of Quasi-permanent Systems of Electrons. 455 
Neglecting higher powers he finds, for each value of l\ the 
following frequencies (relative): 
Axial vibrations — undamped (k = 0). 
q t J-K < h _ J-K 
6J 2^ CO 2v 
Orbited vibrations. 
Two undamped vibrations (« = 0). 
4N-L-2K-4M ? 4 _ 4N-L-2K + 43I 
yg =1+ ^i_ ^~ _, ^ = _i 
CO 
2i 
One damped vibration. 
qs _ 2M k 5 _ /3N 
w 
One vibration of instability of the same frequency. 
q% _ 2M K e _ _ /3^r 
ft) V CO V V 
The first four vibrations have relative frequencies very 
nearly equal to + &>. It must be noted that a negative fre- 
quency is to be interpreted as equivalent to an equal positive 
frequency. Hence in future negative frequencies will not 
be specially distinguished from equal positive ones. 
§ 25. These vibrations give rise to the following waves. 
Axial vibrations — two sets of undamped wave* for which 
the absolute frequencies are given by 
N, J-K N 2 -.J-K 
co Zv CO iv 
where h takes n values between + „ (§ 15). 
These frequencies are not all different. Since J— K is an 
even function of k, the frequencies (Nj) for k= — 1, — 2,... 
are the same as the frequencies (N 2 ) for k= -fl, +2, . . . and 
vice versa. Further we have J = 0, Ji=K. Thus omitting 
all zero frequencies we get finally a set of frequencies given 
by the scheme 
iv J 
Onlv those frequencies have been written down which can 
