SECT. 1.] TO POSITION IN THE ORBIT. 11 



Given v = 310 55 29 / .64, c; = 14 12 1&quot;.87, log r = 0.3307640 ; p, a, E, M, 

 are required. 



log sin (f . . . . 9.3897262 

 log cosy .... 9.8162877 



9.2060139 whence e cos v = 0.1606993 



log (1 + e cost ) . . 0.0647197 

 logr 0.3307640 



logp 0.3954837 



log cos 2 tp .... 9.9730448 



log a 0.4224389 



log sin z; .... 9.8782740 n* 

 logi/jj .... 0.0323598.5 



9.8459141.5 

 log sin 9 ... 9.0920395 



logsmi(w E) . 8.9379536.5M, hence J( E} = 458 22&quot;.94; 



v -&quot; = 9 56 45&quot;.88 ; ^= 320 52 15&quot;.52. 

 Further, we have 



Calculation of log sin E by formula VIII. 



loge . . . . 9.3897262 r 



i oncocx o Koi^on log- sin y .... 9.8135543re 



log 206264.8 . 5.3144251 p 



log e in seconds 4.70415T3 log cosy 9.9865224 



logsin.E . . . 9.8000767 logsin.E ..... 9.8000767 



4.5042280 n, hence e sin E in seconds = 31932&quot;.14 = 8 52 

 12*14 ; and M= 329 44 27&quot;.66. 



The computation of E by formula VII. would be as follows : 



i = 15527 44&quot;.82 log tan iv .... 9.6594579w 



45 iy = 3753 59&quot;.065 log tan (45 iy) . 9.8912427 



log tan IE . . . . 9.55070067 

 whence $E= 16026 7&quot;.76, and E= 320 52 15&quot;. 52, as above. 



* The letter n affixed to a logarithm signifies that the number corresponding to it is negative. 



