REPORT ON THE STRENGTH 6f MATERIALS. 95 



multiplied by the distance of the centre of gravity of their sec- 

 tion from the lowest point ; about which point, according to 

 this hypothesis, the motion must necessarily take place. 



The fallacy of these assumptions was noticed, but not cor- 

 rected, by several subsequent authors. Leibnitz objected to 

 the doctrine of the fibres resisting equally under all degrees 

 of tension, but admitted their incompressibility, thereby still 

 making the motion take place about the lowest point of the sec- 

 tion; but he assumed for the law of resistance to extension that 

 it was always proportional to the quantity of extension. Ac- 

 cordingly as the one or the other of these hypotheses was 

 adopted, the computed transverse resistance of a beam, as de- 

 pending on the absolute strength of its fibres, varied in the 

 ratio of 3 to 2 ; and many fanciful conclusions have been drawn 

 by different authors relative to the strength of differently formed 

 beams, founded upon the one or the other of these assumptions, 

 which, however, it will be unnecessary to refer to more parti- 

 cularly in this article. 



We have seen that each of these distinguished philosophers 

 supposed the incompressibility of the fibres ; but James Ber- 

 noulli rejected this part of Leibnitz's hypothesis, and considered 

 the fibres as both compressible and extensible, and that the 

 resistance to each force was proportional to the degree of ex- 

 tension or compression. Consequently, the motion instead of 

 taking place, as hitherto considered, about the lowest point of 

 the section, was now necessarily about a point within it ; and 

 his conclusion was, that whatever be the position of the axis of 

 motion, or, as it is now commonly called, the neutral axis, the 

 same force applied to the same arm of a lever will always pro- 

 duce the same effect, whether all the fibres act by extension 

 or by compression, or whether only a part of them be extended, 

 and a part compressed. Dr. Robison, in an elaboi'ate article 

 on this subject, also assumes the compressibility and exten- 

 sibility of the fibres, and as a conseqvience, assumes the centre 

 of compression as a fulcrum, about which the forces to exten- 

 sion are exerted, and the resistance of both forces to be directly 

 proportional to the degree of compression or extension to which 

 they are exposed; that is, he assumed each force, although 

 not necessarily offering equal power of resistance, to be indivi- 

 dually subject to the law of action appertaining to perfectly 

 elastic bodies. In carrying on the experiments which laid the 

 foundation of my Essay on the Strength of Timber, Sfc, in 1817, 

 I was led by several circumstances I had observed to doubt 

 whether, in the case of timber, this assumption of perfect elas- 

 ticity was admissible. And as some of the specimens used in 



