( 679 ) 
on the square of v. Let there be a single radiating particle in the 
origin of coordinates, and let it have an electric moment 
mM, = a cos nt, 
in the direction of O Y. In order to find the dielectric displacement ò 
and the magnetic force in the surrounding field, we may start 
from the formulae, I have developed in $ 33 of my „Versuch einer 
Theorie der electrischen und optischen Erscheinungen in bewegten 
Korpern”. Let the velocity v of the earth be in the direction of 
OX, let r be the distance to O, 
Papo ee. . ° . . . . id . (1) 
3 
and 
as — cos n (e — =). 
c 
Then 
4% 1 dw 
o— An Oxon oy : 
1/8 ay vB 
je alse xa) Anc? Ot'dx’ 
— pene Bo ’ 
Dr = aye 
dw 
Dy ins # Oeay ’ 
dw dw zy, 
bs = a9, sti): 
The auxiliary quantity w is to be regarded as a function of 2, y, z, ¢, 
and it is only after the differentiations have been performed, that 
the value (1) must be substituted. 
We may further confine ourselves to values of r, very much larger 
than the wave-length 4. In this case we have only to retain the 
terms whose denominator has the first power of 7, all other terms 
9 
À2 
À 
being, with respect to these, of the order — or a For points 
7 lod - 
situated on the positive axis of «, we find 
o>; = 05.0; = Fe 
De — 0 Pl Dy = 0, 
n° v\ a vz 
A) Wied al + =) * cos n}e— (1 > -)=\, 
c PAN 2 ( e/e j 
45 
Proceedings Royal Acad. Amsterdam Vol. IV. 
