591 



for the presumption that " charlatanism sometimes extended even to 

 the domain of the mathematics." 



The first day of the present century was signalized by the discovery 

 of the planet Ceres at Palermo, and before the first observations of 

 the discoverer only two in number had been made known to astro- 

 nomers, the planet had ceased to be observable from her proximity 

 to the sun. The planet Uranus had been discovered twenty years 

 before, when near opposition ; this was a critical position, which at 

 once gave a near approximation to the elements of his orbit : a sta- 

 tionary elongation of Ceres, though less fertile in its results, was 

 sufficient to assign her such a place between Mars and Jupiter as was 

 required to satisfy Bode's singular law, the recent announcement of 

 which had already stimulated an enthusiastic band of German astro- 

 nomers to commence a systematic search for the planet, which Kepler 

 had found wanting for the fulfilment of one of that series of cosmical 

 speculations which had guided him to the discovery of his laws. The 

 complete determination, however, of the elements of a planet's orbit 

 from three geocentric longitudes and latitudes or from four of the 

 first and two of the second in those cases where the latitudes are 

 evanescent or small was still therefore a new problem which had 

 only been completely solved in the case of comets moving in para- 

 bolic orbits, and which Newton, to whom its first solution was due, 

 had pronounced to be problema omnium longe difficillimum. 



It was not until the month of October following the discovery of 

 Ceres, that Gauss came into possession of the requisite observations, 

 and in the course of a few weeks he had determined the elements of 

 her orbit with an accuracy fully commensurate with the observations ; 

 so much so, indeed, that the Baron de Zach was enabled to rediscover 

 the planet at the very first attempt which he made for that purpose 

 on the 7th of December following. The elements of Pallas, Juno, 

 and Vesta, the discovery of which followed that of Ceres at no great 

 distance of time, were promptly determined by methods substantially 

 the same, but materially improved by new artifices and adaptations 

 of formulae which an enlarged study and application had enabled him 

 to give them. 



The " Theoria motuum corporum coelestium in conicis sectionibus 

 circa solem ambientium," which contains not only the exposition of 

 these methods and their detailed exemplifications, but a most elabo- 



VOL. VII. 3 F 



