DR. S. CHAPMAN ON THE SOLAR AND LUNAR 
26 
potential in a way which allows of a comparison with Fritsche’s and the present 
results. 
Table E.—Comparison of the Potential Functions determined by Fritsche and in 
this Paper, from Vertical Force Data. 
Annual terms. 
Seasonal terms. 
Present paper. 
Present paper. 
Fritsche. 
Fritsche. 
1902. 
1905. 
1902. 
1905. 
AA 
-32 
-39 
-25 
Al 1 
- 10 
-4 
-25 
Bo 1 
6 
13 
31 
BP 
0 
- 1 
- 16 
A3 3 
-5-5 
-7-9 
-3-4 
A3 1 
-7-7 
- 14-0 
- 12-4 
0-5 
-0-2 
3-3 
B3 1 
-3-5 
- 2-5 
o-o 
a 4 * 
-0-58 
-0-79 
-0-66 
Ao 2 
-3-4 
- 1-5 
- 3-9 
b 4 * 
0-26 
0-30 
0-30 
B-P 
2-5 
2-6 
5-6 
Ad 
-0-8 
- D4 
o-i 
Bd 
-0-4 
- 0-4 
- 1-4 
11. The Separation of the External and Internal Solar Diurnal Variation Fields. 
The equations (ll) and (12) indicate how we may determine the respectively 
internal and external parts of the magnetic variation fields by means of the 
horizontal and vertical force potential coefficients A m n , B m ", A m n , B,/. Thus we have 
= (»»+1 )A;iA; f , (771+1) B,;, n + B,' 
2m +1 ’ 2m +1 
(15) 
E rt 
(a) 
(16) 
T n 
1 m(a) 
= mAf-Af 
2 m+ 1 
Tn 
7)i ( b) 
mB„, w -B„; 
2 m+ 1 
At the earth’s surface (r = R) the value of the term ff/V in the magnetic 
variation potential is (cf. (3)) 
(D) W/B = {(E” m(a) + I n m fo)) cos nt+ (E n m (« + P m «,)) sin nt} Qf 
= - { E m n cos (nt + e m n ) + If cos (nt + if) } Q f. 
where in the last two lines the external and internal parts have been transformed in 
terms of their amplitudes and phases ; these are connected with E* m ( 0 ), &c., by the 
equations 
(18) 
(19) 
E" 
m (a) 
■E,y cos e„ 
E n m(b) = E,/ sin e 
I n m (b) = I m” sin i„ 
I n m(a) = COS if, 
