DIURNAL VARIATIONS OF TERRESTRIAL MAGNETISM. 
65 
Only the external variation field is considered here, of course. The corresponding 
terms in the current function IX are consequently (cf 68) given by 
(85) ^ y - 10 IX - 63Q.J 1 cos (£ + 33°) + 87Q 3 2 cos (2£ + 26°) + 0'70Q i 3 cos (3£ + 40°) 
Xi/ 
= 189 sin 6 cos 6 cos (t + 33) +130 sin 2 6 cos 6 cos (2£ + 26°) 
+ 74 sin 3 6 cos 6 cos (3£ + 40°) 
neglecting the factors (Rfor simplicity. 
The energy expended per second in overcoming the resistance to current flow, in 
the conducting layer of thickness e, as given by 
( 86 ) 
+ 
six 
8IX 
,R d6j ' \R sin 6 8a 
R 2 sin 0 dO d\. 
In order to avoid excessive calculation, several approximations will be made. The 
current function (85) is such that the currents in the dark hemisphere are small, the 
various harmonics largely neutralizing one another there, and reinforcing one another 
in the sun-lit hemisphere. We shall imagine the three terms of (85) combined into 
one, however, which we shall suppose confined to one hemisphere. Since the sum of 
their squares is less than the square of their sum, we shall represent IX, for this 
purpose, by the approximation 
(87) 
200B • ,, „ 
-— sin 6 cos 6 cos 2 1. 
4tt . 10 b 
Also instead of the variable factor l/pe we shall use the constant approximation 
l/(pe) m , where (pe) m is an average value of (82) over the daylight hemisphere. The 
adopted value of ( pe) m will be # 8 . 10~ 6 or, allowing for the correction due to self- 
induction, approximately 10 -5 . 
When these values are substituted in (86), and the integration is taken over one 
hemisphere, the total expenditure of energy per second is found to be 
( 88 ) 
or, in watts, 
(89) 
2001 { \ 2 1 
v4tt. 107 10 •' ’ 
IQ"7 200R A 
10 -5 \47t . 107 
The mean value over this hemisphere, per unit area, expressed in gramme-water- 
centigrade units, is consequently 
(90) 
1 16 10~7 20OR r 
4'18 35 10- 5 Ut r. 107 
io- KJ . 
* Cf. the table of values of 1 + 3 cos w + f cos 2 <o on p. 303, 1 Phil, Trans.,’ A. vol. 213, 
VOL. COXVIII. A. K 
