Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/160

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144
DETERMINATION OF ELLIPTIC ORBITS.


{{c|VIII. The logarithms of the calculated values of the intervals of time exceed those of the given values by .0002416 for the first interval () and .0002365 for the second (). Therefore, since the corrections for aberration have been incorporated in the data, we set for the correction of the formula (for the second hypothesis)

This gives


The new values of the logarithms of are

Applying these corrections to equations [1] we get the following:

corrected.


+ .002887 –.0000217
2.5142140 2.5145027 2.5144810
.4282377 .4282816 .4282782
8.3838110 8.3838793 8.3838894
.0103847 .0103863 .0103865
.3389910 .3389784 .3389796
1.2866654 1.2868124 1.2868024
.0249593 .0249619 .0249617
.1241571


corrected.


– .0000955 +.0000187
2.5704563 2.5703608 2.5703795
0.4132937 .4132778 .4132809
9.0780129 9.0780605 9.0780513
9.9446418 9.9446353 9.9446365
.6401725 .6401487 .6401532
2.1806412 2.1805261 2.1805482
.1827615 .1827481 .1827507
.3579174
  1. The corrections may be made without rewriting the equation.