of Quasi-permanent Systems of Electrons. 449 
On the hypothesis of expanding electrons, the intrinsic 
electromagnetic energy of each electron of the ring diminishes 
at the rate C 2 /3 2 m -, where a is the radius of the electron. 
a 
In consequence a tangential pull is exerted on each electron 
by the aether, due to the expansion, and a drag, due to the 
radiation ; the velocity of the ring increases or decreases until 
the pull and drag balance. When this state is reached the 
radiation from the ring takes place at the expense of the 
intrinsic energy of its electrons ; and we have 
a 
Hence we get 
v' 
/I'y.exp. 2^7-i-log 1 _ \ = ^/2ir--f--=ct, . (bj 
when n is large ; and 
\'2n±l tW ~ 2 -J- a 2a/2tt' 
when n is small. 
§ 19. If we do not accept the hypothesis of an expanding 
electron, but adopt hypothesis (B), all we can assert is that the 
radiation R is at most at the rate of one 10~ 12 th of the instan- 
taneous kinetic energy, or thereabouts (§ 16). 
The kinetic energy of the ring is of the order 
inC 2 m/3 2 . 
Hence we get 
R<10- 12 .inC 2 m/3 2 , 
V« 3 7 • exp. 2n (y-ilog £*) < \J\ . 10-».9j£<«>, (8) 
when n is large ; and 
n8(n + 1) (*aY»»<i 10-12 CW<— ?L- m (9 ) 
when n is small 
We notice that the conditions (6), (7) and (8), (9) differ 
only by having a sign of equality replaced by one of inequality. 
