50 Royal Society : — 



March 29, 1855.— Tliomas Bell, Esq., V.P., in the Chair. 



The following communications were read : — 



" On the existence of an element of Strength in beams subjected 

 to Transverse Strain, arising from the Lateral Action of the fibres or 

 particles on each other, and named by the author the ' Resistance to 

 Flexure.' " By Peter William Barlow, Esq., F.R.S. 



The author commences by observing, that under the existing 

 theory of beams, which recognizes only two elements of resistance, 

 namely tension and compression, the strength of a beam of cast 

 iron cannot be reconciled with the results of experiments on the 

 direct tensile strength, if the neutral axis is in the centre of the 

 beam. 



He then proceeds to describe experiments made on two solid 

 beams of cast iron to determine the position of the neutral axis. 

 The beams employed were 7 feet long, 6 inches deep and 2 inches 

 thick, on each of which small vertical ribs were cast, 12 inches 

 apart ; nine small holes were drilled opposite to each other in each 

 rib, for the purpose of inserting the pins of a delicate measuring in- 

 strument. Tlie distances of the holes of the centre division of both 

 beams were measured under various strains, and the results show 

 that the extensions and compressions proceed in an arithmetical 

 ratio from the centre to the upper and lower sides of the beam ; and 

 that at any given distance on either side of the centre, the amount 

 of extension is equal to the amount of compression. 



Tiie position of the neutral axis being thus conclusively ascertained 

 to be in the centre, it is shown that, not only the ultimate strength, 

 but also the amount of extension and compression with a given 

 strain, indicates the existence of another element of resistance, in 

 addition to the resistances to extension and compression. 



The author then points out, that in applying the law of " vt 

 tensio sic vis " to contiguous fibres, under different degrees of exten- 

 sion and compression, the effect of the lateral adhesion has been 

 omitted, and each fibre has been supposed to be capable of taking 

 up the same degree of extension or compression as if it acted sepa- 

 rately, and independently of the adjoining fibres. 



It is then shown that this supposed independent action of the 

 fibres is inconsistent with other ])ractical results, and evidence is 

 exhibited of a powerful lateral action when unequal strains are 

 exerted. 



From these and other considerations, the author is led to think 

 that the effect of the lateral action, tending to modify the effect of 

 the unequal and opposite strains in a beam, constitutes, in effect, a 

 " resistance to flexure " acting in addition to the resistances of 

 tension and compression. 



In order to ascertain whether the apparent difference in the 

 amount of tensile strength when excited by direct and transverse 

 strains is due to flexure, the author cau.'-ed ojjen beams or girders to 

 be made, each of which was formed by two bars of metal ; the upper 



