18 The Strength of Columns. 



a very long blade of finely-tempered steel, which behaved in 

 a manner very closely approximating to that predicted by 

 Euler; and I have myself obtained corresponding results 

 from a straight piece of clock-spring very carefully loaded. 

 The reason why Hodgkinson's cast-iron rods began to bend 

 so soon was, I believe, this, that the material was not homo- 

 geneous, or the load possibly applied slightly eccentrically. 

 Let us suppose that a solid circular column is softer and 

 more elastic on one side than the other. The smallest load 

 will now bend it ; for even if at first the centres of pressure 

 and of figure are perfectly coincident, the more elastic side 

 will yield more than the other ; this will cause the bar to 

 bend, the more elastic material being on the concave side ; 

 this bending will cause the centre of pressure of each cross 

 section to deviate from the centre of figure toward the softer 

 or more elastic side of the bar, thus throwing a greatly 

 increased portion of the total pressure on that part of the 

 column most afiected by it. In this way a perceptible 

 flexure may be produced by a load minute compared with 

 that necessary for fracture. That this is the true explana- 

 tion of the anomaly is, I think, rendered certain by two 

 facts observed by Hodgkinson. The first of these is that 

 the amount of flexure produced by the same load on columns 

 of the same size and material varied very greatly, thus 

 indicating that it depended upon some slight accidental 

 peculiarity in apparently similar bars. Some of the bars 

 tested bent visibly under less than one-fifth of their breaking 

 load, while others remained straight until two-thirds of 

 that load was applied, thus approximating to Euler's 

 theoretical case. The second fact is that certain hollow 

 columns through defective casting were much thicker on one 

 side than the other, and that these when tested bent so that 

 the thick side was concave and the thin convex ; the greater 

 hardness and higher co-efficient of the elasticity of the thin 

 and more rapidly cooled side of the casting more than com- 

 pensating for its deficiency in substance. If, then, the softer 

 side became concave in these hollow columns, much more 

 would it tend to do so in solid ones, where the counter- 

 vailing influence of extra thickness was absent. 



The next discrepancy is this : — Euler predicted that the 

 strength would vary as the 4th power of the diameter; 

 Hodgkinson found it to be the 3.6th. Now this is nothing 

 more than I think might have been expected by any one 

 acquainted with the softness of large castings as compared 



