434 Remarks on the Article " Strength ofMateriah" 



contal position ; Bernoulli, Eiiler and Lagrange, the strength in 

 a vertical position : in the former the depth is the variable 

 cjuantitv, in the latter the length and depth are both of them 

 variable: licnce the theory of Eiiler differs from that of Galileo 

 or Lciliiiitz only in the position of the beam. 



Leibnitz, Bclidor*, Emerson f, and other writers, have fol- 

 lowed only part of Marriotte's theory, admitting the extension 

 to be as the force, but supposing the axis of fracture to be at the 

 lower side of the beam. Leibnitz and Emerson have on these 

 principles attpmpted to determine the strength of triangular 

 prisms, Sec. and have arrived at the most absurd conclusions. 



The author treats the subject under three separate heads, and 

 begins with " the direct cohesion of bodies." The strength of 

 bodies to resist a strain in direction of their length is stated to 

 be as their areas; but, allowing the material to be uniform, this 

 can only be the case under a certain limitation, which is not 

 even hinted at in the present article, though it is the cause of 

 the irregularity of Buffon's experiments on the strength of iron. 

 As every material will extend in some degree before fracture 

 takes place, there is a point in the section of fracture tiirough 

 which the direction of the weight must pass; otherwise, the 

 section will not be ecpiallv strained, and consequently the 

 strength will not be as the area. 



To determine the centre of resistance, and to find the law 

 which the strength would follow, when the direction of the 

 weiglit does not pass through it, would be a curious as well as an 

 useful subject of mathematical inquiry. 



A want of attention to the direction of the weight is the most 

 likely cause of the strength in certain experiments not being as 

 the area (see Phi!. Mag. vol. x. p. 51). As to the different re- 

 Stilts obtained by different experimentalists, — the various qualities 

 of the same kind of material, the duration of the experiments, 

 and other physical circumstances colisidered, — they agree as well 

 as coukl be expected; the highest numbers are most likely to be 

 correct, provided tliat sufficient time has been allowed for tiie ex- 

 periments: but the time, in these experiments, is seldom if ever 

 specified. The next division is " on the resistance of bodies 

 when pros: ed longtudinallv," &c., which certainly should have 

 followed that on the transverse strength, not only on' account of 

 its being more difficult, but also because it is only a modification 

 of the transverse strain in which the deflexion becomes the lever- 

 age. Tlic author passes over tiiis division of his subject without 

 ev^n attempting a tlieoretical investigation ; indeed the " intri- 

 cate" methods pursued by Lagrange and other continental wri- 



• Science dcs Inginie/irs, liv. iv. chap. 2. Arcki Hydruliquef toine iii. 

 f Mechanics, props. Tf and 73. 4to, 1773. 



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