ON PASSIVE STRENGTH AXD FRICTION. liQ 



The transverse strength of a perfectly elastic substance, fixed at one end, 

 is to its direct cohesive strength as the depth of the substance to six times its 

 length. This proportion is equally applicable to such substances as resist 

 compression more strongly than extension: for their immediate repulsive 

 force is probably not greater than their cohesive force, when their dimensions 

 are equally changed, so that the middle of the beam is always in its natural state; 

 and when the curvature is sufficient to overcome the cohesive force, the 

 whole beam must give way. When, however, the substance is less capable 

 of resisting compression than extension, the concave surface gives way first, 

 and the strength depends immediately on the repulsive strength of the sub- 

 stance. This is perhaps the reason, that, in experiments on beams of oak, 

 the transverse strength has seldom been tbund in a greater ratio to the whole 

 cohesive strength than that of the depth to nine times the length. 



It may be inferred from the consideration of the nature of the different 

 kinds of resistance which have been explained, that if we have a cylindrical 

 tree a foot in diameter, which is-to be formed into a prismatic beam by flat- 

 tening its sides, we shall gain the greatest stiflPness by making the breadth or 

 thickness 6 inches, and the depth 104^, the greatest strength by making the 

 breadth 7 inches and the depth 9-1, and the greatest resilience by making the ' 

 beam square. The stiffness and the strength of the beam may be much in- 

 creased by cutting the tree into, four pieces, turning their edges outwards, 

 and uniting them so as to make a hollow beam: but it will require great 

 strength of union, to make the whole act as one piece, and the resilience of 

 the bean> will be rather diminished than increased by the operation. 



The adoption of the hollow masts and beams which an ingenious mechanic 

 has lately introduced, requires, therefore, some caution. For where an im- 

 pulse is to be resisted, such a mast is no stronger than a solid mast of the 

 same weight, and much weaker than a solid mast of the same diameter. The 

 force of the wind is, however, rather to be considered as constituting a pres- 

 sure than a finite impulse, except when a sudden scpiall carries a loose sail 

 before it with considerable velocity. A similar caution may also be extended 

 to some other attempts to make improvements in naval architecture: it is a 

 common opinion, and perhaps a well founded one, that flexibility is of great 



