DIURNAL VARIATIONS OF TERRESTRIAL MAGNETISM. 
37 
The simplest hypothesis, that of a uniformly conducting earth, will first be 
considered. Lamb’s theory enables the amplitude ratio f and phase difference a, to 
be calculated for a uniformly conducting sphere of radius R and specific resistance p 
for any harmonic term Q m n in the potential of the external primary variation field. 
Tables giving equivalent results for certain values of p and m are to be found in 
Schuster’s paper, but as they are insufficient for the more extensive observational 
data of Table I further calculations have been made which are summarized in 
Table K. Where the two sets of values of f and a overlap they are in agreement. 
The Table K gives the values of f and a corresponding to the two variables m and S 
on which they depend ; S is defined by the equation 
1 8ir 2 nR? 
N p ’ 
where N, the number of seconds in a day (the period corresponding to n — l), is 
equal to 86,400 in the case of the solar diurnal magnetic variation, and 89,500 
(approximately) in the case of the lunar diurnal variations. 
On the hypothesis that the whole earth is uniformly conducting, we must take 
it = R (| 9), and 2-7tR = 4 . 10 9 cm. Hence for the solar diurnal magnetic variations 
4 . 10 H n . 
1'08 P ' 
and for the lunar diurnal variations 
4. 10 li n 
112 p 
Table K.—Amplitude Ratios /’and Phase Difference a between a Primary (External) 
and Secondary (Internal) Magnetic Field, Induced in a Sphere of Uniform 
Conductivity corresponding to Spherical Harmonics of Various Degrees m, 
and for Various Values of S, or the Ratio Frequency/Resistivity. 
a 
m = 
= 1. 
m = 
_ O 
m = 
= 3. 
m = 
= 4. 
m = 
= 5. 
./'■ 
CL. 
/■ 
cl. 
./• 
a. 
/. 
CL. 
/• 
CL. 
10 
4-21 
o 
47-9 
5-82 
0 
66 ■ 5 
8 
•73 
o 
75 • 4 
12-60 
o 
80-4 
17-32 
o 
83-1 
20 
3-24 
31-9 
3-59 
50-5 
4 
•82 
63-5 
6-62 
71-5 
8-89 
76-5 
30 
2-95 
25-2^ 
2-96 
41-1 
3 
•64 
54-2 
4-73 
63-8 
6-17 
70-5 
50 
2-70 
18-9 
2-50 
31-2 
2 
•80 
42-6 
3 ■ 35 
52 -5 
4-12 
60 o 
80 
2-53 
14-6 
2-24 
24-3 
2 
•36 
33-6 
2-65 
42-1 
3-07 
50-0 
100 
2-47 
13-1 
2-14 
21-6 
2 
■21 
29-9 
2-43 
37-8 
2-76 
45-0 
162 
2-36 
10-1 
1-98 
16-7 
i 
•98 
23-3 
2-10 
29-5 
2-27 
35-9 
200 
2-32 
9-0 
1-93 
15-0 
i 
•90 
20-9 
1-98 
26-7 
2-11 
32-3 
288 
2-27 
7-3 
1-85 
12-4 
i 
•79 
17-4 
1-83 
22 * 2 
1-92 
27-0 
338 
— 
— 
— 
i 
• 75 
15-9 
1-77 
20-4 
1 • 85 
24-9 
450 
— 
— 
— 
— 
i 
■68 
13-8 
1 • 69 
17-7 
1-74 
21-5 
612 
. 
— — 
• 
— 
— 
— 
1-65 
18-4 
