218 



DETERMINATION OF AN ORBIT FROM 



[BOOK II. 



Hence we have the following places of Pallas, for the basis of the compu 

 tation : 



157. 



Now in the first place we will determine the positions of the great circles 

 drawn from the heliocentric places of the earth to the geocentric places of the 

 planet. We take the symbols 2t, 2f, 21&quot;, for the intersections of these circles 

 with the equator, or, if you please, for their ascending nodes, and we denote the 

 distances of the points B, B, B&quot; from the former points by J, z/ , J&quot;. In the 

 greater part of the work it will be necessary to substitute the symbols 2(, 21 , 21&quot;, 

 for A, A , A , and also //, // , A&quot; for d, 8 , 8&quot; ; but the careful reader will readily 

 understand when it is necessary to retain A, A, A , d, d , 8&quot;, even if we fail to 

 advise him. 



The calculation being made, we find 

 Riffht ascensions of the 



233 54 57&quot;.10 

 51 17 15 .74 

 215 58 49 .27 

 56 26 34 .19 

 23 54 52 .13 

 33 3 26 .35 

 47 1 54 .69 

 9.8643525 



points 2t, 21 , 21&quot; . 



, 21 77, 

 , 3TZX, W 



logarithms of the sines 

 log sin 

 log cos 



e 



e 



253 8 57&quot;.01 

 90 1 3 .19 



212 52 48 .96 

 55 26 31 .79 



30 18 3 .25 



31 59 21 .14 

 89 34 57 .17 



9.9999885 

 9.8478971 

 9.8510614 



276 40 25&quot;.87 



131 59 58 .03 



220 9 12 .96 



69 10 57 .84 



29 8 43 .32 



22 20 6 .91 



42 33 41 .17 



9.8301910 



