The Strength of Columns. 19 



with small ones. The strength of large castings is never 

 quite so great as that of smaller of the same material, and 

 the difference between the 3.6th and 4th powers of the 

 diameter appears to me to be a reasonable allowance for the 

 effect of this variation of hardness and strength. 



To reconcile the square of the length given by Euler with 

 the 1.7th power of Hodgkinson is perhaps not quite so easy, 

 and I should prefer not to express an opinion with regard 

 to it at present. 



To determine the breaking load of a pillar is, however, 

 after all, only a means to an end, only a step towards obtain- 

 ing that practically valuable I'esult, the safe luorking load ; 

 and the next question that arises is — What is the factor of 

 safety to be ? what proportion of the breaking load can we 

 safely apply in actual construction ? And this question 

 appears to me — and I would wish to say it with all due 

 deference to such eminent names as Rankine, Unwin, 

 Stoney, and Baker — to have been hitherto answered in an 

 utterly unreasonable and illogical manner. These writers, 

 one and all, apply a factor of safety to the case of a long 

 column in the same manner as they would apply it in the 

 case of a tie-rod or beam, altogether overlooking the fact 

 that under any ordinary working load the column is either 

 not bent at all, or at any rate is not bent nearly so much as 

 it is immediately before fracture, and that consequently the 

 stress is not only less, but is distributed over each cross- 

 section with a much nearer approach to uniformity. 



In a tie rod a double load implies double tensile stress — 

 the stress is increased but its distribution is unaffected ; in 

 a beam we believe the same to be the case, but in a long 

 column a double load not only means double average stress 

 on any given cross section, but also increased flexure, causing 

 a very large increase in the ratio in which the maximum 

 stress exceeds the average. In fact, a double load may 

 involve quadruple, sextuple, or even tenfold stress, according 

 to the proportions of the column and the amount of its 

 flexure. 



By a YQYj simple and conclusive mathematical process I 

 find that in a certain column, tested by Hodgkinson, the 

 maximum compression upon any part was 43,820 lbs. per 

 square inch under a load of 124,000 lbs., but only 24,500 lbs. 

 per square inch under a load of 109,000. In other words, 

 an increase of 14 per cent, in the load caused an increase of 

 no less than 78 per cent, in the maximum stress. Now, the 



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