t 183 ] 



XXXII; ExtraB from the Report made to the French Beard 

 vf Longitude by C. Lagrange, Laplace, Mechain, 

 and Delambre, on the Lunar Tables fent to the Board 

 to compete for the Prize propofed on that Subjetl. 



T, 



HE public will recollect with what intereft the National 

 Inftitute received, two years ago, the memoirs of the aftro- 

 liomers Biirg and Bouvart refpecling fome of the elements of 

 the lunar tables. Struck with the importance and immenfity 

 of their labour, the elate of the mathematical and phyfical 

 fciences, the prefident of which at that time was of all its 

 members the one who could bed enfure the eclat and fuccefs 

 of its deliberations, decreed that the prize to be offered mould 

 be doubled. By doing much more than w as .required of 

 them, the competitors gave birth to a queiiion far more diffi- 

 cult than that which thev had folved. The fame mean mo- 

 tion was not capable of fatisfying the epochs which they had 

 eftablifhed for the commencement, the end, and the middle 

 of the 1 8th century. 



This irregularity, fo alarming for the future precifion of 

 the tables, could not be explained but by fuppofing, either 

 that the inequalities already comprehended in the tables were 

 not fufficiently well known, or that there were ftill wanting 

 fome equations which had hitherto efcaped the rcfearches of 

 all geometricians. 



The terrible labour which thefe new confiderations required 

 did not permit us to hope for fo fpeedy a folution as was ne- 

 cefiary to the wants of agronomy and navigation. It was 

 requi.fi te that an appeal (honld be made to all aflronomcrs, in 

 the hope that foiire of them might have colle&ed a feries oi 

 the necelTary materials. The board of longitude applied with 

 confidence to a. Government compofed in fuch a manner as to 

 be fenfible, much better than any other that ever exiited,of the 

 value of the fciences and of the utility of their application. 

 With its content, the m milters of tire interior and marine 

 contributed in equal portions towards an extraordinary prize 

 of 6000 francs (240I. (IcHing), which they haiiened to pro- 

 pofe to the emulation of the altronomers of all countries. 

 Twenty months after this prize was announced, the board of 

 iongitude received the new tables of which we arc going to 

 give an account. 



To verify the tables conftrucrxd from the whole mafs of 

 the good observation* publifhed till that period, it was ne- 

 ceflary to have other obfervations, equally good, but more 

 recent. Choree was made of 150, both from the regi Iters of 



N 3 the 



