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. 359
In the case n = 1, the equation (71) takes the form tan z= z; whence
z/7r =1-4303, 2-4590, 3-4709,...........................(73)".
Corresponding to any one of these roots we have a simple-harmonie electric oscillation of
frequency
o z C.................................. (7 4 ),
27r 7r 2K2a(
and wave-length
X = 2K a.......................................(75).
77
To calculate the rate of decay of the oscillations, which is relatively very slow, we should
have to proceed to a higher degree of approximation.
In the second type, we have, from (32), with / = 1,
han',' (ha) kafn' (ka)
++(() =fnff()).................................. (76),
4n(ha) f,,(ka)(7,,,n- (ha) f_ (ka)
or....- f (C.................(77).
01 n(ha) fq,(ka) *** ** ** *- *(*),
This is satisfied approximately by ha = z, where z is a root of
(z) = 0.........................................(78),
and more accurately by
ha={1-(2n-l)K} z......................(.. 79).
When n= 1, (78) takes the form sinz = 0, whence
z/ r= 1, 2, 3,.........................................(80).
7. When in the problem of ~ 2 the extraneous disturbance has a period coincident,
or nearly coincident, with that of a free vibration, the approximate formulae (33) and
(34) will no longer apply. If in the accurate formula (31) we make the substitution
f (ka) = (ka)- in (ka)................................. (81),
we find that it takes the form
T __ g (ha)
Til 0G(ha)-ig(ha)...(82),
where g(ha) stands for the expression in the numeratort of (31), and G(ha) is derived
from g (ha) by the substitution of *, (ka) for, (ka). The modulus of the expression
* The lines of electric force in the sphere are for the in Electricity and Mlagnetism, p. 317.
most part closed curves in planes through the axis of the t Which may be regarded as a function of ha since the
harmonic T1. Their forms are given in Phil. Trans., Pt. ii. ratio of hk to 17 is fixed.
1883, p. 532; and in J. J. Thomson's Recent Researches