ON PASSIVE STRENGTH AND FRICTION. 115 



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 sub- 

 stance is less capable of resisting compression than extension, the concave 

 surface gives way first, and the strength depends immediately on the repul- 

 sive strength of the substance. This is perhaps the reason that, in experi- 

 ments on beams of oak, the transverse strength has seldom been found 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 

 flattening its sides, we shall gain the greatest stiffness by making the 

 breadth or thickness 6 inches, and the depth 10, the greatest strength by 

 making the breadth 7 inches and the depth 9|, and the greatest resilience 

 by making the beam square. The stiffness and the strength of the beam 

 may be much increased 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 beam will be rather diminished than increased by 

 the operation. 



The adoption of the hollow masts and beams which an ingenious me- 

 chanic has lately introduced, requires, therefore, some caution. For where 

 an impulse 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 pressure than a finite impulse, except when a sudden squall 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 archi- 

 tecture : it is a common opinion, and perhaps a well-founded one, that 

 flexibility is of great advantage to a ship's sailing ; if therefore we sacrifice 

 too much resilience to strength, and too much of both to stiffness, we may 

 perhaps create greater evils than those which we wish to avoid. 



We have hitherto supposed the beams of which the strength has been 

 compared, to be prismatic, that is, of equal breadth and thickness through- 

 out, which is not only the simplest form in theory but the most generally 

 useful in practice. If, however, we have the power of giving any form 

 that we please to materials of a certain weight, which may often be done 

 where several smaller pieces are to be cut out of a larger one, or a larger 

 one to be composed of several smaller ones, or where the materials are 

 either ductile or fusible, it is frequently possible to determine a more ad- 

 vantageous form than that of an equable beam or column. For since the 

 extension which the parts of the substance admit without giving way, is the 

 limit of their strength, if the depth of a beam be everywhere equal, and the 

 curvature unequal, the fracture will first take place where the curvature 

 is greatest, and the superfluous strength of the other parts will be lost ; so 

 that, in order to have the greatest strength that a given quantity of mate- 

 rials is capable of affording in a beam of given length, the form must be 



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