The Strength of Columns. 17 



fectly, or even approximately, in accordance with Hodgkin- 

 son's rule in the case of large hollow cast-iron columns. 

 The breaking load of the great central column supporting 

 the water tank from which the town of Echuca is supplied, 

 for example, is 1320 tons by Hodgkinson's rule, and only 

 1030 tons by Gordon's. 



More recently still, Professor Cawthorne Unwin, of 

 Cooper's Hill Engineering College, has in his work on 

 Machine Design advocated a return to Euler's original for- 

 mula, to the exclusion of those subsequently arrived at. 

 The ultimate strength of the Echuca column will be 900 

 tons, according to his version of Euler's results. 



Thus it will be seen that most serious differences of 

 opinion exist with reference to the behaviour of long 

 columns under strain, and to the proper algebraical expres- 

 sion for their breaking loads. With the exception of 

 Hodgkinson the writers above referred to appear to base 

 their formula rather upon theii' opinion of what ought to be 

 than upon their observations of what is. Hodgkinson, on 

 the other hand, abandons in despair the attempt scientifically 

 to explain the facts, and is content carefully to observe and 

 record actual casesof fracture, and empirically to construct 

 a formula having no a priori signification, but simply 

 approximating to the average result of his experiments. 



The question now suggests itself — Is it possible to re- 

 concile these differences of opinion, and show any approach 

 to harmony, or at any rate explanation of the discrepancies 

 between Euler's a priori anticipations and Hodgkinson's 

 observed results. I think it is, and will endeavour to throw 

 some slight further light upon this vexed subject. The first 

 serious discrepancy is as to the behaviour under an increas- 

 ing load. Euler says that a column originally straight will 

 remain so until its load reaches a certain critical amount, 

 when it will suddenly double up. Hodgkinson says his 

 columns behaved quite differently — commencing to bend 

 under loads very small compared with those required for 

 fracture. These diverse statements may be accounted for as 

 follows : — Euler necessarily assumed that his column con- 

 sisted of perfectly uniform material, and that the load was 

 applied fairly, its line of action passing through the centre 

 of gravity of each cross section. And I believe that could 

 these conditions be faithfully complied with in practice, 

 Euler's predictions would be verified. Baker, in his work on 

 Beams, Columns, and Arches, describes an experiment upon 



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