94 Journal of the Pot^ttchnic Schcsl at Paris. 



in order that tlie angles of two contiguous key-ftoncs being refpe£livc!y equal, tlicy may 

 alike refill difunlon by the aclion they exercife upon each other. ^. They muft be per- 

 pendicular between the Hones, for the fame reafon. 3. They mull be generated by the 

 motion of a right line ; for the furfaces generated in this manner are alone fufccptible of 

 being accurately wrought ; ami it is neceflliry that the joints of the contiguous Hones Ihould 

 be perfc£lly weir executed, becaufe very flight irregularities would produce a rupture of 

 the arch." 



-Ml thcfe conditions may be ob'ained by dividing the curved furfaces of a vault by lines 

 drawn from the one to the other of the two curves; and formed by the movement of a 

 point of the furface which meets a feries of normals placed in the fame direftion. Tlie 

 diilance between thefc lines mud be a finite quantity, dependent on the nature of the 

 materials. 



" The operations of artifts having been conllantly directed to this general folution, they 

 liavc obtained it only for the molt eafy cafes of cylinJric and conical furfaces, and fuch as arc 

 generated by the revolution of a plane. But with regard to curved furfaces of which they 

 know not the lines of curvature, they almofl generally excluded them from the conllrucliou 

 of arches, even when circumllances urgently demanded them; and it is principally to this 

 that we are to attribute the bad effe£l generally produced in architeclure by leaning arches, 

 or portions of arch-work (les morceaux de trait de coupe des picrres), becaufe, in order to 

 render this pradicable, a furface or curvature is chofen for the arch which is not always 

 fuch as the nature of things demands." 



The example chofen by Monge for the application of his principles, is apparently the 

 rooll happy he could have fele£led in the prcfent Ctuation of the French government, in 

 which architeifls arc bufied in the conllruflion of halls dcllined for the fittings of the Le- 

 giflative Council. Now the form mod favourable to the dillribution of the members of 

 a deliberative aflembly, and the fituation of the orator, is the elliptic curve commonly 

 called an oval. From the projeiflion of thefe curves, traced on the defigns at the end of 

 this memoir, it may be fecn what agreeable and elegant forms arc thus produced ; and 

 how eminently the architccl may avail himfelf of the principles here eftablinied, even 

 for the obje£l3 of decoration. Students in architedure will find this memoir highly 

 deferving of their perufal. It will more and more convince them of the immenfe refources 

 afforded by the ftudy of llereotomy for the folidity of conllrutlion, and even for beauty of 

 new forms, afforded by this theory to the fyllem of ornament. 



The art of fecuring thofe v;ho defend a rampart from the ftroke of balls and fliot is 

 known in French b^ the term defilement. Say, afTiftant profefl'or in the Polytechnic 

 School, has given a memoir on this fubjetH in the fourth cahier of the Journal of that 

 inllituiion. 



He (liews in the firll place, that the outline of the defilement is the fame as that of a 

 fhadow afforded by a row of luminous points fituatcd in tlic fpace from which the de- 

 fenders of a fortification may be fired on. 



He dividers his ground into two parts : the exterior fpace in which the attacking party may 

 be placed, and the interior fpace which is to be defended. 



He examines the art of fecuring a work (de filer) in two diiTerent cafes : i. That in 

 which the parapet is determined. 2. That in which tlie ground plan is given, but not ab- 



folutcly 



