176 



Prof. Encke on the Calculation 



For the greatest and smallest distance the following equa- 

 tion is to be solved : 



sin(2E' + 72°2l'16"-8) = [0-131624] sin (E' + 17° 37' 7"-8) 

 a few trials give: 1809-6152 ... smallest distance = l"-8332: 

 E' = 22'" 57' 2G"-3, greatest angular velocity = 16°-911 an- 

 nually: 1835-5026 ... greatest distance = ri"-6513: E' = 

 151° 20' 18"-3 smallest angular velocity = l°-776 annually. 



Finally, the two planes in which the motion takes place are 

 found parallel to these planes : 



Ascending node on the equator = 138° 4' 2l"-0 



Inclination = 68 49 32 -4 



Ascending node on the equator = 41 3 2 '4 



Inclination = 64 59 26 '9 



or, referred to the ecliptic: 



S = 141 °23' 2l"-6 S = 52° 23' 8"-9 



J = 86 50 30 -5 J = 48 42 18 '1 



for which we have adopted the position of the star agreeably 

 to Piazzi ... a = 268° 50' 18"-0 S = + 2° 33' 3l"-5. 



If we now compare the observations above given with this 

 orbit, we find the following differences : 



In the second volume of the excellent observations of 

 double stars, by Messrs. Herschel and South, another set of 

 observations of the year 1825 was allerwards found; and, at 

 my request, the former of these gentlemen, with the distin- 

 guished kindness with which he gratifies all applications of 

 that nature, made some new observations, which he communi- 

 cated to me. All these compared with the former orbit present 

 the followinc: results : 



Year 



