ON THE STEENOTH OP PILLAES OP CAST lEON. 
853 
1. Before referring to the experiments which form the basis of the present memoir, I 
will give some notice of the principal matters contained in the former, but not suffi- 
ciently dilated upon ; especially as they have an important bearing upon what will 
follow, and will themselves receive further illustration, or perhaps be capable of demon- 
stration. 
The profound and beautiful researches of Euler on the strength of pillars * are 
entirely theoretical ; they proceed on the supposition that the strength of a pillar is 
bounded by its power of resisting being bent out of a straight line, the resistance to 
incipient flexure being supposed to be the measure of its strength, which in long pillars, 
whose length is I and external and internal diameters d and is ^ or ^ * , according 
as they are solid or hollow f. 
2. 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 pro- 
duce 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. Having been unsuccessful in 
seeking for the weight which would first produce flexure in columns, and being con- 
vinced that if it were foimd it would be of little or no use in practice, I sought in 
future for the weights necessary to drea^ the pillars tried, and in most instances for the 
deflection and decrement of length produced by the weights laid on. 
3, The pillars broken were placed in a vertical position during the experiments, and 
their ends were pressed between two horizontal plates of hardened steel, which, from 
the nature of the machine, were kept perfectly parallel. It was found that in cylin- 
drical pillars of cast iron, whose ends were turned perfectly flat, parallel and perpen- 
dicular to the axis, the breaking weight varied as the 3-55th power of the diameter 
^ 3-55 _ 
nearly, and inversely as the I’Tth power of the length, or as instead of as in the 
73.55 d^'^^ 
theory of Euler. In hollow pillars it is as - — ‘ . The fractional indices above 
were found to apply to all solid pillars of cast iron, whose lengths varied from 120 times 
the diameter to as low as 30 times the diameter, or thereabouts. For pillars shorter 
than these it wiU be necessary to correct the results obtained, by considerations dependent 
on the crushing strength of the material. See pp. 403 to 406 of the former research 
4. The first experiments were made upon long uniform pillars, with their ends 
rounded in such a manner that the pressure applied to them would act in the direction 
of their axis, to meet the requirements of Euler’s theory of the strength of pillars ; but 
* Berlin Memoirs, 1757. t Poisson, Mecanique, 2nd edition. 
X Philosophical Transactions, 1840, Part II. 
MDCCCLVIl. 5 T 
