l8o French National Injlituti. 



in which, unfortunately, they have had too many imitators 

 among tlic moderns. 



La Hire was the firft, at leafl: in France, who deterniined, 

 by the theory of the wedge, the proportion according to 

 which the weio-ht of the arch ftones ouo;ht to be augmented 

 in a femi-circular arch. 



In T 704, Parent determined bv points the figure of the 

 extrados of an arch the intrados of which is a femi-circle. 

 He determined alfo the pufli of fuch an arch on tl^e abut- 

 ments. 



James and John Bernoulli, Huygcns, and Leibnitz, having 

 relolved the probletn of the catenarian curve, it was Iboii per- 

 ceived that this curve was that of the equilibrium for an arch 

 compofed of arched ftones infmitely fmall and equally heavy. 

 David Gregory fliowed this facl, and it is deduced fiill more 

 diTe^lIy from a method given by James Bernoulli. A fecond 

 method of the fame autlior, corrected by C. Boflut, conduds 

 to the fame conclufion. 



La Hire in 17 13 gave a method, founded on fome experi- 

 ments, which, on account of its great facility, was adopted 

 by praftical workmen, who gave themfelves no trouble to 

 inquire whether it was applicable to all cafes. Not content 

 with following it in femi-circular arches, thev applied it even 

 to domes, though the equation of the equ^librium in this 

 cafe is of the third degree, and not of the fecond, as in the 

 preceding cafe. 



" Couplet has treated of the pufh of femi-circular arches, 

 and of the thicknels of their abutments ; firft, by confidering 

 the arch ftones as infinitely fmooth, and experiencing no re- 

 fiftance from frlftioa; and then he endeavours to corre6t 

 what niay be defecilive in this fuppofition : but he does not 

 gb further than Parent and La Hire. 



Bouguer has treated of domes. He has-fhown that a va- 

 riety of curves may be emploved in them, and of thefe he 

 points out thofc moft advantageous. But he has not calcu 

 Jatcd the pufti, nor lias he examined the law of the forces 

 which muft aft on the arch ftones when the generating curve 

 is fubjefted to given conditions; a fubjedl fertile in curious 

 and ufeful problems. 



' In 1770 C. BofTut undertook to treat of the queftion in its 

 whole extent, both in regard to femi-circular arches and 

 domes. He examined every thing that relates to the form 

 and piifti of arches. His memoirs were printed in the Tranf- 

 a&ions ot" the Academy of Sciences for the years 1774 and 

 1776. ' ' , 



Mafcheroni, 



