176 
ME. ARTHUE SCHUSTER ON THE 
The left-hand side is transformed, as shown in the Appendix, the result being given 
in (22). We thus find R/ expressible as a sum of four terms— 
2(2n+l)(n+l)R„W +1 = ynQ n+1 ' + \ 
2 (2 n+ 1 ) n. R n _ 1 °' +1 = — y (n+ 1) Q n _i°’ +1 , 
2 ( 2?i + 1) (n + 1) ft n+1 tr 1 = — yn (n — <j +1) (n — cr + 2) Q n +P 1 , 
2 (2 n +1 )n (n— 1) R^p -1 = y(n— 1) (n+ 1) (n + cr) (n + a— 1) Q^W 1 - 
For Q/ we must substitute -g-CA^ 1 and u-CA 2 ^ 3 2 when treating of the diurnal 
and semidiurnal variations respectively, where i// 2 x and are the harmonics of type 
and degree indicated which have the same factors as the current functions \pi and \jj 2 2 . 
To get the magnetic potential, a further multiplication by — in (n + l)/2n +1 is 
required. We see that each barometric variation now leads to six terms in the 
magnetic potential, the factors of —npoeAGCl/ being collected in the following 
table :— 
Diurnal Variation. 
Velocity Potential : A 1 xf/ 1 \ Magnetic Potential : — 7r/) 0 eA 1 C2B„ o Tl/. 
Values of B/: 
n = 1. 
n = 2. 
n — 3. 
o 
II 
b 
2 
16 
5 7 
105 7 
0 
9 
QO 
1 
> 
5 7 
5 
O- j 
Ms 7 
2 
— 
— 
8 
315 7 
Semidiurnal Variation. 
Velocity Potential : — Trp 0 eA 2 G'AQ H a £l/. Barometric Variation : A 2 i|/ 2 2 . 
Values of B/ :—- 
<H 
II 
n — 3. 
n = 4. 
cr = 1 
64 
2 
105 7 
~ 21 7 
2 
32 , 
105 7 
32 
«>| 
Oil 
105 
3 
— 
— 
1 
63 7 
C = Vertical force at geographical North Pole„ measured upwards. 
p 0 = Electric conductivity of atmospheric shell. 
e = Thickness of atmospheric shell. 
