SECT. 2.] TO POSITION IN SPACE. 97 



5218 9&quot;.30) by II, and the true anomaly by v, the longitude in orbit will be 

 u-\-Q=v-}-lT, and therefore dw A v -\-AIT dS, which value being sub 

 stituted in the preceding formulas, d/and Ab will be expressed in terms of Ar, 

 d v, d IT, d a , d i. Nothing, therefore, now remains, except to express d r and d v, ac 

 cording to the method of articles 15, 16, by means of the differential variations 

 of the elliptic elements.* 



We had in our example, article 14, 



log!j = 9.90355 = log Q 

 log- 0.19290 lo S fl ..... - 42244 



O rvt 



i nnccKo log tan 9 .... 9.40320 



log cos ep .... 9.98652 



log sin v .... 9.84931 n 

 log( T -) .... 0.17942 



= 1.80085 

 = 0.06018 



log ...... o.24072 



log^f ..... 0.19290 lo s 0.25862 w 



log sin E .... 9.76634 n 



log(^) .... 0.19996 n 



Hence is collected 



dv = -f 1.51154 AM 1.58475 dg&amp;gt; 

 dr = 0.47310 d JfcT 1.81393 dy + 0.80085 da ; 

 which values being substituted in the preceding formulas, give 



dl= + 2.41287 AM 3.00531 dg&amp;gt; + 0.16488 da -f 1.66073 AIT 



- 0.11152 d + 0.04385 AQ, 



Ab = 0.66572 d M + 0.61331 dy -f 0.02925 da 0.42895 d77 

 0.47335 Ai+ 0.38090 d8. 



* It will be perceived, at once, that the symbol M, in the following calculation, no longer expresses 

 our auxiliary angle, but (as in section 1) the mean anomaly. 



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