222 DETERMINATION OF AN ORBIT FROM [BOOK IE. 



267 6 10&quot;.75 

 ._43 39 4 .00 



22 32 8&quot;.69 



2/ 13 1 54 .65 



2/&quot; 9 30 14 .38 



The difference 0.&quot;34, between 2/ and 2/-f2/&quot;is to be so distributed, as to 

 make 2/= 13 1 54&quot;.45, 2/&quot; = 9 30 14&quot;.24. 



If it is thought worth while to recompute here the corrections of the times, 

 there will be found for the first observation, 0.009169, for the second, 0.008742, 

 for the third, 0.009236, and thus the corrected times, November 5.564905, Novem 

 ber 36.466293, November 76.340280. Hence we have 



logd 9.8362703 logr/ 0.0017413 



log 6&quot; 9.7255594 logP 7 9.8907268 



log TJ 0.0031790 i log^ 9.5710593 



Accordingly, the results from the second hypothesis are 



.X= 0.0000244, F= 0.0002271. 

 Finally, in the third hypothesis, in which we put 

 x log P = 9.8907268 

 y = log = 9.5710593 

 the chief results of the calculation are as follows : 



w+ff . . . . 20 8 1&quot;.62 log/ .... 0.3369536 



log^csinw . . 0.0370857 i(tt&quot;-ftt). . . 267 553.09 



z 21 12 4 .60 i(&quot; u) . . .43 39 4.19 



log/ 0.3507191 2/ 22 32 7 .67 



C 195 16 54 .08 



C&quot; . . 196 52 44 .45 



2/ 13 1 57 .42 



2/&quot; 9 30 10 .63 



logr 0.3630960 



The difference 0&quot;.38 will be here distributed in such a manner as to make 

 2/= 13 1 57&quot;.20, 2/&quot; = 9 30 10&quot;.47.* 



* This somewhat increased difference, nearly equal in all the hypotheses, has arisen chiefly from 

 this, that a had been got too little by almost two hundredths of a second, and the logarithm of 6 too 

 great by several units. 



