VI. 



ON THE USE OF THE VECTOR METHOD IN THE 

 DETERMINATION OF ORBITS 



LETTER TO DR. HUGO BUCHHOLZ, EDITOR OF KLINKERFUES' Theoretische 



Astronomic* 



New Haven, October, 1898. 

 Dr. HUGO BUCHHOLZ, 



My dear Sir, The opinion of Fabritius t on the comparative con- 

 venience 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 formulae. 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 ri = r 2 and r 3 = r 2 in equation second of (2) of Fabritius, which 

 will give p 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 



* [In which the preceding memoir, and also that of Beebe and Phillips referred to 

 below, are translated.] 



t[See Fabritius, W. "Ueber eine leichte Methode der Bahnbestimmung mit 

 Zugrundelegung des Princips von Gibbs," also " Weitere Anwendungen des Gibbs'chen 

 Princips," Astronomische Nachrichten, No. 3061, 3065 (1891)]. 



U"The Orbit of Swift's comet, 1880 V, Determined by Gibbs's Vector Method," 

 W. Beebe and A. W. Phillips. Gould's Astronomical Journal, vol. ix, Dec. 1889.] 



