1525 
dently equal to the already calculated one in (2, y, 2) from a moment 
in O. Terms with sin/é in that force will not yield a resistance 
to the motion (6). Therefore we further only need consider the 
9 
terms with cost. For the coefficient of 1,608 kt we find 
470 
Pre P82]. k kr 8d f 
on eh [sin = ue $2) — "cos (ne tr) (2) 
ik ( 4 c 
Comer r : c rt 
4. We might now add the expression (7) for every molecule, 
except the one in the origin. We can also find at once the mean 
value of that sum, by multiplying by the mean density in (we, y, 2) 
and afterwards integrating through the whole space. But here the 
difficulty arises that the integrals do not converge. Therefore we 
make use of the known fact that no extinction arises, and no resist- 
ance against the motion of the electrons, if the oscillators are quite 
regularly distributed through the whole space. The phenomenon 
which we want to calculate can thus only be caused by the devia- 
tion from the homogeneous distribution, as it is caused by the action 
of the molecule in the origin. The mean deviation of density at a 
distance r is exactly g(r). So we multiply (7) by g and by the 
element of volume dv dy dz and integrate through the whole space. 
To this end we introduce spherical coordinates, such that 
PLS y=rsin } sin ¢ 2 =rsin d cos p 
then the integration over g may be performed without difficulty 
and there remains 
k = ke Scos?d —1 k 
rf sin vanf gdr | | =7(1-+- eos? 3) — — ATR sin] = (Leco + 
& k 
+ 2 (5 cos ® — 1) cos a + u cos }) a (8) 
In this I put for g the value (5) and then performed the inte- 
grations over r. About the rather complicated calculations I will 
only mention that the integrations from O to d — the region for 
which the integrals appearing in (5) are variable — were separately 
performed, and that approximate values for a small # could be 
used for the integrals from d to co, which are of the type of the 
cosine-integral. 
The expression in cos 9 thus obtained, contains many terms which 
vanish afterwards by the integration with respect to 9. The other 
terms can be reduced to an integral of a rational fraction in cos 8, 
and these give finally the following result for (8) 
o 
98* 
