APPENDIX. 323 



the polar coordinates of the third place of the comet, (that is, the distance, longi 

 tude and latitude,) referred to the point N as the origin. 



IV. 



cos C cos ( G H] = cos (f ffsirnp=A 



cos ft cos ( A ) cos if) B sin y = ff 



cos ft &quot; cos ( &quot; A&quot;) = cos y &quot; #&quot; sin y &quot; = ff&quot; 

 By means of 9, i//, r/&quot;, -4, -B , -B&quot; , Olbers s formulas, become : - 



F =(^9 &amp;lt;7COS 9 ) 2 -f-yl 2 



r 2 =(Q sec|3 R cos yj + ff 2 



r &quot; z = (Mo sec ft&quot; R&quot; cos i^ &quot;) 2 + B&quot; * 



The computation would be somewhat easier by 



V. 



h cos (i =f, g cos (f / R cos y = c 



=/ &quot; ^ cos v / &quot; 7T&quot; cos /&quot;= c &quot; 



/ 



in which 



u=^h () g cos y 



VI. 



A value of u is to be found by trial which will satisfy the equation 



(/ + ,&quot;+ *)*-(/+ /&quot;-*)* - ^, 



in which 



log = 0.9862673 



If no approximate value for (&amp;gt; or for / or r&quot; is otherwise known, by means 

 of which an approximate value of u can be found, we may begin with 



