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. 355
If we substitute the above values of Tn and Un in the formulæe (31) and (32) we
obtain the expressions for the scattered waves.
4. We have now to examine the form which the scattered waves assume at a great
distance from the origin. When kr is large we have
-.......................................
Hence, in the first type of solution, analogous to (14), we have
)nZ — i d / n S
Y - - _ p-k ( r nxrN"- - |
(kr)n e —ikr n - Zrn-2 T, )
n-i C -2
Y = e r T - yr T......................... (48),
(ïkr)n eik2 n nyrCl ln) "*
(kcr)n (C n d )),kry - z ) n Tn
knrn+l dz dyr
=n-inr d c\
i = in+ e-'kr -- r Tn\
( d
=brn+l e-ik ( ~d -Y dx ) rtrX!..
We notice that X, Y, Z are ultimately of the order 1/r, whilst the radial electric
force (X + y Y + zZ)/r is zero to the present order of approximation. It is really of
the order l /r2. The radial magnetic force (xa + y/3 + zy)/r is accurately zero. If the
contour-lines of the harmonic Tn' be traced on a sphere of large radius r, for equal
infinitesimal increments of Tn, the (alternating) magnetic force is everywhere in the
direction of these contours, and its amplitude is inversely proportional to the distance
between consecutive contours. The electric force is everywhere orthogonal to the contours,
and its amplitude is in a constant ratio to that of the- magnetic force*.
For instance, in the case n = 1, if T\` be of the type (45), the lines of electric
and magnetic force have the configuration of meridians and parallels of latitude, the
polar axis being represented by the axis of y.
In the second type, analogous to (20), we have
a - (k -ikr n __ n
r = -,e akr (Sd n UT\ - Zrn-2 Un )
* Cf. Proc. Lond. Math. Soc., t. xIII., p. 194.
45-2