SECT. 1.] THREE COMPLETE OBSERVATIONS. 213 



hypothesis, as the values of P, Q. Putting, therefore, 



z = log P 0.0790167 

 # = log (2 = 8.5476110 



the following are found to be the principal results of the calculation : 



210 8 25&quot;.65 

 0.3307640 

 0.3222239 

 205 22 14 .57 

 3 14 4 .78 

 7 34 53 .73 



3 29 .39 



4 5 53 .34 



All these numbers differ so little from those which the second hypothesis fur 

 nished, that we may safely conclude that the third hypothesis requires no further 

 correction.* We may, therefore, proceed to the determination of the elements 

 from 2/ , r, r&quot;, 6 , which we dispense with transcribing here, since it has already 

 been given in detail in the example of article 97. Nothing, therefore, remains 

 but to compute the position of the plane of the orbit by the method of article 

 149, and to transfer the epoch to the beginning of the year 1805. This computa 

 tion is to be based upon the following numbers : 



C= 955 5r.41 



18 13 .855 

 i( y _ M ) = _6 18 5 .495 

 whence we obtain 



i(0-|-A) = 19643 14&quot;.62 

 l(g h) = 4 37 24 .41 

 it = 6 33 22 .05 



* If the calculation should be carried through in the same manner as in the preceding hypotheses, 

 we should obtain X=0, and T= -(-0.0000003, which value must be regarded as vanishing, and, 

 in fact, it hardly exceeds the uncertainty always remaining in the last decimal place. 



