192 DETERMINATION OF AN ORBIT FROM [BooK II. 



If now we designate the arc C ff by s, substitute for r, r\ r&quot; their values in 

 the preceding article, and, for the sake of brevity, put 



nl1 R sin a sin (A&quot;jyd&quot;)_ 

 L U J R&amp;gt; sin sin (AU d) ~ 



_, 



~ 



.R&quot; sin 5&quot; sin (A D 5 -f a) 

 our equation will become 



, / sin (z q) . 



HI. = on - -\-n 



sin z 



The coefficient may be computed by the following formula, which is easily 

 derived from the equations just introduced : 



_ 



a X ^ B in8in(^ Zy o -fq)- 



For verifying the computation, it will be expedient to use both the formulas 12 

 and 13. When sm(A D&quot; &amp;lt;? -(- a) is greater than sm(A Dd -\-a), the latter 

 formula is less affected by the unavoidable errors of the tables than the former, 

 and so will be preferred to it, if some small discrepancy to be explained in this 

 way should result in the values of b ; on the other hand, the former formula is 

 most to be relied upon, when sin (A D&quot; &amp;lt;f-|- a) is less than sin (A D d -(- a); 

 a suitable mean between both values will be adopted, if preferred. The follow 

 ing formulas can be made to answer for examining the calculation ; their not very 

 difficult derivation we suppress for the sake, of brevity. 



ft _ a sin (I&quot; I ) _ bain (I* 1) sin (8 q) , sm(l l) 



B ~R sin d ~~K 



,_ _ - 

 ~ 



in which (article 138, equation 10,) U expresses the quotient 



S 



sin(&amp;lt;5 q) cos(&amp;lt;J q) 



141. 



From P = , and equation HI. of the preceding article, we have 



/ , ,/, P-\-a , i sin (z q) 



(n-4-n )^H -r = bn - -*-\ 



P-\-\ smz 



