( 465 ) 



nicht iingeheuer gross ist". He therefore puts 



1 



f = 



l/l -f- (g" -^ l)cos* 1|? 

 As the rrgorous formula is at least equally simple there is no reason 

 for the substitution. If we put the expression of Myers = /*', we have 



ƒ ^ 



1 + ( ^^^— )sm'2i|?. 



7t 



Greatest values, for if; =r - 



4 



1.2 



ƒ , 

 — 1.02 



/'I 



1.3 

 1.03 



2q J 



1.4 



1-06 



1.5 

 1.08 



There thus is introduced a systematic error, which, already for 

 small elongations, cannot be neglected. 



4. As soon as, with the aid of provisional elements, a light-curve 

 has been calculated, we try to vary these elements in such a way 

 that the differences between observation and computation are dimi- 

 nished. We have to investigate, therefore, in what way the light- 

 intensity varies with the elements. 



We have already: J ^ F {f, M, X,y^^). We will now, tirst of all, 

 express df and clM in function of d{yJ^), d'^, dq. 



In the first place we have to consider that X is fully determined 

 by x', in the case, which as we shall presently see must be admitted, 

 that during the minima E^ is projected v^^holly on E^. For, if 

 fm = Vl — 6" siii^'i (:= value of ƒ in both the minima), then, on the 

 same supposition : 



;. 



Jm • 



A + x' 



A 1- 



x'A 



From these, after division 



const. 1 (= intensity at the principal minimum) 



= const., (= „ „ ,, secondary 



dX 



— d(y,^) and - — z= 



5«' fm X+il' 



d7i' = — 



d{s^sin^{) 



With the aid of the latter formula we get without difficulty 



e sm I cos^ 3 X 



sin 2/3f//3 -\ ~ (1— «» sin'' i) ^^ — - <f(x») ; 



2/ ■ ■ • ƒ 



which is independent of the variation of i 



;i + >t' 



