French National Infnluic. l8l 



made of his principles, the author applies them to a great 

 number of theorems and proportions, feveral of which are 

 remarkable for their fimplicity and elegance. What he fays 

 of chords; the new idea he gives of fines; and the addrefs 

 with which he has found means to render fenfible to the eyes, 

 in one figure, the principle relations that exitt between the line 

 and the cofine of two angles, and the fine and cofine of their 

 fum, or their difference, will be in particular di(iingui(hed. 



Memoir on the theory of the moon. — C. Laplace has col- 

 lected in this memoir the molt inlerefting refuhs of his ana- 

 lytical calculations refpe6ting the theory of the moon. The 

 equations which he found for the mean longitude, the apo- 

 geum and the node, and the happy manner in which he 

 employed the inequalities, either in longitude or latitude, 

 to deduce from them the oblate form of the earth, are aiready 

 known. He now announces a determination no lefs curious, 

 that of the parallax of the fun. Mayer made a fimilar cal- 

 culation; but, befldes that the analyfis of that great attro- 

 nomer was lefs profound, he was far from having fo great 

 a number of observations to enable him to determine the 

 precife value of the inequality which the parallax may give. 

 He found it therefore about ,- too fmall ; whereas C. La- 

 place has attained preeifely to the fame quantity as Lexell and 

 Lalande deduced from palfagcs of Venus, that is to fay, 8 7 6. 

 An aftronomer, therefore, without going out of his obferva- 

 tory, by uniting analyfis with obfervation, might have de- 

 termined what has colt fo many voyages to countries fo dif- 

 ferent in climate. We mull however obferve, that this me- 

 thod would have required much more time, and that much 

 fewer perfons would have been in a (late to appreciate the. 

 juftnefs of the refult. There is no reafon, therefore, to regret 

 the long voyages undertaken, nor even to prevent people 

 from braving fuch dangers, when an opportunity occurs. 

 Too many different means cannot be employed to eftabliih 

 truths which, on the one hand, are furRciently aftoni (l)ing to 

 juftify, to a certain point, the incredulity of thofe who refufe 

 to admit them, becaufe they do not comprehend the demon- 

 ilrations ; and, on the other hand, are fo delicate that one 

 can never be certain of knowing them with the utmolt pre- 

 cifion. 



Trigonometric tables. — C. Prony has read to the Clafs a 

 memoir on a work called Opus Palatinum di Triangulis. 

 Thefe tables, the moll complete that ever appeared in regard 

 to trigonometric lines in natural numbers, were not calcu- 

 lated in all their parts with the fame exactnefs. It was footl 

 found that the tangents and feeants of the lad degrees had 



. M 3 need 



