686 Mr. W. Sutherland on the Electric 
between % in the first pair and b in the second be e,e9/7*, and 
vice versa. Let the repulsion between $ in the first and J in 
the second be (1—d)e,?/7?, and the repulsion between b in 
the first and ) in the second be (1—c)e,?/r*. The fractions 
b and ¢ will be shown to be small and of opposite sign. 
Probably the law of attraction between =i in one doublet and 
fy in another is more strictly (1+6)e,e,/7", where 6 is of the 
order L? or c2, but we neglect & for the present. The total 
attraction between the two doublets is 
{—e (1 —b)—e,?(1—e) + 2¢,e9\/7? 
= {—(e, 9}? + be? + ce7h/r?.. . (1) 
Now by J. J. Thomson’s evaluation of. the inertia 2 of an 
electron of charge e in electrostatic units spread over the 
surface of a sphere of radius a, we have 1= 2e?/3aV’, where V 
is the velocity of light. For other distributions of the charge 
é the coefficient 2/3 must be altered. Let us then write 
2 2 ey 2 2 Cy 
i= 3 aV.?” lg= = aoVe? Ps . = ° (2) 
and then for the attraction between two doublets we write 
(1) in the form 
a — (4,0, V1 "/e — 12 V9"/e3) : 
+ bia? Vy" /e,? + ctg°ay” Vo*/e97}/477. . . (8) 
The first point to notice about this expression is that, if } 
and ¢ are 0, the foree must be a repulsion and could not 
account for gravitation. ‘This fact gives the clue to the most 
convenient simplification to be made in (8), namely, that of 
assuming that the repulsive term (i,a,V, */[e1 = ta V9" [e2)? 
vanishes. We may also try the effect of assuming V,= V,= V 
and we then have e,=¢,, and may denote each by . We 
have also 1,4, = 1242, and may denote each by ia. The attrac- 
tion (8) now becomes 
9(b-+-c)2? a" V*/Ae*r*. 4. 2. en 
If now there are n, doublets in one atom of mass m,, and 
my in another of mass my, at distance 7, the total attraction 
between the atoms is n,n times (4). 
But 2nji=in, and oe so that the attraction is 
9(b+¢)m,meV*/l6er". . . ae 
If G is the constant of gravitation (C.G.s.) then (5) ex- 
presses the electric origin of gravitation on condition that 
G=90+0)eV4/162... 2 a 
