92 
the equation of no dilatation, and the conditions of the 
problem. While the terms 
7 ] -1 
hxz^ 
rn _ ^ 
contribute no components to the XT’s and Y’s for the limit 
r = ^17, and finite terms at all boundaries. The addition of 
these terms merely makes the solution symmetrical, and aids 
us in comparison. If I had also added 
ru _ ^ 
I should have obtained a solution identical with that of 
Professor Stokes, but although these terms do not contribute 
components to the U’s and V’s for the limit r = x, they con- 
tribute finite terms if the boundary is a circle whether the 
circle be great or small. The solutions also differ in the 
addition in my theory of a complementary function de- 
pendent upon the form of a finite boundary. The possi- 
bility of the existence of such a function, and the way 
in which it has been used to provide terms in and C-i 
vitiates altogether the argument of Professor Stokes as to 
the direction of the displacement which (Papers vol. II., page 
284) he makes to depend upon = r : 0 : which will 
not be the case unless we admit the terms which I maintain 
not to be admissible, and even then not unless the boundaries 
are such that the complementary function vanishes. 
Note, Jan. 8, 188G. — ^The resultant displacement following 
from (4) agrees in magnitude with that found by Prof Stokes 
for sound. Vol. 2, page 286, note. — E.F.G. 
X. 
In the Philosophical Magazine for June, 1884, Professor 
Kowland published a paper on “ Spherical Waves of Light 
and the Dynamical Theory of Diffraction,” proposing a form 
