y (3) 



Computation of certain Harmonic Components. 65 

 Pl = •06583{d +[* lt A 5 ] + J«}, 

 g, = •06583{^ + [^ 1 , 

 p 2 = •06699{2 + [2 1 + 2 2 ]-[2 4 + 2 5 ]}, 

 2g = •06699{2 3 +[2 1 + 2 a ] + [2 4 +2 5 ]}, 

 p, = •O69O4{0 o +0 1 -0 3 } = •06904{[<Z +A 1 ]-[A 3 , A 5 ]} = «, 

 2s = •O69O4{0 1 + 2 + 3 } = •06904{[« 1 , S 3 ]-[<5 5 + cy } = A 



J>4 = Mfo+fi-**} = ■0625{y, + y, 1 -^ 2 }, 

 2 4 = •07217{^ 1 + ^ 2 }- 



The expressions before given for p 6 , q 6 , and p 8 , q 8 , are very readily 

 computed, the multiplier for q 8 , sin 60 = '07217, being the same 

 as that for q±. 



The computation of p h , q^ and p 7 , q 7 , may be rendered somewhat 

 easier as follows : — 



i>5 = TzC^do + A 4 ) + "102 ( Aj_ + A 5 ) —pu 



p 7 = T V(2d + A 4 ) + -059(A 1 + 2A 8 -A B )- i , ll 



25 = i 3 2(2d 6 + « 2 ) + -102(« 1 + « B )- 2l , 



27= -^(2^ 6 +^) + -059(5 1 -2a 3 -^) + 2l . ' 



Assuming that the probable errors in the observed quantities are 

 all equal, and that (e) represents the error in a pair of observations 

 combined (corresponding to the quantities (d) and (s)), then the 

 probable error of all the p, q coefficients calculated by the formula? 

 (2) will be tW(6) -e = '204 e. 



The probable errors, calculated in the manner now proposed from 

 equations (3), will be, — 



p 1 or q Y = 



■06583 </(12).e = 



•238 e, 



p 2 or q» == 



•06699 </(10).e = 



•212 e, 



p s or q 3 = 



•06904^/(9) .e = 



•207 e, 



i>4 = 



^✓(12). 6 = 



•216 e, 



24 = 



•07217 v/(8) .e = 



•204 e. 



VOL. XLII. 



