16 . The Strength of Columns. 



elasticity of the material and inversely as the square of its 

 length between points of inflexion, and the column if origi- 

 nally straight, will remain so until the load reaches this 

 critical amount, when equilibrium becoming unstable, some 

 trivial cause will produce an infinitesimal lateral deflection, 

 which, rapidly increasing, results in fracture. 



Euler's rules possess the recommendations of mathe- 

 matical completeness and consistency, and therein contrast 

 favourably with those of some of his successors. 



In 1840 Professor Eaton Hodgkinson communicated to the 

 Royal Society (of England) an account of a very extensive 

 series of experiments on columns of various materials, 

 accompanied by a set of rules empirically deduced there- 

 from, and in 1857 contributed the results of a further set of 

 trials on a comparatively large and practical scale. In his 

 paper of 1857 he says : — " In commencing experiments in 

 my former research on this subject, and keeping in view the 

 theory of Euler, I sought with great care for the weight 

 which would produce incipient flexure in columns, and more 

 particularly in those of cast-iron. In this metal flexure 

 commenced with very small weights, much smaller than 

 would be useful to load pillars with in practice ; and I 

 became convinced that no such point existed in cast-iron, or, 

 at any rate, none that would be useful to the engineer ; and 

 my subsequent experiments upon wrought-iron pillars have 

 been attended with very little more success in seeking for 

 the weight producing incipient flexure." 



Failing thus to reconcile his observations with Euler's 

 investigation, he abandoned that investigation altogether, 

 and proceeded to obtain a purely empirical formula, based 

 upon no theory whatever, and simply intended to represent 

 in a concise but merely approximate form the average result 

 of a ver}^ extended series of experiments. According to 

 these experimental researches the ultimate strength of a 

 solid circular cast-iron column varies directly as the 3.6th 

 power of the diameter and inversely as the 1.7th power oi 

 the length between points of inflection. 



Professor Gordon, Professor Kankine's predecessor in the 

 chair of engineering at Glasgow, next proposed a formula 

 of more convenient form, and apparently based upon a 

 scientific hypothesis, as to the nature of the stress at the 

 instant of fracture. This formula is stated by Rankine to 

 have been deduced from Hodgkinson's experiments ; but I 

 find by actual trial that it gives results by no means per- 



