( 482 ) 



With the notations of Wilsing these observations lead to the 

 following normal equations: 



+ 14^^„-3.17 a^ + 1.56 />, — 3.41 a, — 1.28 />, = — 42.00 



— 3.17 ^„-1-7.64 a^ - 1.68 />j + 1.81 «, + 1.02 6, = -f 90.78 

 4-1.56 ^„-1.68 «, + 6.36 />^ - 2.71 «, — 0.27 6, ==— 37.81 



— 3.41 g,-{-l.81 a, -2.17 ^^ + 8.52 a, + 0.32 6, = + 30.74 



— 1.28 g, + 1.02 a, - 0.27 b, -f 0.32 a, + 5.48 h^ = + 8.57 

 Solution : 



g^=^ — 0.097 G.M. =: constant velocity towards the sun. 



ttj = — an sin i si?! (to' -[--/l/^o)= 4' ^ 1 • ^ ^^ 5 h^zrzan sin i cos (tt>'-|--^/o) = — 2.953 



a^z= — ean sin i sin (to' -|- 27I/„)r= -\- 0.498 ; b^^^ean sin i cos{o)-\- 2M^):=: — 0.708 



to' is the longitude of the periastron, counted from ,Q, ; M^ the 

 mean anomaly at the beginning of the light-period, consequently : 



an5mz=:11.579;(o' = 115°20';J/„=139°54'; ^ = 0.075. 



As io' -{- M, = 180^ 4- 75°12', the elements belong to the body 

 which, during the principal minimum, eclipses the other. Conjunction 

 takes place, when to' -\- v = 270^, i.e. 0''.39 days after the time of 

 the principal minimum, as computed from the empirical formula. 



In the following table the 4^'' column shows the computed velo- 

 cities, the 6^'! the outstanding deviations. 



16. Spectrographs of 1897. 



The velocities (in G. M), derived by B. from the displacements 

 of the dark J/^-line X = 448.16 [i u, have been taken u]ichanged from 

 the Memorie delta Soc. degli Spettr. It. vol XXVI. The empirical 

 formula leads to the epoch 1897 June 22 16^^. 24 M. T. Pulkowa 

 for the principal minimum. 



In a first approximation I determined a circular orbit and found: 

 g, = — 2.094 ; an sin i = 24=.2l0 ; to' + i/„ =: 89°.30'.l. 



Afterwards corrections were derived by the aid of the formula : 



dz 

 d — -=i dg^ -\- KndT sin (to' + v) -4- dK . cos (to' + r) -f 

 dt 



4- Ke cos to' cos 2 {to' -\- v) -{- Ke sin (o' sin 2 {to' -\- v). 



in which K=iansini, 7'= time of periastron-passage. 



This formula is obtained from the general differential-formula ^), 

 by patting f/ji = 0, (ho = and by further neglecting 2"^ and 

 higher powers of e. We thus find the following normal equations : 



^) Vide: Bauschinger, Die Bahnbesliramung der Himmelskörper, N^. 199. 



