
of Lqects of Motion through the dither. 623 
had already led to the recognition of absence of optical result 
up to the second order of the ratio of the velocities. Thus 
the question was suggested whether the above correspondence 
between the resting and convected systems can be effectively 
extended up to the second order. It is, in fact, found that 
the Maxwellian cireuital equations of ethereal activity, in 
the ambient ether, referred to axes moving along with the 
uniform velocity of convection v. can be reduced to the same 
form as for axes at rest, up to and including (v/c)’, but not 
(v/c)*, by adopting a local time e—?(¢—va/c?) as before, but 
1 
with a new unit e~®, and also areduced unit of length parallel 
zh 
to x equal to e~ ®, where here and in what follows e represents 
1+ v?/c?, the units of length along y andz remaining unaltered. 
It is found that for two ether-tields, one referred to fixed 
axes and the other to moving axes, standing in this mutual 
correlation, the electrons, or poles, in approaching which the 
zethereal electric vector becomes infinite as er}, are situated at 
corresponding points and are of equal values: the relation, 
exact to the second order, is now that 
(7, 9, h) and (a, 6, ¢) 
in the field belonging to the fixed system of poles correspond 
tO 
G 
tole 
€ 
v U 
—s . g—_- ——— } ieee; 
(< Jo I tare is tac? \) 
and e(€—2d, b+-47rvh, c—47ug) 
for the field belonging to the convected system; where 
éis 1+v?/c’, as above, the factor e& being needed to make 
corresponding poles equal in value instead of merely pro- 
portional. 
If each pole or electron is connected with a molecule pos- 
sessing extraneous mass, and it may be having an extraneous 
field of gravitational and other force of its own, and thereby 
interacting with other molecules, we shall want to know the 
forces exerted on that molecule by the surrounding ether, in 
order to form its own equations of motion, which must be 
combined with those of the ather-field around it in order to 
constitute a complete system. But if such other forces are 
molecularly insignificant, or better, if the electron is a mere 
passive pole—nucleus of beknottedness in some way—in 
the zther, conditioned and controlled entirely by the sether 
around it, just as a vortex ring is conditioned by the 
fuid in which it subsists and is also carried along thereby, 
then, as in the familiar hydrodynamics of vortices, the motion 
ot the ether determines the motion of the entirely passive 
