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



Let P=tlie utmost pressure the pillar would bear without 



being weakened by crushing. 

 ^= breaking- weight as calculated by the preceding 



formulse. 

 2/ = the actual breaking- weight of short pillars. 



.•.^ = ^ where P=— . 



h h^l 4 



c 4 



The value of c is obtained from the formula 



c = (area of section) x 109^801 lbs. 



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 Iron. 



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 formulae 

 for the breaking- weight of hollow pillars, as derived from 

 experiment, are as follows : — 



2^= breaking- weight in lbs. 

 D= external diameter in inches. 

 <;?= internal diameter in inches. 

 L= length in feet. 



For pillars with rounded ends, 



^^ = 29074 — lt^ . 



For pillars with flat ends, 



^=99318 — ^^ — . 



The strength of short hollow pillars must be calculated 



