ON PASSIVE STRENGTH AND FRICTION. 113 



so great a proportion as this to its cohesive strength ; and where the sub- 

 stance is in any degree composed of fibres, they must naturally produce 

 great irregularities by their flexure. The strength in resisting compression, 

 must, according to this statement, be simply proportional to the magnitude 

 of the section of the substance, although some experiments on freestone 

 appear to indicate, that when the section is increased, the strength is in- 

 creased in a greater proportion ; and there is no reason to suppose that it 

 can be influenced either way by the length. A cylindrical or prismatic 

 form is therefore the best that can be given to materials of a given bulk, in 

 order to enable them to resist a force which tends to crush them, except 

 that the additional pressure of their own weight on the lower parts, re- 

 quires that those parts should be a little stronger than the upper parts. It 

 appears, also, that something is gained by making the outline a little con- 

 vex externally ; for it may be demonstrated, that for a column or upright 

 beam to be cut out of a slab of equable thickness, supposing the strength 

 to be independent of pressure, the strongest form is a circle. (Plate X. 

 Fig. 126, 127.) 



When a body is broken by a transverse force applied very near to a 

 fixed point, its lateral adhesion is overpowered by the effect which we have 

 called detrusion, and its strength in this case is, therefore, generally some- 

 what greater than its direct cohesive strength. But when the part to which 

 the force is immediately applied is at a distance from the fixed point 

 greater than about one sixth of the depth, the fracture is no longer the 

 immediate consequence of detrusion, but of flexure. 



Flexure is the most usual manner in which fracture is produced ; the 

 superficial parts on the convex side are most extended, and usually give 

 w r ay first, except in soft fibrous substances, such as moist or green wood, 

 which is more easily crushed than torn ; and in this case the concave side 

 fails first, and becomes crippled, and the piece still remains suspended by 

 the cohesion of the fibres. After the convex surface has been cracked, the 

 whole substance is usually separated, but not always ; for example, a 

 triangular beam, with one of the edges uppermost, may be charged with 

 such a weight that the upper edge may be divided and the lower part may 

 remain intire. 



When a column or rafter is broken by the operation of a longitudinal 

 pressure, the stiffness of the column being once overcome, a small addition 

 of force is usually sufficient to produce fracture, unless the pressure has 

 been applied to a part more or less distant from the axis ; for in this case 

 a moderate force may produce a moderate flexure, and a much greater 

 force may be required to break the column. But in general, the stiffness 

 of columns is of more consequence than their strength in resisting trans- 

 verse fracture. 



The strength of beams of the same kind, and fixed in the same manner, 

 in resisting a transverse force, is simply as their fcreadth, as the square of 

 their depth, and inversely as their length.* Thus, if a beam be twice as 

 biDad as another, it will also be twice as strong, but if it be twice as deep, 

 it will be four times as strong ; for the increase of depth not only doubles 

 * Robison's Mech. Phil. i. 374, &c. 



