ON THE EARTH’S MAGNETISM. 
391 
coefficients of that of the Earth or Venus, and vice versd ; for which purpose we must 
use equations (12) of Section II., viz. — 
2 w=R— i 2 1 r~ • /* *1 
[a m cosmz]— P s cos s - mz + Q a sin s ^ mz cos mz, 
which we will suppose to give the Earth’s coefficient p l} P s and Q s being the coefficients 
f 
of Mercury, and ~ being the ratio of the periods of the Earth and Mercury, which we 
108 54 
may take as near enough to -^r or 2 = 30 °, and R=288; inserting these values 
(12) becomes 
J m=287 1 m= 287 p -54 54 “I 
_ 2 ?j= — % . [« ro cos wnz\—Y^i% [JPjcoss jgmx30 o +Q s sinsY§ mx 30°Jcosmx 30°. • (37) 
But the time of 314 observations is equal to 26 years, or 108 periods of Mercury, 
therefore 
m= 313 r XA KA -i 
% |JP+oss 30°+Q s siny|mX 30 c Jcosmx30°=0 ; .... (38) 
and adding -jti of this to (37), we have 
1 m=287 I m = 313 p KA F.A -i 
-^ 1== 144 ^ [ a mCosrn30°]+^^ jjP s cos m X 30°-}- Q s sins 30°Jcosmx 30°; (39) 
and calculating the last term from the approximate coefficients of Mercury given in 
paragraph 18, we find its value to be, for Easterly disturbance, + 0-006; therefore 
I m=287 
[a OT cosm30°] +0-006. 
m=0 
Similarly we find 
1 m=287 
^ 1= 144 ^ [a m sinrn30°] — 0 - 021 , 
1 m=287 
-^ 2= 144 ^ [a ro cos 2m 30°] + 0-071, 
I m=287 
^=144- [«» sin 2m 30°] -0-132; 
and for Westerly disturbance 
I m=287 
•^ 1 = i 44 ^ [« m cosm30°] +0-035, 
4 m=28 7 
Si = J 44 ^ \_ K m sin m 30 ] +0-061, 
4 m=287 
-^ 2= 144^ [“» cos 2m 30°] — 0-013, 
1 m = 287 
^ 2= 144^ [a ro sin 2m 30°] — 0-101, 
in all of which the last terms are small 
enough to be neglected, in comparison 
with the absolute range of any of the 
component periodical variations, as may 
be seen by simple inspection of the 
. values of the several coefficients given in 
paragraph 18. And as these calcula- 
tions are given more in illustration of 
the method than for any intrinsic value 
of the result, we need carry them no 
further. 
