fore, be considered a useful practical rule, that, however soft a stone may be, if it resist the liability of damage until out of the masons' hands, there can be little doubt of its possessing sufficient cohesive strength for any kind of architectural work. If the foundation be insufficient, or any part of the edifice give way, so as to cause an unfair or unequal pressure, a soft stone will, of course, yield sooner than a hard one." 1502d. " Unfortunately," writes Warr, Dynamics, 1851, "those experimental results which we possess were obtained without attention to the fact that the specimens should be of a certain height to show a proper compressive strength. The bulk of the examples are with cubes, a fault excusable with those experimenters who made their work public before those peculiarities were well known, but the same cannot be said of the investigations conducted by the Commissioners; these experiments, executed with singular minuteness on some points, would have been useful, from their variety and specification of the localities, but they were made on (2-inch) cubes, at a period when the laws of fracture were as public as at present, and are therefore of limited value." 1502e. Hodgkinson (Phil. Trans., 1840, p. 385), found that in small columns of one inch to one and three-quarters inch square, and from one to forty inches long, a great falling off occurred when the height was greater than twelve times the side of the base. Thus, when the length was— 12 times the size of the base, the strength was 138 a little less 96 75 52 He also found that with pillars shorter than thirty times the thickness, fracture occurred by one of the ends failing, and as the longer columns deflected more than the shorter, they presented less of the base to resist the pressure, and therefore more readily gave way. Thus the practical view from these experiments points out an increase of area at the ends as being most economical, and that in proportion to the middle as 13,766 to 9,595 nearly. From the experiments it would appear that the Grecian columns, which seldom had their length more than about ten times the diameter, were nearly of the form capable of bearing the greatest weight when their shafts were uniform; and that columns, tapering from the bottom to the top, were only capable of bearing weights due to the smallest part of their section, though the larger end might serve to prevent lateral thrust. This last remark applies, too, to the Egyptian columns, the strength of the column being only that of the smallest part of the section. (British Association for the Advancement of Science, 15th Report, 1845, p. 27.) 1502f. It might be asked, how does this apply to those small shafts or colonettes so freely used with piers in pointed architecture, and which are generally in height upwards of thirty times their diameter. We would refer the student to the paragraph 1502c., respecting the mullions in windows, and to the circumstance that the small shafts are not pinned-in to the work, but are left free, so that they only apparently carry the weight imposed on their capitals. Where no attention has been paid to this necessary precaution, in modern work, the shaft has fractured when of soft, or shaky, stone. 1502g. Table oF THE STRENGTH OF SHAFTS 12 INCHES LONG, 3 INCHES DIAMETER, (Being experiments made by a committee of the Institute, as above-mentioned. ) 1502h. l'airbairn, in a paper read at the Manchester Philosophical Society, and given in vol. xiv. of the Proceedings; and also in his Useful Information, &c., 2nd Series, has detailed the following results of his researches: 1502i. He further shows that the resistance of strong sandstone to crushing in a direc tion parallel to the layers, is only six-sevenths of the resistance to crushing in a direction perpendicular to the layers. The hardest stones alone give way to crushing at once, without previous warning. All others begin to crack or split under a load less than that which finally crushes them, in a proportion which ranges from a fraction little less than unity in the harder stones, down to about one half in the softest. The mode in which stone gives way to a crushing load is in general by shearing. The factor of safety in structures of stone should not be less than eight, in order to provide for variations in the strength of the material, as well as for other contingencies. In some structures which have stood it is less; but there can be no doubt that these err on the side of boldness, as urged by Rankine, Civil Engineering, page 361. A brick made by Beale's machine being placed on bearers seven inches apart, was broken in the middle by the weight of 2,625 lbs. A common hand-made brick was broken by 645 lbs. The hollow or frog formed in the underside of a brick necessarily lessens its resisting power. Young (Nat. Phil.) states that the cohesive strength of a square inch of brick is 300 lbs., but the quality is not stated. Other experiments give the following strength of bricks: 15021. Brickwork.-Brick piers 9 inches square, 2 feet 3 inches high, made of good sound Cowley stocks, set in cement, and proved two days afterwards : Cracked at 25 tons Broke at 30 tons 35 " Brick flat, compressed quarter of an inch Brick on edge, did not compress 1502m. Mr. L. Clarke's experiments for the works at the Britannia and Conway tubular bridges, on brickwork in cubes, showed that— 9 inches, cemented, No. 1 or best quality, set between deal boards, weighing 54 lbs., crushed with 19 tons 18 cwt. 2 qrs. 22 lbs. = 9 inches, No. 1, set in cement, weighing 53 lbs., crushed with 22 tons 3 cwt. O qrs. 17 lbs. 551.3 lbs. per square inch. =612.7 lbs. The three last cubes continued to support the weight, although cracked in all directions; they fell to pieces when the load was removed. All began to show irregular cracks a considerable time before it gave way. The average weight supported by these bricks was S3.5 tons per square foot, equal to a column 583.69 feet high of such brickwork. (Fairbairn, Application, &c., page 192.) 1502n. To crush a mass of solid brickwork 1 foot square, requires 300,000 lbs. avoirdupois, or 134 tons 7 cwt. 15020. Besides compression, stone is subject to detrusion and a transverse strain, as when used in a lintel. Of these strengths in stone little is officially known, but we are perfectly aware of the danger of using any kind of stone for beams where there is much chance of serious or of irregular pressures. Its weakness in respect to this strain is manifest from all experimental evidence concerning it. Gauthey states the value of a constant S, for hard limestone = 78 lbs. ; for soft limestone 69 lbs. Hodgkinson, taking the power of resisting a crushing force as = 1000, notices 1502p. The danger above noticed is so great, that it becomes essentially necessary in all rough rubble work to insert over an opening either an iron or timber lintel, or a brick or stone arch, to carry the superincumbent weight, and thus prevent any pressure upon the stone. This must be done more especially when beams or lintels of soft stone are used; the harder stones, as Portland, may in ashlar work support themselves without much danger. In rubble masonry, the stone arch may be shown without hesitation in the face of the work; and also in domestic architecture, the brick arch may exhibit itself in the facework if thought desirable. Portland stone has been constantly used to extend over a comparatively wide opening. All blocks set upon it should have a clear bed along the middle of its length. Thus cills to windows should always be set with clear beds, or, as the new work settles, they are certain to be broken. Lintels over even small openings worked in Bath or some of the softer stones, are very likely to crack across by very slight settlements, especially when supported in their length by a mullion or small pier, as is often introduced. We need hardly add that where impact or collision is likely to occur, no lintel of stone should be used. 1502q. Marble mantles may sometimes be seen to have become bent by their own weight. Beams of marble have been employed in Grecian temples as much as 18 feet in the clear in the propylæa at Athens; and marble beams 2 feet wide and 13 inches deep were hollowed out, leaving 4 inches thickness at the sides and 3 inches at the bottom; these beams were about 13 feet in the clear in the north portico of the temple at Bassæ near Phigaleia. 1502r. The cohesive power of stone is seldom tested. The subject of crushing weights, or the compression of timber and metals, will be treated in a subsequent section (1631e. et seq.); and the strength of some other materials will be given in the chapter MATERIALS. OF THE STABILITY OF WALLS. 1503. In the construction of edifices there are three degrees of stability assignable to walls. I. One of undoubted stability; II. A mean between the last; and the III. The least thickness which they ought to possess. 1504. The first case is that in which from many examples we find the thickness equal to one eighth part of the height: a mean stability is obtained when the thickness is one tenth We are, part of the height; and the minimum of stability when one twelfth of its height. however, to recollect that in most buildings one wall becomes connected with another, so that stability may be obtained by considering them otherwise than as independent walls. 1505. That some idea may be formed of the difference between a wall entirely isolated and one connected with one or two others at right angles, we here give figs. 591, 592, and 593. It is obvious that in the first case (fig. 591.), a wall acted upon by the horizontal force MN, will have no resistance but from the breadth of its base; that in the second case (fig. 592.) the wall GF is opposed to the force MN. so that only the triangle of it HIF can be detached; lastly, in fig. 593. the force MN would only be effective against the triangle CGH, which would, of course, be greater in proportion to the increased distance of the walls CD, HI. 1506. In the first case, the unequal settlement of the soil or of the construction may produce the effect of the force MN. The wall will fall on the occurrence of an horizontal disunion between the parts. 1507. In the second case the disunion must take place obliquely, which will require a greater effort of the power MN. 1508. In the third case, in order to overturn the wall, there must be three fractures through the effort of MN, requiring a much more considerable force than in the second case. 1509. We may easily conceive that the resistance of a wall standing between two others will be greater or less as the walls CD, HI are more or less distant; so that, in an extreme approximation to one another, the fracture would be impossible, and, in the opposite case, the intermediate wall approaches the case of an isolated wall. 1510. Walls enclosing a space are in the preceding predicament, because they mutually tend to sustain one another at their extremities; hence their thickness should increase as their length increases. 1511. The result of a vast number of experiments by Rondelet, whose work we are still using, will be detailed in the following observations and calculations. 1512. Let ABCD (fig. 594.) be the face of one of the walls for enclosing a rectangular B 6 C E Fig. 594. Fig. 595. space, EFGH (fig. 595.). Draw the diagonal BD, and about B make Bd equal to one eighth part of the height, if great stability be required; for a mean stability, the ninth or tenth part; and, for a light stability, the eleventh or twelfth part. If through the point d a parallel to AB be drawn, the interval will give the thickness to be assigned to the great walls EF, GH, whose length is equal to AD. 1513. The thickness of the walls EG, FH is obtained by making AD' equal to their length, and, having drawn the diagonal as before, pursuing the same operation. 1514. When the walls are of the same height but of different lengths, as in fig. 596., the operation may be abridged by describing on the point B (fig. 597.) as a centre with a radius equal to one eighth, one tenth, or one twelfth, or such other part of the height as may be considered necessary for a solid, mean, or lighter construction, then transferring their lengths, EF, FG, GH, and HE from A to D, D', D', and D""; and having made the rectangles AC, AC', AC", and AC", draw from the common point B the diagonals BD, BD', BD", and BD", cutting the small circle described on the point B in different points, through which parallels to AB are to be drawn, and they will give the thickness of each in proportion to its length. 1515. In figs. 598. to 602. are given the operations for finding the thicknesses of walls enclosing polygonal areas supposed to be of the same height; thus AD represents the side of the hexagon (fig. 602.); AD' that of the pentagon (fig. 601.); AD" the side of the square (fig. 599.); and AD"" that of the equilateral triangle (fig. 600.). 1516. It is manifest that, by this method, we increase the thicknesses of the walls in proportion to their heights and lengths; for one or the other, or both, cannot increase or diminish without the same happening to the diagonal. 1517. It is obvious that it is easy to calculate in numbers the results thus geometrically obtained by the simple rule of three; for, knowing the three sides of the triangle ABD, |