20 The Strength of Golurans. 



true factor of safety is the ratio of the ultimate resistance of 

 the material to fracture to the maximum^ stress endured hy 

 any part of the piece under strain, and taking the ultimate 

 resistance to crushing of the material at 90,000 lbs. per 

 square inch, the true factor of safety was 2.04 under a load 

 of 124,000 lbs., and no less than 3.67 under the slightly 

 diminished load of 109,000. 



We are therefore led to the following conclusions : — 



1. That in a column of perfectly uniform material, loaded 

 in a perfectly symmetrical manner with a load less than that 

 required to produce unstable equilibrium, there will be no 

 flexure, and the stress will be independent of the length, and 

 may be but a very small fraction of the ultimate compressive 

 resistance of the material, even under a load closely approxi- 

 mating to that which would destroy the column. 



2. That actual columns will approximate more or less 

 closely in their behaviour to the above theoretical case, 

 according to their proportions, the nature of the material, 

 and the mode of applying the load. 



3. That the true factor of safety of a long column cannot 

 be found by dividing its breaking load by its working load, 

 but is a function of its flexure also ; and that this flexure 

 depends on slight accidental peculiarities in the material, or 

 in the way of applying the load, and is therefore not 

 calculable. 



4. That the true factor of safety, or the ratio in which the 

 ultimate resistance of the material exceeds its working stress 

 in a long column, is always greater, and generally very much 

 greater, than the ratio in which its breaking load exceeds 

 its working load ; and that consequently the present method 

 of dimensioning errs on the side of safety, and involves 

 waste of material. 



5. That in order to arrive at a rational method of dimen- 

 sioning, we must determine by numerous experiments, under 

 practical conditions, the greatest probable flexure, under 

 working loads, of columns of different materials and of 

 various cross sections. 



The term breaking load as applied to long columns 

 appears to me objectionable and likely to lead to confusion, 

 not being properly analogous to that of tension rods and 

 beams. I would suggest the term " critical load" as prefer- 

 able, on the analogy of the " critical angle" in optics. 



