166 DETERMINATION OF AN ORBIT FROM [BOOK II. 



What, therefore, is to be done with our problem, if, in such a case, a solution 

 exact with respect to aberration is required? The simplest course undoubtedly 

 is, to determine the orbit neglecting at first the aberration, the effect of which can 

 never be important ; the distances will thence be obtained with at least such pre 

 cision that the observations can be freed from aberration by some one of the 

 methods just explained, and the determination of the orbit can be repeated with 

 greater accuracy. Now, in this case the third method will be far preferable to the 

 others : for, in the first method all the computations depending on the position of 

 the earth must be commenced again from the very beginning; in the second (which 

 in fact is never applicable, unless the number of observations is sufficient to obtain 

 from them the diurnal motion), it is necessary to begin anew all the computations 

 depending upon the geocentric place of the heavenly body ; in the third, on the 

 contrary, (if the first calculation had been already based on geocentric places 

 freed from the aberration of the fixed stars) all the preliminary computations 

 depending upon the position of the earth and the geocentric place of the heavenly 

 body, can be retained unchanged in the new computation. But in this way it 

 will even be possible to include the aberration directly in the first calculation, if 

 the method used for the determination of the orbit has been so arranged, that 

 the values of the distances are obtained before it shall have been necessary to 

 introduce into the computation the corrected times. Then the double compu 

 tation on account of the aberration will not be necessary, as will appear more 

 clearly in the further treatment of our problem. 



119. 



It would not be difficult, from the connection between the data and unknown 

 quantities of our problem, to reduce its statement to six equations, or even to less, 

 since one or another of the unknown quantities might, conveniently enough, be 

 eliminated : but since this connection is most complicated, these equations woxild 

 become very intractable ; such a separation of the unknown quantities as finally 

 to produce an equation containing only one, can, generally speaking, be regarded 



