496 
PROFESSOR A. SCHUSTER ON THE DIURNAL 
where p is equal to and m is equal to 1 for the diurnal variation, and equal to 
2 for the semidiurnal variation. 
Table XXL gives the same quantities for n =■ 4. 
An example may render the use of the Table more intelligible. Let the Earth, for 
instance, have a uniform specific resistance, which in C.G.S. units is 1'23 X 10^®, and 
consider that term of the magnetic potential which, on the surface of the Earth, has 
the form . . 
A sm u cos u cos > 
where T is the time of the revolution of the Earth. This term alone represents 
fairly well the characteristic features of the diurnal variation. Here, as n = 2, we 
may use Table XX. The value of S corresponding to the assumed resistance is 30) 
and we find c = — ‘5 approximately, which means that the vertical force due to the 
induced currents has half the amplitude of the vertical force due to the primary 
currents; also, the difference in phase is 41°; as the sign of the amplitude is changed, 
this means that the minimum of the vertical force due to induced currents takes place 
not quite three hours after the maximum of the corresponding primary force. Similarly 
the horizontal force due to the inside current is only one-third of the corresponding 
horizontal force due to the outside potential, and here the maximum due to the 
secondary currents takes place nearly three hours after the maximum due to the 
secondary currents. To get similar numbers for the semidiurnal variation we should 
have to put m = 2, and find c, c, and a for 8 = 60, because p = 1'23 X 10^® 
— 2 X 6T5 X 10^^, and looking up 6T5 X 10^^ in the last column we should find the 
corresponding number in the first column to be 60. 
Table XX.—Comparison of the magnetic forces due to a system of varying electric 
currents outside the Earth, with the forces due to the currents induced mside 
the Earth, n = 2. 
d. 
c. 
Ratio of normal 
forces due to 
secondary and primary 
variation. 
c'. 
Ratio of tangential 
forces due to 
secondary and primary 
variation. 
a. 
Difference of phase. 
Corresponding value of p. 
1 
- -02854 
+ -01903 
87 27i 
3-70 X 10^^ X m. 
2 
•05688 
•03792 
84 65| 
1-85 X 101^ 
3 
•08484 
•05656 
82 25 
1-23 X 101^ 
4 
•11226 
•07484 
79 57 
9-25 X 1013 
5 
•13895 
•09263 
77 32i 
7-40 X 1013 
6 
•16479 
•10986 
75 lOi 
6-17 X 1013 
7 
•18968 
•12645 
72 53 
5-29 X 1013 
8 
•21354 
•14236 
70 41 
4-63 X 1013 
9 
•23633 
•15755 
68 32 
4-11 X 1013 
10 
•25799 
•17199 
66 29 
3-70 X 1013 
20 
•41771 
•27847 
60 32 
1-85 X 1013 
30 
•50520 
•33680 
41 03 
1-23 X 1013 
40 
•56158 
•37439 
35 11 
9-25 X 1012 
60 
•59864 
•39909 
31 11 
7-40 X 1012 
100 
•69949 
•46632 
21 33 
3-70 X 1012 
