176 MEMOIR OF THE LATE PROF. E. HODGKINSON,, F.R.S. 



flat and tlie other end rounded, and the result is summed 

 up in the following interesting and important law : — 



With pillars of the same diameter and length, both ends 

 rounded, one end rounded and the other flat, and both ends 

 flat, their strengths are as i, 2, ^ respectively. 



When the pillars were uniform, and the same shape at 

 both ends, the fracture took place in the middle. This was 

 not the case when one end was flat and the other rounded, 

 as the fracture then took place at about one-third of the 

 length from the rounded end. Hence in these pillars the 

 metal may be economized by increasing the thickness in 

 the point of fracture. 



It follows from Euler^s theory, that the strength of 

 pillars to bear incipient flexure is directly as the fourth 

 power of the diameter, and inversely as the square of the 

 length. 



This incipient flexure was sought for by Mr. Hodgkinson 

 without success, and he states his conviction that flexure 

 commences with very small weights, such as could be of 

 little use to load pillars with in practice. Although Mr. 

 Hodgkinson was unable to find the point to which Euler^s 

 computations refer, still he has shown that Euler's formula 

 is not widely from the truth when applied to the breaking- 

 point of the pillar. From a great number of experiments, 

 Mr. Hodgkinson deduced the following formula for pillars 

 with rounded ends : — 



D= diameter of pillar in inches. 

 L = length of pillar in feet. 

 W= breaking- weight in tons. 



D376 



Then, ■W= 14-9 j^. 



The above rule applies to pillars the length of which is 

 fifteen times the diameter and upwards. Perhaps not quite 

 so low as fifteen times the diameter in large pillars, as there 



