308 The Orbit and Motion of 



defcribed by the Planet. This was a very difficult taflc ; for 

 the very fmall inequality of the motion fhowed that the orbit 

 was nearly circular ; and the arch already defcribed was not 

 much more than the fiftieth part of the 'whole circumference. 

 The folution of the problem requires us to determine, from 

 the variation of curvature difcoverable in this fmall arch, to 

 what part of the circumference it belongs. This requires the 

 utmoft accuracy in the obfervations, and great fagacity in making 

 deductions from them *. But, taking it for granted that the 

 p64th Star of MAYER'S Catalogue was the new Planet, the 

 problem becomes fufceptible of a very eafy folution ; for that 

 Star is fituated more than a quarter of a revolution from the 

 place of the Planet in 1782, and fo fortunately, that almoft 

 the whole effect of the excentricity and inequality of the mo- 

 tion is accumulated. Aftronomers, therefore, availed them- 

 felves of this obfervation of Mr BODE, and quickly found, by 

 repeated trials, elements of the motions, which correfponded 

 perfectly with MAYER'S obfervation, and all thofe made fince 

 Mr HERSCHEL firft got fight of the Planet. But they do not 

 all feem difpofed to confefs their obligation to Mr BODE. 

 Some of them affect to have deduced their elements directly 

 from obfervations, by the formulae expreffive of the elliptical 

 motion of the Planets, and to be agreeably furprifed with after- 

 wards obferving the coincidence of their elements with this ob- 

 fervation of MAY^R. They have not given a detail of their 

 methods of inveftigation. 



OF 



* THE firft perfon who obtained any direft information of the elliptical orbit ofthe 

 Planet was the celebrated Abbe BOSCOVICH, who, in October or November 1781, dedu- 

 ced elements of its orbit from the obfervations of Mr MECHAIN. His method is ex- 

 ceedingly ingenious, and remarkable for that fimplicity and geometrical elegance which 

 charatterife all his performances. It did not come to my knowledge till the beginning 

 of this prefent year 1787, when 1 found it in the Collection which he publiflied at Baflano, 

 in 1785, in five volumes. He makes ufe ofthe fame phyfical principles which I employed 

 in January 1783, to determine the orbit by the two oppofitions which had then been ob- 

 ferved, combined with another obfervation, made at the diftance of a fydereal year 

 from one of the oppofitions. This method 1 communicated to Dr MASKEJ.YNE in 1783. 



