26 
Y _ _ _ <^[Q2] _ 
= + -smX — cos\ 
a a 
E . F 
+ 3-cosiisinX - 3-cos'?^cos\ 
a a 
+ 6— siiiwsin2\ - 6?sin«cos2\ 
a a 
-i- 
( 3 ) 
Limiting ourselves to terms in V of the first and second 
degrees, the determinations of X^, obtained by calcula- 
tion from the observed values of horizontal force and of 
declination, may easily be put in the form— 
Picos0 + QisinO + P 2 COS 20 + Q2sin20 + 
and these, being put on the left sides of equations (2) and 
(3) respectively, afibrd, in each case, as many equations of 
condition as there are stations of observation of the form— 
aPi = psiiiw -^;cositcos\ - pcosiisinX 
lA IB 1C 
3 
+ - 3pcos2?^cos\ - 3^:>cos2'(!^sin\ 
^ID IE IF 
- 3^:)siu2?^cos2X - 3^siii2?^siii2\ 
IG IH 
or— 
aV =^:)sinX -^cos\ 
lY IB 1C 
+ 3pcos^^siIlX - 3^cosi^cosX 
IB IF 
+ 6psin'i^sin2X - 6psiimcos2X 
IG IH 
for the determination of the numerical coefficients p, p, 
lA IB 
p, &c., where— it will be observed — P, P are numerical 
1C ^ ^ . . IX lY 
quantities, and the additional suffixes of p refer to the 
1 
particular periodical factor to which the undetermined co- 
efficients belong. Similar equations of condition serve, in like 
manner, for the determination of p, p, p, &c. ; q, q, q, 
sA sB sC sA sB sC 
Sia; where s stands for 1, 2, 3, &c., successively. 
In order, now, that we may be able to see the full signifi- 
cance of the suppositions and assumptions made by the 
