246 DETERMINATION OF AN ORBIT FROM FOUR OBSERVATIONS, [BOOK II. 



log P 0.05944, log Q = 9.60374, 

 log P&quot; 9.97219, log Q&quot;= 9.69581, 



upon which the second hypothesis will be constructed. The principal results of this 

 are as follows : 



c 7.67820, log d = 0.045736 n 

 c&quot;= + 2.21061, logrf&quot;= 0.126054 

 of = 2.03308, z = 23 47 54&quot;, log / = 0.346747, 

 af = 1.94290, z&quot;=27 12 25, log r&quot; = 0.339373 

 C C&quot;=v&quot; v =\T 8 0&quot; 

 v v = 14 21 36&quot;, log r = 0.354687 

 v &quot;v&quot;=18 5043, logr &quot; = 0.334564 



log (n 01) = 0.004359, log (n 12) = 0.006102, log ( 23) = 0.007280. 

 Hence result newly corrected values of F, P&quot;, Q , Q&quot;, 



log P 1 == 0.059426, log Q = 9.604749 

 log P&quot; = 9.972249, log Q&quot; = 9.697564, 



from which, if we proceed to the third hypothesis, the following numbers result : - 

 c =--7.67815, logrf == 0.045729 n 

 c&quot; = -- + 2.21076, log d&quot;= 0.126082 

 x = 2.03255, = 23 48 14&quot;, log / = 0.346653 

 z&quot; = 1.94235, z&quot;=27 12 49, log r&quot;= 0.339276 

 C 0&quot; if ff=lT 8 4&quot; 

 v v= 14 21 49&quot;, logr =0.354522 

 v &quot;v&quot;=l% 51 7, log/&quot; =0.334290 



log (n 01) = 0.004363, log (n 12) = 0.006106, log (n 23) = 0.007290. 

 If now the distances from the earth are computed according to the precepts of 

 the preceding article, there appears : 



(/ = 1.5635, 9&quot; =2.1319 



log Q cos = 0.09876 log (&amp;gt; &quot; cos /? &quot; = 0.42842 



log Q sin ft = 9.44252 log &amp;lt;&amp;gt;&quot; sin /? &quot; = 9.30905 



= 12 26 40&quot; p &quot; = 4 20 39&quot; 



log ? = 0.10909 log &amp;lt;;/&quot; = 0.42967. 



