40

If we suppose circles touching one another at thevertex were described with the different radii dueto different materials obtained from the formula

c = --— and arches cut off by the same span or the

same versed sine, the specific heights or versed sinesand specific semi-spans of a circular arch will be ob-tained from the common formulae.

x = c — v"V —y*

y ~ s/ ( 2 c — 3C ') X

all the dimensions in feet, and n

c

<w' — n

M. de Prony, in his Nouvelle Hydraulique, vol. i. del’equilibredes voutes, art. 373. deduces a formula to determine the heightof the key of an arch, and one to determine (art. 375.) the greatestspan with relation to the strength of the stone. He observes, whenexperiments showing the strength of stones are given and applica-tions of the formulae made ; it will be seen with astonishment howmuch more hardy the results of calculation give the dimensions,than those which are used in practice. He proposes to discuss ata future time the modifications which physical causes and theobstacles of construction will render necessary in such results,and to elicite the limits of hardiness possible in construction, or thebounds which nature has assigned to art. M. Gamier has an-nexed to the commencement of the second volume, by the consentofM. de Prony, what he calls an ^claircissement to art. 373; andfrom the formula has calculated a table, the data drawn from theBridge of Neuilly. This table makes the absolute pressure perfoot square on the joint at the vertex, equivalent to 17612 French

lbs. (or a column of the stone only* = 115,9 feet high of

that base, and = 14 nearly) or of the modulus of fracture,115,9

the same as deduced by M. Gauthe.

* Note, see radius of curvature and weight per foot cube, page 45. of thisTract, and art. S78 of M. de Frony’s work.