404 PROCEEDINGS OF THE AMERICAN ACADEMY 



principles ; fortunately, however, in its application to cases where great 

 weights were to be supported, the errors were on the safe side. Pro- 

 found theoretical investigations have been made by Euler and others 

 on the resistance of pillars to incipient jiexure ; the results are valu- 

 able, but are not directly available for the wants of practice. 



In the year 1840, Mr. Hodgkinson of Manchester, England, pre- 

 sented to the Royal Society his first paper on the strength of cast-iron 

 pillars.* It contains an account of an elaborate series of experiments, 

 on a large scale, made at the expense of William Fairbairn of Man- 

 chester, and affording ample data for determining the formulas for 

 computing the breaking weights of solid and hollow cylindrical pillars 

 of cast-iron, and of ordinary dimensions. The formula determined by 

 Hod'i-kinson from these experiments for hollow cylindrical cast-iron 

 pillars, the lengths being not less than thirty times the external diame- 

 ters, and the ends being flat, that is to say, with the ends finished in 

 planes perpendicular to the axis, the weight being uniformly distributed 

 on these planes, is 



T^3.55 ,7 3.55 



W = 99,318 ^,/ , (1) 



in which 



W = the breaking weight, in pounds. 

 D = the external diameter, in inches. 

 d = the internal diameter, in inches. 

 I = the length in feet. 

 When the pillars were shorter than thirty external diameters, it 

 was found that they would break with less weight than is given by 

 formula (1). In a long pillar the pressure tends to break it by crush- 

 ing as well as by flexure, but it fails from flexure with a weight which 

 is too small to sensibly affect it by crushing alone. In a short pillar, 

 on the other hand, the weight required to break it by flexure is so 

 great that the crushing effect becomes sensible, and it fjiils from the 

 joint effects of the force.' It was found by experiment that the effect 

 of the crushing force became sensible when the pillars with flat ends 

 were shorter than thirty times the external diameter, and the formula 

 given by Hodgkinson for the breaking weight of such pillars is 



* Experimental Researches on the Strength of Pillars of Cast-iron and other 

 Materials. By Eaton Hodgkinson. Philosophical Transactions of the Royal So- 

 ciety of London, for 1840. Part II. 



