SECT. 1.] THBEE COMPLETE OBSERVATIONS. 165 



118. 



If the distance of a heavenly body from the earth answering to any observa 

 tion is already approximately known, it may be freed from the effect of aberra 

 tion in several ways, depending on the different methods given in article 7L 

 Let t be the true time of observation ; 6 the interval of time in which light passes 

 from the heavenly body to the earth, which results from multiplying 493 s into the 

 distance ; I the observed place, t the same place reduced to the time t -\- 6 by 

 means of the diurnal geocentric motion ; I&quot; the place I freed from that part of the 

 aberration which is common to the planets and fixed stars ; L the true place of 

 the earth corresponding to the time t (that is, the tabular place increased by 

 20&quot;.25) ; lastly, L the true place of the earth corresponding to the time t Q. 

 These things being premised, we shall have 



I. I the true place of the heavenly body seen from L at the time t 6. 

 II. f the true place of the heavenly body seen from L at the time i. 

 III. t the true place of the heavenly body seen from L at the time t &. 

 By method L, therefore, the observed place is preserved unchanged, but the fic 

 titious time t 6 is substituted for the true, the place of the earth being com 

 puted for the former ; method II., applies the change to the observation alone, but 

 it requires, together with the distance, the diurnal motion ; in method III., the 

 observation undergoes a correction, not depending on the distance ; the fictitious 

 time t 6 is substituted for the true, but the place of the earth corresponding to 

 the true time is retained. Of these methods, the first is much the most conven 

 ient, whenever the distance is known well enough to enable us to compute the 

 reduction of the time with sufficient accuracy. But if the distance is wholly un 

 known, neither of these methods can be immediately applied : in the first, to be 

 sure, the geocentric place of the heavenly body is known, but the time and the 

 position of the earth are wanting, both depending on the unknown distance ; in 

 the second, on the other hand, the latter are given, and the former is wanting; 

 finally, in the third, the geocentric place of the heavenly body and the position 

 of the earth are given, but the time to be used with these is wanting. 



