690 Mr. W. Sutherland on the Electric 
We ean write 1—d and 1—e in the forms 
2—(1+ 8)? and 2—-(1—f)* . . . a 
It seems to me that we may regard the electrons as attract- 
ing or repelling one another by means of inward or outward 
oncanan radiated with the velocity V of light, so that the — 
force of attraction or repulsion is proportional to Vi.) a 
something, say the ether, is radiating outwards and inwards 
in all directions from and to an electron with velocity V, 
then the mean squared relative velocity of the ether from 
any two electrons is V?+ V%, similarly to the known result 
for the kinetic theory of gases. Now suppose this mean 
squared relative velocity i is an absolute constant of the eether. 
If a positive electron imparts an additional velocity v to the 
ether radiating from or to it, two positive electrons can affect 
one another only as though each had a squared velocity 
2V?—(V +v)? available for mutual action. If each negative 
electron imparts an additional velocity —v to the ether 
leaving or entering it, subject to the condition that for the 
ether the squared relative velocity has the constant value 
2V?, then the negative electrons have each 2V?—(V—v)? 
available for the communication of momentum to one another. 
These take the place of the V? which would be available if v 
were 0; henee the rate of communication of momentum is 
altered by v in the ratio 2V?— Cs ahe V?=2—(1+0/V)? 
for %, and in the ratio 2—(1—v/V)*: 1 tor ». Our fraction 
8 stands thus for v/V. Probably this velocity v exists only 
when the electrons are coupled up as doublets, the positive 
electron pouring out ether like a source, while the negative 
absorbs it like a sink at the same rate. 
For the communication of momentum between $ in one 
doublet and b in another, we may make two assumptions as 
to the available squared velocity ; first we may make it 
2V?—(V+0—v)2= V2, 
a result corresponding to the law e?/r? assumed at the start 
of this investigation: second, we may take the available 
amount to be 
A eS cy, -- v) (V—v) — Vy? a ae 
which would correspond to a law of attraction (1+?) e/9? 
between $ and b in place of our original e’/7*. This secona 
law seems preferable, for it gives for the total available 
squared velocity in the four electrons of two doublets the sum 
2V?2—(V+r}2+2V2—(V —v)? 
+219V2—(Vi— py) =4V2, . (18) 
