220 DETERMINATION OF AN ORBIT FROM [BoOK II. 



The interval of time between the second and third observations is 39.874409 

 days, between the first and second 30.900961 : hence we have 

 log 6 = 9.8362757, log d&quot; = 9.7255533. 

 We put, therefore, for the first hypothesis, 



x = log P= 9.8892776 

 y = log Q = 9.5618290 

 The chief results of the calculation are as follows : 



w + &amp;lt;j = 20 8 46&quot;.72 

 log Qc sin co = 0.0282028 



Thence the true value of z is 2111 / 24&quot;.30, and of log/, 0.3509379. The three 

 remaining values of z satisfying equation IV., article 141, are, in this instance, 



z= 63 41 12&quot; 

 z = 101 12 58 

 2=199 24 7 



the first of which is to be regarded as an approximation to the orbit of the earth, 

 the deviation of which, however, is here much greater than in the preceding 

 example, on account of the too great interval of time. The following numbers 

 result from the subsequent calculation : 



195 12 2&quot;.48 



C&quot; 196 57 50 .78 



logr 0.3647022 



log/ .... 0.3355758 



*K + w) ... 266 4750 .47 



*(M&quot; ) . . .43 39 5 .33 



2/ 22 32 40 .86 



2/ 13 541.17 



2/&quot; 9 27 .05 



&quot;We shall distribute the difference between 2/ and 2/-J-2/&quot;, which in this case 

 is 0&quot;.36, between 2 /and 2/&quot; in such a manner as to make 2/= 13 5 40&quot;.96, 

 and2/&quot;=926 59&quot;.90. 



The times are now to be corrected for aberration, for which purpose we are to 



