200 DETERMINATION OF AN ORBIT FROM [BOOK II. 



Before this is undertaken, of course, the intervals of the times themselves require 

 some correction, if it is decided to take account of the aberration agreeably to the 

 third method of article 118. In this case, evidently, for the true times are to be 

 substituted fictitious ones anterior to the former, respectively, by 493(&amp;gt;, 493(/, 

 493&amp;lt;/ seconds. For computing the distances (),(/, (&amp;gt;&quot;, we have the formulas: 



s!n~(C Aiy-{-6)~ -Bind 



, _ Jfsm(d z) _ / sin (9 z) 



Q - . - . ^ , 



sin z sin o 



But, if the observations should at the beginning have been freed from 

 aberration by the first or second method of article 118, this calculation may be 

 omitted ; so that it will not be necessary to deduce the values of the distances (t, 

 (&amp;gt; , (&amp;gt;&quot;, unless, perhaps, for the sake of proving that those values, upon which the 

 computation of the aberration was based, were sufficiently exact. Finally, it is 

 apparent that all this calculation is also to be omitted whenever it is thought 

 preferable to neglect the aberration altogether. 



146. 



The calculation of the elements on the one hand from /, r&quot;, 2/ and the 

 corrected interval of the time between the second and third observations, the 

 product of which multiplied by the quantity k, (article 1,) we denote by 6, and 

 on the other hand from r, r, 2/&quot; and the interval of time between the first and 

 second observations, the product of which by k will be equal to &&quot; - - is to be car 

 ried, agreeably to the method explained in articles 88-105, only as far as the 

 quantity there denoted by y, the value of which in the first of these combinations 

 we shall call i], in the latter rf . Let then 



* ryoer 



9rj ~ r^t? cos/cos/ cos/&quot;&quot; 



and it is evident, that if the values of the quantities P, Q, upon which the whole 

 calculation hitherto is based, were true, we should have in the result P = P, 



