Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

OF SELECTIVE ABSORPTION OF LIGHT BY A GAS. 353
We have next to consider the conditions to be satisfied at the surface r = a. It
appears at once from (16) and (22) that the solenoidal conditions of electric and magnetic
induction require that
4an (ka) T, + fn (ka) Tn' = KJn (ha) Tn"...........................(27),
qn (ka) Un +f, (hka) Un = =Vîn (ha) U.......................... (28).
Again, it is easily seen that the continuity of the tangential components of electric
and magnetic force implies the continuity of the vectors
(yZ-zY, zX-xZ, xY-yX)
and (yy - z/3, za - xy, x/ - ya), respectively.
Hence from (18), (19), and (24), (25), we have, in addition
'kaJ (a ( 1),' + ( T f' (a) + (n + 1) (k l)fn ('Ca)} Tn
= {haC ' (ha) + (n + 1) n (/ha)} 2...........................(29),
and {kaa,,r (Ia) + (n + 1) (/ca)}n U' + kaf,,' (aa) + (n + 1) f,. (aka)} Un`
= {han,,' (ha) + ( + 1),, (ha)} U,,'...........................(30).
Hence
Tn _ Kn (ha) {karn,, (ka) + (n + 1) n, (Ca)} - {haS,,' (ha) + (n + 1),n (ha)} ', (ka)
Tn ~ K+,n (ha) {af,' (kIa) (+ +)fn. (ka)} - {ha,,'(ha) + (n + 1),n (ha)} fn (ka).....................(31),
Un p î,n (ha) {ka4rn' (ha) + (n + 1) f, (ha)} - {han' (ha) + (n 4+ 1) în (ha)} -n (ka)
Un urn (ha) {kaf,' (ka) + (n + 1) fn (ka)} - {han,,' (ha) + (n + 1),,n (ha)}f,, (ka)..................... (32).
We shall suppose that the wave-length of the disturbance in the aether is large
compared with the circumference of the sphere, so that ka is a small quantity. If we
were further to assume that K and, are not greatly different from unity, so that ha
is also small, we should obtain at once approxiiimate expressions equivalent to those given
by Prof. Love, viz.
nK +(n+) {1.3...(2n-1)}2 (2n, + 1) n..
(n + 1) (/ - 1).... (34).
n= + (n + ) '{1. 3... (2 )(2- z + 1)' U.... --
It is our present object, however, to examine the case where K is large. For
simplicity we shall suppose that /u = 1, so that K = h'/k2. It will be found that the first
factors on the right hand of (33) and (34) must be replaced by
(n + ) (K- - ) n, (ha)-...
(nK+n + l)i n(ha)+...
VOL. XVIII. 45