Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/161

Rh

With these corrected equations the last values of $$q_{1}, q_{2}, q_{3}$$ give the residuals These give the corrections  The next residuals are  which give the corrections  The next residuals are  which must be regarded as entirely insensible.

It remains to determine the ellipse which passes through the points to which the numbers relate in the last columns under the corrected equations $$\text{III}_{1}, \text{III}_{2}, \text{III}_{3},$$ and also the time of perihelion passage. The computations are as follows: