Computation of certain Harmonic Components. 



63 



3. 



The equations involving the harmonic coefficients, arising from the 

 series of observed quantities, are usually solved according to the 

 method of least squares; and, writing A x for (d\ — d n ), and S 1 for 

 (d ± -f d n ), and so on, the resulting values of p q thus obtained are as 

 follows : — 



p 1 = 1 ^-{^o + A 1 sin 75 + A 2 sin 60 + A 3 sin 45 + A 4 sin 30 -> 



+ A 5 sin 15} 



q x = Tt{d 6 + sin 15 -f ? 2 sin 30 + £ 3 sin 45 + $ 4 sin 60 



+ 3 5 sin 75} 



JPa = A{ 2 0+ ( 2 i-2 5 ) sin 60+ (2 3 -2 4 ) sin 30} 

 22 = t 1 2-{2 3 +(2 1 + 2 5 ) sin 30+(2 3 + 2 4 ) sin 60} > (2.) 



2>s = iV{*o+ sin45 l 

 2s = A(0»+ (01+08) sin45 i 

 P, = M+o+(fi-f2) sin 30} 



^4 = T2(fl + Y r 2) Sm 



To these may be added 



p h = T 1 2-{(i + A 1 sin 15 — A 3 sin 60 — A 3 sin 45 + A 4 sin 30 



+ A 5 sin 75}, 



2s — TV{^6 + ^i s i n 75 + ^ 2 sin 30 — £ 3 sin 45— S 4 sin 60 + £ 5 sinl5}, 

 ^6 = tV{2 + 2 4 -S 2 }, 



p 7 = -Tz{d — A 1 sin 15 —A 2 sin 60 + A 3 sin 45 + A 4 sin 30 



-A 5 sin 75}, 



9.1 = Ta { + s i s i n 75 — ^2 s i n 30 — ^3 s i n ^5 + s i n ^O 



+ ^ 5 sin 15}, 



= T2 { Oo + O ~ Ol + <^2 + *4 + a h) sin 30 }> 

 28 = lV { Ol + ~ (*J + ff 5 ) } sin 60 ' 



4. 



The values of the p q coefficients may, however, be obtained 

 otherwise, in a form which is somewhat simpler for computation, and 

 not sensibly less accurate. 



