238 DETERMINATION OF AN ORBIT FROM FOUR OBSERVATIONS, [Book II. 



= ( 23) (&amp;lt;/ cos p sin (a &quot; a } -f R cos B sin (a &quot; J )) 

 - (n 13) (^&quot;cos /?&quot;sin (a &quot; a&quot;) -f 7?&quot; cos B&quot; sin (a &quot; /&quot; )) 



-f (n 12) 72&quot; cos &quot; sin (a &quot; I &quot;}. 

 These equations, by putting 



B cos B sin (/ a) r,/ ,, 7 , 

 , ,-f -- r 2 - - It COS = I 



cos p sin (a a) 



&quot;cousin ( &quot; &quot;) 



cos sn TV x, 



=* 



- 



cos j? sin (or a) 



B cos 5 sin (^ a) _ . 

 cousin ( ) ~ ^ 



R&quot;co&H&quot;sm(af&quot; I &quot;) _ 

 ~~ 



~~^^8in(&quot; a ) 

 cos ^ sin (a a) _ 



_ . 

 ~ 



cos f sin (&quot;) r: 



cos p sin ( &quot; g&quot;)_ 

 cos (3 sin ( &quot; ) &quot; 



and all the reductions being properly made, are transformed into the following: 



&quot; I &quot;I 



1+ 



1+ 



or, by putting besides, 

 into these, 



