ON PASSIVE STRENGTH AND FRICTION. 147 



Flexure is the most usual manner in Avhich fracture is produced ; tlie super- 

 ficial parts on the convex side are most extended, and usually give way fiist; 

 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 be- 

 comes 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 rafteris broken by the operation of a longitudinal pres- 

 sure, 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 con- 

 sequence, than their strength in resisting transverse fracture. 



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

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

 depth, and inversely as their length. Thus if a beam be twice as broad 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 the number 

 of the resisting particles, but also gives each of them a double power, by in- 

 creasing the length of the levers on which they act. The increase of the 

 length of a beam must also obviously weaken it, by giving a mechanical ad- 

 vantage to the power which tends to break it: and some experiments appear 

 "to show, that the strength is diminished in a proportion somewhat greater than 

 that in which the leno;th is increased. 



's' 



The strength of a beam supported at both ends, like its stiffness, is twice 

 as great as that of a single beam of half the length, which is fixed at one end ; 

 and the strength of the whole beam is agiiin doubled if both the ends are 

 firmly fixed. 



The resilience of a prismatic beam, resisting a transverse impulse, follows 



