324 The Orbit and Motion of 



the fuppofition of the moft rapid decreafe of the fecond diffe- 

 rences will agree very well with FLAM^TEAD'S obfervation of 

 that Star on December 1 3. 1 690, being only 40", or perhaps on- 

 ly 1 2", to the weftward of it. But the latitude differs more 

 than two minutes from FLAMSTEAD'S latitude, which is right- 

 ly deduced from the Zenith diftance. This is too great an er- 

 ror for him to commit in the obfervation, and we mould there- 

 fore reject the fuppofition on this account alone. But there are 

 ftronger reafons for rejecting it, arifing from the difagreement 

 of thofe elements with the obfervations made on the ftations of 

 the Planet in October 1781, and March and October 1782, 

 which give us a very near approximation to its diftance from 

 the Sun. When compared with obfervations of the Planet 

 near its ftationary points in the Spring, they give the geocentric 

 longitude confiderably too great, while they give it too fmalL 

 for the fimilar obfervations in Autumn. 



THE appearance of this Planet has ferved to exercife the in- 

 genuity of mathematicians, by a problem confiderably different 

 from that afforded by the motions of comets in very excentric 

 orbits ; and, by this means, has favoured the public with ma- 

 ny improvements in analytical knowledge. My profeffional 

 duty has made me confine myfelf chiefly to the fearch of 

 fuch methods as might be very intelligible to perfons pofleffed 

 of fmall degrees of mathematical knowledge. The method 

 now exhibited has this advantage in an eminent degree ; and 

 therefore, although it will not engage the attention of fkilful 

 mathematicians, I hope it will be ufeful, becaufe it may incite 

 beginners to a zealous profecution of this noble ftudy, by mow- 

 ing them fome of its moft pleafing gratifications. I may add, 

 that the method now exhibited is one of the moft likely to give 

 us an accurate knowledge of the Planet's motion. Another pe- 

 riod of four years will enable us to apply it to arches of double 

 extent, which will diminifh the errors arifing from the unavoid- 

 able inaccuracy of obfervations to one fourth of their prefent 

 quantity, and a comparifon of the new elements with thofe now 



given. 



