THE ELECTRIC AND LUMENTEEROUS MEDIUH. 
813 
now be formed in the Lagrangian manner, and will hold good so long as the motions 
are fairly slow compared with radiation. 
The question however arises whether we should not associate with the electric 
inertia of an ion of this kind a much greater inertia of matter to which the ion 
belongs. When we trace as above the consecjuences of refraining from doing so, we 
arrive at the result that these free electrons can be projected by their mutual actions, 
with velocities which are a considerable fraction of that of radiation. Bearing in 
mind the phenomena of the Solar corona and of comets’ tails, and certain electric 
phenomena in vacuum tubes,^ where some modification of the aether which affects 
light by reflexion and otherwise is projected with velocities of that order, there seems 
to be no reason for the summary exclusion of such an hypothesis as the present,! 
especially as an electrically neutral molecule could attain no such velocities, and would 
comport itself more like ordinary matter. 
118. The circumstances of steady motion may be illustrated by a calculation for 
the case of two electrons ; the same method would clearly also apply to a greater 
number. The kinetic energy of twm electrons and e^, wdiose co-ordinates are 
{rTi s-'j) and {x^ z.^), moving under their mutual influence, is, by § 117, 
T = + yp + rq-j -f + y./ + z^) -f {2x^Xo y^y.j -f 
the axis of x being parallel to their mutual distance r. 
Let us take the case when they revolve steadily in the plane of xy with angular 
velocity o) round a common centre, at distances r\, from it, where vq -f- ro =: r. The 
kinetic reaction on resolved parallel to x is 
(It clx^ 
dl _ T ^ I I Xq 
C-iCci_ 
cos e (2x^x, + y^y., + 
in which 0, the angle between ?■ and x, is null; while rq = Xo = — yi = 
y^ = — &j 7 q. On equating this to the electrostatic attraction, we have 
Similarly 
Hence 
T 9 t 0 ^ ” 
~ ”■) — (^ 2^2 ) ^ 2 ^ 2 ’ 
* Professor FitzGeraj.d suggests the addition to this list of auroras and magnetic storms, 
t Professor J. J. Thomson informs me that he finds the velocity of the negative rays in vacuum tubes 
to be about 2 X 10^ c.g.s. 
