REPORT ON THE STRENGTH OF MATERIALS. 97 



George Rennie, Esq., which contains nearly all the information 

 on this subject that can be desired. But when a beam is of con- 

 siderable length in comparison with its section, it is no longer 

 the crushing force that is to be considered : the beam will bend 

 and be ultimately destroyed by an operation very similar to 

 that which breaks it transversely ; and the investigation of these 

 circumstances has called forth the efforts of Euler, Lagrange, 

 and some other distinguished mathematicians. 



When a cylindric body considered as an aggregate of pa- 

 rallel fibres is pressed vertically in the direction of its length, 

 it is difficult to fix on data to determine the point of flexure, 

 since no reason can be assigned why it should bend in one way 

 rather than in another ; still, however, we know that practically 

 such bending will take place. And it is made to appear, by the 

 investigations of Euler and Lagrange, that with a certain weight 

 this ought theoretically to be the case, but that with a less 

 weight no such an effect is produced, — an apparent interruption 

 of the law of continuity not easily explained, which exhibits 

 itself, however, analytically, by the expression for the ordinate 

 of greatest inflection being imaginary till the weight or pressure 

 amounts to a certain quantity. Another mysterious result from 

 these investigations is, that while the column has any definite di- 

 mensions, and is loaded with a certain weight, inflection as above 

 stated takes place ; but if the column be supposed infinitely 

 thin, then it will not bend till the weight is infinitely great. 

 These investigations of two such distinguished geometers are 

 highly interesting as analytical processes, but the hypothesis 

 on which they are founded, namely, that of the perfect elas- 

 ticity of the materials, is inconsistent with the nature of bodies 

 employed in practice : they form, therefore, rather an exercise 

 of analytical skill than of useful practical deductions. There 

 is, however, one useful result to be drawn from these processes, 

 which is, that the weight under which a given column begins 

 to bend is directly as its absolute elasticity ; so that, having de- 

 termined experimentally the weight which a column of given 

 elasticity will support safely, or that at which inflection would 

 commence, we may determine the weight which another column 

 of the same dimensions, but of different elasticity, may be 

 charged with without danger. 



M. Gerard, a member of the Institute of France, aware of 

 the little practical information to be drawn from investigations 

 wholly hypothetical, has given the detail of a great number of 

 actual experimental results connected with this subject on oak 

 and fir beams of considerable dimensions, carried on at the ex- 



1833. H 



