218 MEMOIR OF EATON HODGKINSON. 



SHORT PILLARS. 



In order to estimate tlie breaking-strength of short pillars, Mr. Hodgkinson 

 considered the strength of the pillar to be made up of two functions. 



1. To support the weight. 



2. To resist flexure. 



When the breaking-weight is small, as in long pillars with small diameters, 

 then the strength of the pillar will be eiuployed in resisting flexure. When the 

 breaking-weight is one-half the pressure required to crush the pillar, one-half of 

 the strength may be considered available to resist flexure, and the other half to 

 resist crushing. And when the breaking-weight is so great as in the case of short 

 pillars, it may be considered that no part of the strength of the pillar is applied 

 to resist flexure. These two effects may be separated in all pillars by dividing 

 the pillar into two portions, one of which would support the weight without 

 flexure, and the other would support the flexure without crushing, to the extent 

 indicated by the preceding formulae. 



Let c = the force which would crush the pillar without flexure. 



Let P = the utmost pressure the pillar would bear without being weakened 

 by crushing. 

 b = breaking-weight as calculated by the preceding formulae. 

 y = the actual breaking-weight of short pillars. 



. •.-^=^ where P=-^- 



The value of c is obtained from the formula 



c = (area of section) X 109,801 pounds. 



The reasoning by which the above formulae are established is well deserving 

 of attention, and shows that the author was a worthy successor of Euler, Lagrange, 

 and Poisson in this important branch of practical science. 



HOLLOW PILLARS OF CAST IROIT. 



Mr. Hodgkinson has shown that solid pillars with rounded ends and enlarged 

 in the middle are stronger than uniform pillars of the same length and weight. 

 This is proved to be the case in hollow pillars. The fonnulae for the breaking- 

 weight of hollow pillars, as derived from experiment, are as follows : 

 tv = breaking- weight in pounds. 

 D = external diameter in inches. 

 d ■= internal diameter in inches. 

 L = length in feet. 

 For pillars with rounded ends. 



w = 29074 

 For pillars with flat ends, 



m;=99318 



L1-' 



J)3.55_^3.J 



The strength of short hollow pillars must be calculated in the same manner 

 as the strength of short solid pillars. These formulae, derived from experiments 

 made with great judgment and care, embody our present knowledge and prac- 

 tice of cast-iron pillars for bearing-purposes. 



'' The Power of Cast-u'on Pillars to Resist Long-continued Pressure." 

 Mr. Hodgkinson has recorded in this paper several very interesting experi- 

 ments on this subject. Two beams, rounded at the ends, six feet long and one 

 inch diameter, were cast of Low Moor iron, No. 3. The fii'st bore a weight of 



