106 



Prof. Encke on the Calculation 



to 360°, and if we denote the right ascension and declination 

 of the pole of the plane of motion by A and D, we have 

 these equations: 



sin D = cos i' sin S + sin i' cos 8 sin £3 ' 



cos D sin (a — A) = + sin i' cos 8 



cos D cos (a — A) = cos i' cos 8 + sin i' sin 8 sin £3 ' 

 which may be simplified for the calculation by introducing 

 some auxiliary angles. By these equations the two planes 

 will be determined, respecting the choice of which the nature 

 of the problem leaves us in uncertainty. 



As an example, 1 shall give the first application which 

 I have made of these formula?, to the remarkable double star 

 10 p Ophiuchi, in order to ascertain their utility. I need hardly 

 remark, that the following numbers are only to serve as an 

 example, and that they are not to be deemed entitled to the 

 character of a determination of the orbit. The observations to 

 which I first confined my calculations were the following, in 

 which the angles p are counted from the eastern part of the 

 parallel through the north. 



70 jy Ophiuchi. 



With regard to the differences between the observations, I 

 have to observe that they are mostly observations of one eve- 

 ning, and that the scanty means then at the disposal of Struve 

 are not to be compared to the very perfect ones which he 

 now possesses. The first measurements depended partly on 



methods, 



