Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/165



New Haven, October, 1898. Dr. ,

My dear Sir,—The opinion of Fabritius on the comparative convenience of different methods is entitled to far more weight than mine, for I am no astronomer, and have calculated very few orbits, none, indeed, except for the trial of my own formulæ. The object of my paper was to show to astronomers, who are rather conservative (and with right, for astronomy is the oldest of the exact sciences), the advantage in the use of vector notations, which I had learned in Physics from Maxwell. This object could be best obtained, not by showing, as I might have done, that much in the classic methods could be conveniently and perspicuously represented by vector notations, but rather by showing that these notations so simplify the subject, that it is easy to construct a method for the complete solution of the problem. That the method given is the best possible, I certainly do not claim, but only that it is much better than I could have found without the use of vector notations. Some of the more obvious crudities in my paper have been corrected in that of Beebe and Phillips. Doubtless many more remain, even if the general method be preserved.

My first efforts, however, to solve the fundamental approximative equation were along the same lines which Fabritius has followed:—to set $$r_{1} = r_{2}$$ and $$r_{3} = r_{2}$$ in equation second of (2) of Fabritius, which will give $$\rho_{2}$$ and $$r_{2}$$, then to get $$r_{1}$$ from the first of (3) of Fabritius, and then $$r_{3}$$ either from equation second of (3) or from some other