322 APPENDIX. 



FORMULAS FOE COMPUTING THE ORBIT OF A COMET. 



Given 



Mean times of the observations in days, t , f, if&quot; 



Observed longitudes of the comet, , a&quot;, a &quot; 



Observed latitudes of the comet, ft , ft&quot;, ft &quot; 



Longitudes of the sun, A , A&quot;, A &quot; 



Distances of the sun from the earth, R, R&quot;, R&quot; 



Required 



The curtate distances from the earth, 9 , (&amp;gt;&quot;, Q &quot; 



Compute 



L 



tan (3&quot; ,, _ If&quot; if TO sin (a! A&quot;) tan/T 



~8in(a&quot; A&quot;) if tf tan/3&quot; ~ msin(a&quot; A&quot;) 



and by means of this, approximately, 



n. 



R&quot; cos (A &quot; A ) K = ffcos(G A ) 

 R&quot; sin (A &quot; A) ff wa(G A ) 



g is the chord of the earth s orbit between the first and third places of the earth. 

 G the longitude of the first place of the earth as seen from the third place. 



III. 



M cos (a &quot; a ) = h cos cos (H a &quot;) 

 sin ( &quot;_ a ) h cos sin (II a &quot;) 

 Mian ft &quot; tan ft = h sin f . 



h is always positive. If JVis a point, the coordinates of which, referred to the 

 third place of the earth, are 



(/ cos a , (/ sin a , ^ tan /3, 

 then are 



A? , ^ C, 



