62 Lieut-General Strachey. On the 



A» = p 1 cos (n . 15°) -f 2i s i n ( n • 15°), 



A ?2+4 = p 1 cos (^.15° + 60°) + 2l sm (>. l5° + 60°), 



A„ +8 = ^ cos (» . 15° + 120°) +2i sin in . 15° + 120°), 

 and therefore 



A« A w+ 4 -|- A w _|_ 8 = 0. 



Wherefore 



n = 2(C W — C w+ 4 + Cn+s) = 6C W ; and C w = ^0 n , 



and A re = id n — j=0 n . 



In like manner, 



S w = a» + a» + i2 = 2(p + B n + 'Dn), 

 and 



2 ra = Sre—Sre+e = 2{B n — Bre+e+Dre— Dw+s) = 4B M ; and B w = 

 also 



ff „ = S„+S (l+6 = 2(2? + B fl + B fl+fl +D ll + D« +6 ) = 2(> + 2D M ), 



and 



°"w+3— S w+3 + S M+ 9 = 2(p — 2D M ), 

 whence 



Y r H = ^»— ff M+3"= 8D n ; and D M = ly^. 



The successive valnes of A, B, C, and D, thus obtained will give 

 with a considerable degree of accuracy, the p q coefficients, and the 

 entire series of harmonic components of the observed quantities. It 

 will at once be seen that — 



A o=lh'> B =p 2 ; C = p 3 ; T> Q =p±. 



A 6 = 2i 5 B 3 = C 2 = 23 5 D x + D 2 = 2 sin 60g 4 = |# 4 , nearly, 

 and Vi = ¥o-i e o'> 9.1 = 



P2=4 2 o; 22 = i 2 3- 



\ (1.) 



P3 = 6^0 =6(^0-^4 + ^) 5 ?3 = G^2 = C ( d 2~ d 6 + <*lo) • 



