When a column is crushed, its resistance to com pressiOn seems to depend in great measure on the force of lateral adhesion, assisted by a kind of inter nal friction, dependent on the magnitude of the and it commonly gives way by the separa tion of a wedge in an oblique direction. If the ad hesion were simply proportional to the section, it may be shown that a square column would be most easily crushed when the angle of the wedge is equal to half of a right angle ; but, if the adhesion is in creased by pressure, this angle will be diminished by half the angle of repose appropriate to the sub stance. In a wedge separated by a direct force from a prism of cast iron, the angle was found equal to consequently" the angle of repose was 2 X = 25°, and the internal friction to the pressure as 1 to .466, the tangent of this angle : there was, -however, a little bubble in the course of the fracture,- which. may have changed its direction in a slight degree. The magnitude of the. lateral adhesion is measured by twice the height. of the wedge, whatever its angle may be: in this instance the height was to the depth as 1.57 to 1, conse quently the surface, affording an adhesion equal to the force, was somewhat more than three times as great as the transverse section, and the lateral ad hesioa of a square inch of east iron would be equal to about 46,000 pounds: the direct cohesive force of the same iron was found by experiment equal to about 20,000 pounds fot a square' inch. It is ob vious that experiments on the strength of a sub stance in resisting compression ought to be tried on pieces rather longer than cubes, since a cube would not allow of the free separation of a single wedge so acute as was observed in this experiment ; at though, indeed, the force required to separate a shorter wedge on each side would be little or no greater than for a single wedge. The same consi deration of the oblique direction of the plane of easiest fracture would induce us to make the outline of a column a little convex externally, as the com mon practice has been : for a circle cut out of a plank possesses the advantage of resisting equally in every section, and consequently of exhibiting the strongest form, when there is no lateral adhesion ; and in the case of an additional resistance propor. 5ional to the pressure, the strongest form is afforded by an oval' consisting of two circular segments, each containing twice the angle formed by the plane of fracture with the horizon. If we wish to obtain a direct measure of the lateral adhesion, we must take oars to apply the forces concerned at a distance from each other not greater than one sixth of the depth of the substance, otherwise the fracture will probably be rather the consequence of flexure than of detrusion. Professor Robison found this force in
some instances twice as great as the direct cohesion, or nearly in the same proportion, as it appears to have been in the experiment on the strength of east iron ; Mr Coulomb thinks it most commonly equal only to the cohesion : and in fibrous substances, especially where the fibres are not perfectly straight, the repulsive strength is generally much leas than would be inferred from this equality, and sometimes even less than the cohesive strength.
It is well known that the transverse strength of a beam is directly as the breadth, and as the square of the depth, and inversely as the length : and the variation of the results of some experiments from this law can only have depended an accidental cif curnstanoes. If we wish to find the number of hun dred weights that will break a. beam of oak, support. ed at both ends, supposing dean to be placed exact. ly on tho middle, we may multiply theof the depth, in inches, by 100 times the b and di vide by the length ; and we may venture in practice to load a beam with at least an. eighth as much as this, or in case of necessity, even a fourth. And if the load be distributed equally throughout the length of the beam, it will support twice as much : but for a beam of fir, the strength is somewhat less than for oak. A cylinder will bear the same curvature as the circumscribing prism, and it may be shown that its strength, as well as its' stiffness, us to that of the prism as vine fourth of its bulk is to one third of the bulk of the prism. The strength of a beam sup ed at its extremities may be doubled by firmly ' the ends, where it is practicable ; and we have . ready seen that the stiffness is quadrupled: but 'the resilience remains unaltered, since the resistance is doubled, and the space through which it acts is re duced to a hale It is therefore obviously of im portance to consider the nature of the resistance that is required from the fabric which we are C011 'Eructing. A floor, considered alone, requires to be strong; but in connexion with a ceiling, its statues; requires more particular attention, in order that the ceiling may remain free from cracks. A coach spring requires resilience, for resisting the relative motions of the carriage, and we obtain this kind of strength as effectually by combining a number of separate plates, as if we united them into a single mass, while we avoid the stiffness, which would ren• der the changes of motion inconveniently abrupt.
In all calculations respecting atiffuess, it is nem. nary to be acquainted with the modulus of elasticity, which may be found, for a variety of substances, in the annexed table..
Height of the Modulus of Elasticity in Thousands of Feet. '