( 468 ) 



6. We thus have consecutively expressed dM and df in function 

 of c/(x^), d[i and dQ; and afterwards c//5 and dg in function off/a, t'% 

 c/il/o, '^^ and y. If now we differentiate the expression 

 ^ / M 



jr (A 4- x'')^ 



valid in the vicinity of the lirst minimum, we find, by consecutive 

 substitution, the following expression for dJ-^-. 



n {X + x^) dJ, — K^ d{-K^) -^ A,da ^ I, i" + X,x J- Y,y + A, {dM^ -y), 

 in which : 



7t). { 1—X''\ , , 2;. (> 



2osinw' 7'^cos^nt, 



^.t= ; ij = siwy ; 



r Q 



Xj = Aj sm nt^ — Qsinif' cosnt^ ; Fj -_ Aj (1 - cosnt^) — QsijKp' sinnt^ ; 



r' .s'm 2/iL 6m «)' £* 



A, = ^ + — ^sm 2n«, |jr (A + ^:^) J, - 2q sin <p'\ . 



Q *-/ 



If we treat in the same way the expression : 



valid in the vicinity of the second minimum, we find, putting 

 U 



^ ^i^ dJ, = K, d{z'-) ^A,da-^ I,i!' + X,:c + Y,y + A, {dM, + y) 



9 



X, =: — Aj sin n«, -f- () sin g>' cos nt, ; F, = — A, (1 — cos nt,) -\- q sin (p'sin nt^ 

 r' sin 2nt, sin g)' *' . o f ^' '^' ^^ 



A. = 



Q 



s' , / ;. 4 x' . \ 



H sin 2nt. ( jr J, — 2p sin w' 1. 



^2/» 'V ^ J 



7. If the observations do not give the light-intensity, but the 

 brightness expressed in magnitudes or in grades, then we have still 

 to express the variation of the number indicating the magnitude or 

 the grade, in the variation of the light-intensity. 



