99 



in Ward's hypothcfis : max. of error in BouUiald's : : 3 : Se nearly 

 when e is fmalJ. Hence, for all the planets the hypothefis of Boul- 

 liald is more accurate then that of Ward, and by no means deferves 

 the cenfure that has been paffed upon it, by fome authors. Emerfon 

 obferves,'* the correftion of Seth Ward's hypothefis given by Boulliald, 

 only mends it in fome places, and in others makes it worfe. Simp- 

 fou, as I obferved, millook this correftion. He fuppofedf Q^H A to 

 be the mean anomaly, and R the place of the planet. On this fuppo-- 

 fition he found the error much the fame as the error of Seth Ward's 

 anomaly.' Montuclat fays, that BouUiald's hypothefis « ne vaut pas 

 mieux." 



Indeed, it is remarkable how much Boulliald has been mifreprefented, 

 - Adam Smith, in his Hiftory of Aftronomy| fays " Thus Boul- 

 " liald, who cenfured this hypothefis of Ward, invented another of 

 " the fame kind, infinitely more whimfical and capricious." Then he 

 proceeds to give, not the fecond hypothefis of Boulliald, but the firft: 

 hypothefis to which Ward had ftiewn his own hypothefis equivalent. 



Of Mercator's Hypothefis. 



Mercator, not fatisfied with either of the hypothefes above men- 

 tioned, invented what he calls his new hypothefis, which he coiifidered 

 as more accurate than any preceding one. With what juftice, I (hall 

 proceed to examine, by comparing his anomaly with the true ano- 

 maly. He himfelf compared it with forty-two places of Mars obferved 

 by Tycho Brahe. 



His hypothefis was as follows, 



N 2 Let 



* Emerfon's Aftren. p. io8. 



t E%«, p. 48. 



' t Hift. Math. Tom. 2. Edit. 2, page 340. 



