Value of y or or. Value of w or o r.
7.0309 2 7.1243 3 7.2806 4 7.5015 5 7.7888 6 8.1452 7 8.5737 8 9.0781 9 9.6628 10 10.3333" Otherwise : Instead of making a the number of the log. c y A, if we put m = the natural number of the log. c y w —only ; them m = , andam—w= (LP — or by squaring, &c. as — 2 a m w = 1 — and hence w x a ; to which the numbers being applied, the very same conclusions result as in the fore going calculation and table." The following description of a method of stone-roofing in the Southern Duncan. in the East Indies, was communicated to the Institution of Civil Engineers by lieutenant Outrarn, of the Bombay Engineers. Though hardly applicable to the climate of this country, it seems of considerable value as relating to an important part of the British Empire. The few houses which had been constructed on this plan were found to answer so well, at the time this paper was written, that government had given orders to construct, on this prin ciple, all the public buildings, wherever suitable materials could be found.
The roofing with stone (iron-clay, or laterite) in the Southern Concan, is of a compound nature, of two kinds of arches ; the first being parallel to each other, from 2 to 3 feet apart, and very light, their average section being from 12 by 10 inches to 15 by 12 ; i, e. for roofs of from 25 to :35 feet span ; so that when any two of these arches or ribs are complete, they are strong enough to bear slabs of stone 5 or 6 inches thick, extending a few inches over each, begin ning from the wall and meeting at the top, thus forming a second complete arch, and making, with the ribs, a compound much stronger than vaulting of equal solidity over the same extent, made in the usual way.
The lateral thrust of the arches of one room are counter acted by those of the rooms on its sides, and so on tier any extent ; those of the end-rooms being counteracted on their outer sides by buttresses, or by the walls of baths, &c., so that the walls are required to be only sufficiently strong to support the mere weight of the masonry of the roofs, which has an average thickness of about if inches, excepting the plaster or tiles, and, thereflfre, in rooms of -1110 square feet, %%mild be about one-fifth the weight of the upper wails of a two-storied house. As the roof itself is of considerable alti tude, the walls supporting it need not be of more than two thirds the usual height.
One advantage of the lightness of these roofs is, that of whatever form the arches may be, very little loading will suffice ; of course some arches would require no loadino., but such are not the most convenient for roofs in general. The best appears to be a compound of two segments of a of 50°or their chords intersecting at an angle of about such compound arch requiring a little loading ut the top ?nd the haunches, which, when duly added, gives an cutter sa•ff•e of two inclined planes to each roof, a hich may he then either plastered or tiled. But instead of binding the haunches throughout with solid rubble, it is better to 110 so partly with hollow masonry, to the upper stirlimce of which may be !riven any slopes which, by the connection of the opposite slopes of any two adjacent roofs, form a gutter of the securest kind. The average height of this gutter should be about one-third that of the roof; if to be plastered, but not so much if the roof is to be tiled.
The expense of these roofs, including the outer plaster, has been ilmnd by myself' and suceessor. in the Concan, to be much less than that of tiled roofs over the same extent. The walls should cost no more than those of a substantial bungalow; for although the transverse walls have a greater weight to support, yet, as they need be only two-thirds the height, their total expense should not be than that of the walls of a substantial house. The only part of which the comparative expense remains to he considered, is time ceiling. The inner surface of the stone roofs, when finely plastered, forms an excellent ceiling; being light awl cleanly, and most durable. The expense of this plastering, it' not much orna mented, is below one-third that of the lath-and-plaster gene rally used. Hence it is plain, and has been practically found, that the total expense of stone-roofed houses in the Concan, if properly constructed, is less than that of tiled h,,uses of the same size ; but the sums saved in annual and special repairs are of fitr greater consideration. In the Wean, where timber is so expensive, the comparative cost of these build ings would be still less, in all those parts of it where proper stone is met with.