he observed by means of a good microscope, con- 
tains air compressed to 11 atmospheres only. 
When the bubble is detached from the fluid each of its surfaces 
contributes its share to the excess of internal, over external pres- 
sure. (W. Thomson, Proc, R. S. 1858.) In this case the equation 
above becomes 
4T 
(e) (e) “ ^ ~ 
at least until r becomes so small that the thickness of the film 
must be taken into account. The following numbers, therefore, 
refer to the case of vesicular vapour which is supposed by Clausius 
and others to account for the blue of the sky and the morning and 
evening red. As I have considered it unnecessary to allow for the 
thickness of the film, the later results are too large : — 
r. 
in. 
■R 
Po 
0-0001 
•62 
4-: 
0-00001 
•22 
94 
0-000001 
■07 
2740 
0-0000001 
•022 
98,000. 
Little is gained towards a closer approximation by applying 
analysis such as that of Laplace or G-auss to this question. If we 
express by c/)(r) the law of molecular action as depending on the 
distance, we know merely that <j> is insensible for sensible values 
of r. The complete solution of the problem can, no doubt, be given 
by a direct application of Laplace’s process. Thus, if we write 
ij/ (r) z=z frdr f ^ (r) cZr, 
the attraction of a uniform spherical shell, of radius a, on an 
