64 RELATIONS PERTAINING SIMPLY [BOOK 1. 



a = -731 46&quot;.3 i(8 n)= -345 53&quot;.15 



-{- = 58 556.9 J (-{-?) = 29 258.45 



i e= 1110 5.3 i(i e) = 535 2.65 



logsini(8 n) . . 8.8173026 n logcosj(8 w) . . 9.9990618 



logsini(t + e) . . . 9.6862484 logsin$(t e) . . . 8.9881405 



logcosi(t + e) . . . 9.9416108 logcos i (i e) . . . 9.9979342. 



IK-: 1 . f \v have 



logHinifsrai(8 -{-^) 8.5035510 logcos H sin * (8 ^) 8.7589134 

 logsinKcosifa +J) 8.9872023 logcos Jt&quot; cos i (8 //) 9.9969960 



whence i ( 8 + J) = 341 49 19&quot;.01 whence i ( 8 //) = 356 41 31&quot;.43 

 log sin it* 9.0094368 log cos H 9.9977202. 



Thus we obtain H = 5 51 56&quot;.445, i = 11 43 52&quot;.89, 8 = 338 30 50&quot;.43, 

 .-/ =; 14 52 12&quot;.42. Finally, the point n evidently corresponds in the celestial 

 sphere to the autumnal equinox ; for which reason, the distance of the ascending 

 node of the orbit on the equator from the vernal equinox (its right ascension) 

 will be 15830 50&quot;.43. 



In order to illustrate article 53, we will continue this example still further, 

 and will develop the formulas for the coordinates with reference to the three 

 planes passing through the sun, of which, let one be parallel to the equator, and 

 let the positive poles of the two others be situated in right ascension and 90: 

 let the distances from these planes be respectively s, x, y. If now, moreover, 

 the distances of the heliocentric place in the celestial sphere from the points 8, 

 8 , are denoted respectively by u, u , we shall have u =n 4 = u -\- 14 52 12&quot;.42, 

 and the quantities which in article 53 were represented by i, IV 8, u, will here 

 be {, 180 8 , w 7 . Thus, from the formulas there given, follow, 



log a sin A . . . . 9.9687197 re log b sin B . . . . 9.5638058 

 logacos.4 .... 9.5546380 logicos^ .... 9.9595519w 



whence A = 248 55 22&quot;.97 whence B = 158 5 54&quot;.97 



log a 9.9987923 log b 9.9920848. 



We have therefore, 



