TRANSACTIONS OF SECTION A. 437 
The value of the momentum depends of course on the shape of the electron. 
I will not discuss this matter in detail, because the second force of which I shall 
speak is independent of the shape and size of the electron. It is closely connected 
with the radiation of a point-change by the relations 
(8) | “dt 38; = ~ Wary 
1 
(9) | ae RK, =—-G,,, 
1 
where W,,, G,, are the radiated energy and the radiated momentum respectively, 
They are given by 
y a2 (7a (9 4 9)” 
Wi=22 | (9°, G8)") | 
‘a sag a tel a 
r 26 (74, 9 (8, (aH) ) 
a= ag | de 218+ 8571, 
(11) Wom 3e3 [ae 318 +'3 | 
with c®=1— £?. 
I gave these values in ‘ Annalen der Physik 10,’ p. 156, 1903, the paper being 
sent in on October 23, 1902. The same formulee have keen found independently 
by O. Heaviside, ‘ Nature,’ 6 T., p. 6, November 6, 1902. 
Now the required force §;'’, substituted in (8) and (9), must give these values 
of W,,, G,,. Wecan show that with these conditions &;” is determined com- 
pletely, if we take into consideration that the complete value §; of the reaction 
of the field can be regarded as an expansion in ascending powers of 4, G, .. ., 
and that the general value of #;’’ must be of the same dimensions as 6g without 
containing a power of the radius as factor. The most general expression of this 
sort is zero, if it gives zero both for radiated energy and radiated momentum. 
From this it follows that the proposed problem has only one solution. 
This solution is 
(12) Hy’ =35 {3 9099) , 2900), Salo 
Ro et CK | 
Indeed, you get 
kK c? K® 
gi’ =0{99 208), 
\ 
and, because §=o for ¢,, ¢,, integration by parts gives 
fi2298- — (ae (8+ 90)" 
TK 1 kK cK | 
hence 
fae g 8," = —b fae { + (9) |, 
Kt oe? KS 
in agreement with (10). 
On the other hand, you get by integration by parts 
fae {8 +389 ae (28 +5808) , 40090), 
ed deri i Gace Ba A 
kK cK 
Therefore the time integral of #;’’ is equal to — G,,. 
Hence (12) is the general expression of the reaction of the radiation ona 
point-charge, moving with a velocity smaller than the velocity of light. 
Consider some examples. 
2 
a. Uniform Motion along a Cirele—You have § 1 9, §= —9Z,, r being the 
= 
radius of the circle. 
Equation (12) gives 
