324 APPENDIX. 



This trial will be facilitated by Table ITT a , which gives fj, corresponding to 



by means of which is found k, which corresponds rigorously to r, r &quot;, and if&quot; i!\ _ 



x( r-Q 



-(/ + /&quot;)! /* 



in which 



log x = 8.5366114. 



The process may be as follows : For any value of compute k, r, r &quot;, by V, 

 and with /, r&quot;, compute rj, with which /* is to be taken from Table III a , and a value 

 of k is to be computed which corresponds to the /, r &quot;, f- i! used. And u is to 

 be changed until the second value of k shall agree exactly with that computed 

 byV. 



Then we have 



,__ 







vn. 



(&amp;gt; cos ( A ) & = / cos V cos (f A ) 

 &amp;lt;/ gin ( A ) = r cos b sin (t A ) 



q tan /J = / sin V 



cos ( &quot; A&quot;) R&quot; = r &quot; cos V&quot; cos (r A&quot;) 

 (&amp;gt; &quot; sin (of&quot; - A&quot;} = r &quot; cos V&quot; sin (f&quot;A &quot;) 



FIRST CONTROL. 



The values of r , r &quot;, obtained from these formulas, must agree exactly with 

 those before computed. 



/, b ; I&quot;, b &quot;, are heliocentric longitudes and latitudes of the comet. 



The motion is direct when f&quot;- - f is positive, and retrograde when r f is 

 negative. 



