212 



DETERMINATION OF AN ORBIT FROM 



[BOOK II. 



153. 



In the second hypothesis we shall assign to P, Q, the very values, which in the 

 first we have found for P f ) Q , We shall put, therefore, 



x = log P = 0.0790164 

 y = log Q = 8.5475981 



Since the calculation is to be conducted in precisely the same manner as in 

 the first hypothesis, it will be sufficient to set down here its principal results : 



210 8 24&quot;.9S 

 0.3307676 

 0.3222280 

 205 22 15 .58 

 -3 14 4 .79 

 7 34 53 .32 



3 29 .18 



4 5 53 .12 



It would hardly be worth while to compute anew the reductions of the times 

 on account of aberration, for they scarcely differ I s from those which we have 

 got in the first hypothesis. 



The further calculations furnish log ij = 0.00022 70, logi?&quot; = 0.0003173, whence 

 are derived 



log ^=0.0790167 

 log (X= 8.5476110 



X= + 0.0000003 

 Y = 0.0000129 



From this it appears how much more exact the second hypothesis is than the 



first. 



154. 



In order to leave nothing to be desired, we will still construct the third hypothe 

 sis, in which we shall again choose the values of P , Q , obtained in the second 



