Conway—On Series in Spectra. 183 
These are evidently ‘‘asymptotic”? expansions of function 
which have a resemblance to the solutions of Riccatti’s equation 
which differ by factors from Bessel functions. 
In the second place, we consider how this field of force might 
arise. Suppose that it is due to a sphere of electrical matter 
which for brevity we may call the atom. Suppose further that 
this atom is capable of itself vibrating much the same as an 
elastic sphere forming nodal surfaces, and that in consequence the 
electric force due to the disturbed motion is given by £’ (1) cos nt, 
where HE’ cos nt is the amount of disturbed electricity, and 
6 (0) = (sin mr (po BE...) + cos mr Ba sal 
and n/m is the velocity of these elastic vibrations, supposed slow 
compared with that of light. If the electric force in the undis- 
turbed condition is Hw (r) where # is the charge, then, when 
oscillations are set up, the force becomes 
(E — E’ cos nt) p (r) + E’ cos nt ¢ (7), 
so that at a node 7 =a, such that ¢ (a) = 0, equilibrium is usually 
impossible until the amplitude of the “elastic”? vibrations becomes 
so great that H’ = H; then the node is a place of equilibrium when 
cosnt = 0. As these oscillations are slow, an electron can remain 
at a node sufficiently long to give a great number of light 
vibrations. 
ie) 
a 
SCIENT. PROC. R.D.S., VOL. XI., NO. XVI. 
