Prench National Injlitute. 185 



of queftiotis beyond the reach of the ancient geometry have 

 been rcfolved, and form at prefent fo vaft a body of fcience 

 that the mind, occupied with its developements and demon- 

 Itrations, can fcarcely comprehend the whole. This infpired 

 C. Prony with the idea of compofing a methodical table of 

 all the refults difengaged from intermediary calculations. 

 This is what he cd\[?: ynechan'ical plnlnfopkj. He compofed 

 thij work from the leflbns and materials he collefted for the 

 Polytechnic School ; and his obje6l is to furnifli ftudents 

 with the ineans of placing together and arraiiging the dif- 

 ferent parts of inftrliftion they have received. The author 

 quotes the fources from which he derived his information, 

 but his work contains a great many things which belong to 

 himfelf, either as to the matter, or manner in which it is 

 prefcnted ; fuch, for example, as everything that concerns 

 fquilibrium ; a method of obtaining the fundamental equa- 

 tions of ftatlcs without employing in any manner the theory 

 ot momenta ; a general demonltralion which fliows that the 

 theorems refpeti^ling momenta are only a peculiar enunciation 

 of the principle of virtual velocity ; new formuloe for the equi- 

 librium and prelTure of elaftic fluids, taking into confidera- 

 lion the variation of dilatibility, and formulae which may 

 give to the barometer more generality and more certainty in? 

 practice than has hitherto been the cafe in determining the 

 height of mountains. The author alfo makes a very import- 

 ant application of his principles to the calculation of the 

 force with which earth prelTes againft walls. The formula 

 bf Frony are entirely new, and exceedingly (impie. 



In confequence of two papers on the motion of the moon, 

 read in the lad public fitting of the InRitute, and which were 

 deemed worthy of a prize, Laplace has made a new and very 

 happy application of the theories publiOied in his Mecaniqjie 

 CfUjh. M.Burg,ofieof the two authors who gained the prize, 

 had remarked a periodical e<}uality in the moon's motion in 

 latitude, and had found that the duration of this period v/a3 

 eighteen years, lie, however, afligncd no caufe for it, nor 

 gave any law. On the contrary, he requefted both thefc 

 from the author, who has explained in fo complete a man- 

 ner the fecular inequalities of the moon. Jiis expettation 



Vol. VII. B b has 



