APPENDIX. 321 



The difference 0&quot;.2 between 2/ and 2/-f-2/&quot; is divided as in the first 

 hypothesis, making 2/ = 6 57 15&quot;.55, and 2/&quot;= 6 56 43&quot;.39. 



All these numbers differ so little from those given by the second hypothesis 

 that it may safely be concluded that the third hypothesis requires no further cor 

 rection ; if the computation should be continued as in the preceding hypotheses, 

 the result would be X= 0.0000000, F 0.0000001, which last value must be 

 regarded as of no consequence, and not exceeding the unavoidable uncertainty 

 belonging to the last decimal figure. 



We are, therefore, at liberty to proceed to the determination of the elements 

 from 2/ , r, r&quot;, 6 according to the methods contained in articles 88-97. 



The elements are found to be as follows : 



Epoch of the mean longitude, 1845, .... 278 47 13&quot;.79 



Mean daily motion, .... .... 771&quot;.5855 



Longitude of the perihelion, 148 27 49&quot;.70 . 



Angle of eccentricity, 4 33 28 .35 



Logarithm of the major semi-axis .... 0.4417481 



Longitude of the ascending node, .... 80 46 36&quot;.94 



Inclination of the orbit, 10 37 7 .98 



The computation of the middle place from these elements gives 



= 324 34 51&quot;.05, /? = 14 45 28&quot;.31 

 which differ but little from the observed values 



== 324 34 50&quot;.92, fl = 14 45 28&quot;.28. 



41 



