70 HISTORY of the SOCIETY. 



ficulties, and were led into an error of the fame magnitude. 

 It is true, that, on refuming their computations, they found, 

 that they had not carried their approximations to a fufficient 

 length, which when they had, at laft, accomplimed, their re- 

 fults agreed exactly with obfervation. Mr WALMSLEY and 

 Dr STEWART were, I think, the firft Mathematicians, who, 

 employing in the folution of this difficult problem, the one the 

 algebraic calculus, and the other the geometrical method, were 

 led immediately to the truth ; a circumftance fo much for the 

 honour of both, that it ought, by no means, to be forgotten. It 

 was the bufmefs of an impartial critic, while he examined our 

 Author's reafonings, to have remarked, and to have weighed 

 thefe confiderations. 



WE may add, that the accurate meafurement of the fun's di- 

 ftance, and the complete theory of the moon's motions, with 

 which fcience has been enriched, fince the time to which we now 

 refer, fufficiently vindicate the principle of Dr STEWART'S inve- 

 ftigation, and (how how much reafon he had to expect, that the 

 former might be inferred from the latter with confiderable ex- 

 aclnefs. M. MAYER, from one of the lunar irregularities, com- 

 putes the fun's parallax to be 7". 8, nearly a mean between the 

 parallax already mentioned, and that which has been deduced 

 from the tranfit of Venus in i 769 *. 



ON the whole, therefore, while it muft be acknowledged, 

 that Dr STEWART'S determination of the fun's diftance is, by 

 no means, free from error, it may fafely be afTerted, that it con- 

 tains a great deal which will always intereft Geometers, and al- 

 ways be admired by them. Few errors in fcience are redeemed 

 by the difplay of fo much ingenuity, and what is more fingu- 

 lar, of fo much found reafoning. The inveftigation is every 

 where elegant, and will, probably, be long regarded as a fpeci- 

 men of the mod arduous enquiry which has been attempted by 

 mere Geometry ; at the fame time, the miflake into which the 

 geometrical method has betrayed this great Mathematician, will 



ferve 



* Theoria Lunue, fetf. 51. 



