170 
ME. ARTHUR SCHUSTER ON THE 
of about 30 miles which shows itself in its effect on seismic waves, and, according to 
Strutt, contains the radioactive matter. On the other hand, it is quite likely that 
the outer shell is identical with that which the discussion of the propagation of 
seismic waves shows to have different elastic properties from the nucleus, and which, 
according to Wiechert’s recent researches, has a thickness of 1500 kilometres. 
The observations show that the internal potential has a value equal to one-fourth 
of the external one, or that the external potential represents 0 - 8 of the whole. For 
n = 3, using the same value of r 0 , we similarly find that the outside effect is 0'84 
times that of the whole. The coefficients in equation (9) should therefore be 
diminished by multiplying with 0'80 and 0‘84 respectively. 
6. We may now complete the investigation as far as it relates to uniform con¬ 
ductivities. The magnetic and geographical poles of the earth not coinciding, the 
vertical force is not simply proportional to the cosine of the colatitude, but a term 
must be added proportional to sin 6 cos X, where X is measured from the meridian 
68° 31/ west of Greenwich, which is that containing the magnetic axis. I discuss the 
effect of the inclination of the magnetic axis somewhat in detail, as it will give us 
a good test of the proposed theory when suitable observations will be available. 
Leaving out the factor C tan <£, where C represents the vertical force at the 
geographical pole and the colatitude of the magnetic pole, the electric forces, as far 
as they concern us at present, are 
X = cos X^; Y = — sin 0 cos X . 
If these values be substituted in (3), the elimination of S leads to the equation 
cl 2 E 
cl , dxjj cl . 2a , clib 
— COS X -rf- + — Sill 6 COS X -r/r = 
r/X 
clX + eld 
cie 
d • a cl .R 
sin 0 cl\ 2 d0 Sm ~d0' 
( 11 ). 
It will be shown in Part II. that 
is equal to 
cos X ~ + cos X ~ sin 2 6 ~ j ijj/ sin cr (X + t — a) 
w 
here 
I o ' , [_( a i x Pn-\ a r 1 + fri'K+F ') sin {<x(X + /) + X — a} 
-jlC i 1 
+ (cg/u-F - 1 + M'n+i' 7-1 ) sin {cr (X + t)- X —a}], 
cq = n — 1 . n+1 ; 
— hi = n . n + 2 ; — ct 2 = (n— 1) (n+ 1) (r+<x) (n + cr—1) ; 
b 2 = n.n + 2 . (n— o-+1). (n— o- + 2). 
The only case necessary to consider is that in which n = cr, when = 0, so that 
we may disregard the factor a v If n = or — 1, then h x = -3 ; a 2 = 0 ; b 2 = 6 ; and if 
n = cr = 2, then b : — — 8 ; a 2 — — 36 ; b 2 =16. 
