( 476 ) 



wliicli have been derived by repeated approximations from Arge- 

 lander's curve by Dr. Myers. In his opinion tiiese are the best 

 possible circular elements: 



a — 1 8955 ; k = 0.7580 ; q — 1.1993 ; X z= 0.4023 ; f = 

 By their aid I computed the light-grades CV. and 6V.^ of the 

 preceding table. As will be remarked, the deviations — Cm^ are 

 rather considerable in the vicinity of the principal minimum. 



In deriving the following normal equations, the equations of con- 

 dition for ti = ± 6'^ and t^ = ± 6'' have been neglected. 

 Normal-equations : 



18.54 (i(H') + 15.17 da + 16.98 (lOt'^^ 4- 15.3 1 .t' = — 7.670 

 15.17 ,. + 41-68 „+ 18.14 „ + 53.17,, = — 9.673 

 16.98 „ -i 18.14 „+ 20.29 ,, + 20.75., = — 7.720 

 15.31 „ + 53.17 „+ 20.75 „ + 101.96 „ = — 13.227 

 255.69 t/ f 160.37 (r)!i¥„ —3/) = 10.242 

 160.37 y -f 1125.52 [dM^ — y) — 37.759 

 Solution of the first four equations : 

 X = — 0.026 ; lOi'^ = - 0.044 ; da = - 0.0741 ; d{7e) — — 0.2915. 

 As i' becomes imaginary, we put t' = in the equations of con- 

 dition, and then find : 



X = — 0.026 ; da— — 0.0799 ; c?(j«') = — 0.3268. 

 y = + 0,021 ; dM, - y = -f 0.031, 

 which lead to the improved elements : 



a = 1.8156 ; >£ = 0. 1978 ; P. = 0.2249 \q — l 3859 ; e = 0.017; iü = 141°.3. 

 The correction for y.'^ is particularly large, more than half its 

 original value (0.5746). As in such a case dJ cannot any longer be 

 considered to be proportinal to (/(x"), we should have to compute a 

 new light-curve by the aid of the new elements ; we should then 

 have to calculate the differential coefficients in order — if necessary 

 — to find a new approximation. 



In the following table the columns C^ and 6, show the light- 

 grades calculated by means of the improved elements. 



In fig. I has been given a graphical representation of these num- 

 bers. The agreement in the vicinity of the principal minimum is 

 considerably improved. It is true that there remains a deviation 

 exceeding a light-grade, at 18 hours before the minimum. It might 

 perhaps be further diminished by a repetition of the whole process. 

 If, however, we take into account the uncertainty mostly existing 

 when we draw the curve for the vicinity of the minimum, then it 

 seems hardly worth while to repeat the elaborate calculation. At all 



