Gore — On the Orbit of the Binary Stat [3 Ddpltiiii. TjlS 



By drawing an interpolating curve for the observed distances, and 

 tlien comparing the distances thus found with the distances measured 

 at corresponding points in the apparent orbit, the value of a milli- 

 metre in the assumed scale was found to be 0"-00309. 



The actual length of the semi-axis major of the harmonic el- 

 lipse was found to be 148"3 millimetres, and as this is equal to the 

 semi-latus rectum of the real ellipse, we have 



semi-axis major of real ellipse - a = - 

 148-3 



I 



1 -(0-337)' 

 o = 0"-516957. 



X 0"-00309 ; 



Hence we have the following elements of /3 Delphini :- 



Position of IS'ode, 



Inclination, 



Position of periastron, 



Eccentricity, 



Period in years, 



Periastron passage, A. D., 



Semi-axis major, 



Mean annual motion, 



= 2° 38' (1880). 

 y = 59° 20'. 

 A = 327° 46'. 

 e =0-337. 

 P= 30-91. 

 T= 1882-25. 

 a =0"-5l7. 

 /x = + ll°-64. ' 



These elements are of course only provisional, and further ob- 

 servations will be required before an accurate computation of the 

 oi])it can be made. 



For the calculation of an ephemeris, the following formulae are 

 derived from the elements : — 



(1) M- 19°-308 sin M = ll°-64 (^- 1882-25) ; 



(2) tani- r= 1-42 tan i^w; 



(3) tan {9, - 2° 38') = 0-51 tan ( r+ 327° 46') ; 



cos ( V+ 327°-46') _ 



(4) /) = 0"-5l7 (1 -0-337 cos m) 



cos {6 - 2° 38') ' 



where u is the eccentric anomaly, V the true anomaly for the time t, 

 6 the required position angle, and p the distance. 



