This singularly bold platband was made under the conduct of Pere Mourgues, after the design of Cubi sol, an able architect. The stones are I foot thick, their depth is 2 feet towards the key, and 2 feet 4 in 4..hes at each end. It had a camber given it of about 6 or 7 inches, and descended near 3 inches on striking the centres. (Gauti.r.) Wu see, that the horizontal pressure does not de termine die vertical thickness of the arch-stone. But as we pass down the arch, it is plain that the butting surfaces must increase, in proportion to the increasing tangential pressure.
At sixty degrees from the vertex, granting that the arch is equilibrated, the depth of the arch-stones must be doubled ; and though the equilibration be carried no farther, yet, at the springing or horizontal joint, a small increase will still be necessary. The ratio will soon be found. To the square of the weight of the semi-arch, add the square ol tne horizontal thrust, the square root of the sum is the pressure at the springing. If we di vide this by the horizontal thrust, it will give the thick ness at the springing, compared with that which is ne cessary at the crown. Or it we divide it by 3121, it will give the smallest depth ol joint which should he used at the springing. Tile thrust and weight are supposed to be given in soliu feet. It given in pounds, divide the above quoti..n. by 160, or divide at once by 50,000.
_Example. Required the thickness of the lower joints for a semicircular arch, when the weight of a section of a toot in breadth from the crown of the arch to the springing is 60,000/b. and the horizontal thrust is 20,000/b. which answers nearly to a 60 feet arch, 4 feet thick at the crown.
For another example, take a 50 feet arch, having 5 feet thickness at crown. The semi-arch may be lound sufficiently near, by multiplying the half span into the hall height to the road, viz. 25 xl5=375. And the ho rizontal thrust 5x25=125 feet ol stone, their sum is 156250, the square root of which, divided by 3121, gives 1.265, or 1 foot 3 inches ; 125 and here again the vertical section might or 4 inches only.
If we calculate upon the same principles, the depth of arch stone at the spring course of a semicircle of 100 feet span, 10 feet thick at crown, we shall find it to be 5 feet, and at the crown the depth may be 19 inches.
In the great arches of the bridge of Neuilly, the thick ness at the crown is about 4 feet 8 inches, the span 128.2 feet, and height 32. The horizontal thrust is great, the crown being drawn with a radius of 150 feet ; con sequently this arch would require a depth at springing of about 4 feet. But when the centre was struck, the crown of this arch descended 23 inches, which has ren dered it a portion of a much larger circle, and has great ly increased the horizontal thrust. After all, the pres sure at the springing is scarcely greater than in the last example, and the depth of joint there need not have exceeded five feet. It is nearly three times that, and even at the crown the thickness is a greater than the increased thrust would require. We trust, therefore, that, in spite of the great risk this singular arch has run, it may yet long remain a monument ol the skill and boldness ol the able architect who designed it.
It may be proper to observe, that the French archi tects Perronet and Soufflot, made an experiment on the strength of the stone of which it was composed. They found, that a cubic foot of it, which weighs 1521b. re quired 240,0001b. to crush it. In the above investiga tion we have on.y taken it at 50,000.
The thickness at the crown of the arch, cannot, with propriety, be reduced so much as we have supposed in the above examples. This part of the structure is liable to be strained transversely. And it has been found, that when stone, or other matter, is bearing a great pressure longitudinally, its strength against a transverse strain is thereby much diminished. But, independent of that, there is another cause for preserving the crown of a greater thickness. The varying pressure of carriages would be apt to produce some motion among small stones ; this would chip away their angles, and accele rate the destruction of the building. But there is sel dom any need for this reduction. In most cases, it would only be additional labour.