146 



times about the fun. The problem, therefore, was to aflign at any time 

 the place of a planet moving according to fuch a law. Ward, Boulliald 

 and Mercator, however, only adopted the orbit, but not the law of the 

 motion in the orbit. They imagined fuch a law as would readily en- 

 able them to deduce the place of the planet, and then had recourfe 

 to obfervation, to eftablifli the truth of their refpe<ftive hypothefes. No 

 one attempted to compare his own hypothefis with Kepler's difcovery 

 of the equable defcription of areas. Each confidered his own hypothe- 

 fis as reding 1 pon as folid foundations as Kepler's. Till the phyfical 

 difcoveries of the illuftrious Newton, and the more improved Hate of 

 aftronomical inftruments, it might perhaps have been impoffible to have 

 decided between the refpeftive hypothefes of Kepler, Boulliald, and iVTer- 

 cator. In refpeft to Ward's Hypothefis, there could have been no 

 doubt of its imperfection. The fuperior fagacity of Kepler, in eliciting 

 from the obfervations of Tycho Brahe the true law, and not refling 

 upon fuch a conclufion as Ward has done, can be never fufEciently 

 admired. However the extreme fimplicity of the application of Ward's 

 Jiypothefis to pradice, will always occafion it to be noticed. 



After Mercator's, the two praftical folutions given by Sir Ifaac 

 Newton* are examined. From the former of thefe two folu- 

 tions a praftical one may be derived, which appears to be far 

 preferable to any other that has been given. The fecond folution, al- 

 though confidered by its great author, as better adapted for praftice, is 

 not fuiEciently exact for the prefent flate of aftronomy, and by ex- 

 tending its accuracy, nothing would be gained in point of brevity. 



The next folution deferving notice, was given by the fecond 

 Caffini. He pointed out, in 1719,! a very near approximation for 

 the excentric anomaly, and then a correftion of that excentric ano- 

 maly. The approximation was adopted by De la Caille,| and cor- 



reded 



* Schol. 6 Sea. Lib. 1. Princ. Math, 

 t Mem. R. Acad. 171 9. CafTini's A(lr. 

 :;; De la CaiUe's Aftronomy, Art. 144. Vinces Aft. 225. 



