MEMOIR OF THE LATE PROF. E. HODGKINSON_, F.R.S. 177 



is a reduction of the strength of such pillars^ owing to the 

 softness of the metal in large castings. This remark is 

 significant^ and gave rise to many interesting experiments 

 at Portsmouth Dockyard by the Royal Commissioners, 

 conducted by Col. Sir Henry James. 



When the pillars are flat at the ends, the formula 

 becomes 



This rule applies to pillars whose lengths vary from 30 

 to 121 times the diameter. 



Short Pillars. 



In order to estimate the breaking-strength of short 

 pillars, Mr. Hodgkinson considered the strength of the 

 pillar to be made up of two functions. 



1st. To support the weight. 



2nd. To resist flexure. 



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

 small diameters, then the strength of the pillar will be em- 

 ployed 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 break- 

 ing-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 efiects maybe sepa- 

 rated 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 formulse. 



Let c=the force which would crush the pillar without 

 flexure. 



SER. III. VOL. II. N 



