French National Itistitiite. 1 79 



VT?r all the properties of the conic sections, and when Apol- 

 lonius made them the subject of a profound treatise, the 

 books of which haAC been long regretted, and which have 

 not been handed down to us; might not the same reproach 

 of the loss of time in meditations w hich might have been 

 better employed, have been addressed to them ? Who could 

 then foresee the numerous applications which have been 

 made of these curves to several branches of the mathema- 

 tics? and who could suspect that the ellipsis is the figure of 

 all the planetary orbits ? 



Of the most useful elementary problems, none has re* 

 ceived more solutions than that the object of which is to 

 correct the apparent distances of the moon from the sun 

 .and stars, in order to deduce from it tlie longitude at sea. 

 Tliis problem is not indeed very diflicult; but it is of daily 

 U'^e, and those who have occasion to employ it are not al- 

 ways well versed in calculation': on this account, the easiest 

 approximations sufficiently exact for practice have been 

 substituted for the rigorous methods, lire subject was 

 thought to be exhausted, and yet very simple considera- 

 tions, which never before occurred to any one, have fur- 

 nished C. Legendre with an entirely new solution. His 

 formula possesses a remarkable svmmetry, which serves to 

 engrave it on the memory. Nothing was wanting, but a 

 little brevity in the calculation ; and the author has found 

 means to iiive it this merit by including in two tables se- 

 veral terms, the suppression of which shortens the opera- 

 tion a third. Other known formuUe possessed the latter 

 advantage ; but the new solution has, above all others, the 

 merit of elegant symmetry; which ought to be considered of 

 trreat importance, since it contributes to facilitate the ope- 

 ration. 



If the phaenomena of the tides were subjected only to 

 the combined action of the sun and moon, they might be. 

 predicted u ith the same precision as the celestial phaeno- 

 mena. With a few data obtained by observation, one 

 iniu;ht announce before-hand, both the exact moment and 

 ih(r precise elevation of the waves. The action of the 

 winds, which will doubtless always escape our calculation, 

 may serve indeed to account for the principal and periodi- 

 cal causes of the tides : but it at least modifies their effects ; 

 it can increase or diminish, accelerate or retard them ; and 

 if the sun and moon shall happen to be so placed as to 

 produce the strongest tide, and if the wind conspire also to 

 raiee the waters, they may then produce extraordinary in- 

 undations, of which i't is of importance to be forewarned 

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