872 PROCEEDINGS OF THE AMERICAN ACADEMY 



in the inverse ratio of the height. Hodgkinson gives for the ratio of 

 these lengths 1 to 3^, and Euler 1 to 4. 

 Again, I take from these tables a pillar 



8 inches in diameter, 6 feet long, and the breaking weight is 1,315 cwt. 

 8 inches in diameter, 12 feet long, " " " 1,224 " 



Or, it loses only about 9 per cent by being of double height. While 

 the ratios assigned, by Hodgkinson would be, as before, 1 to 3^, and by 

 Euler 1 to 4. 



Again, how do these diameters compare, taking for the same lengths ? 

 We have : 



12 feet long, 2 inches in diameter, bearing ... 32 cwt. 

 1 2 feet long, 8 inches in diameter, bearing . . . 1,224 " 



Or about as 1 to 40. While the formula of Hodgkinson gives the 

 I'atios to these diameters as 1 to 147, and Euler's formula 1 to 256. 



Next for a comparison of hollow pillars. Hodgkinson found that a 

 hollow pillar 7^ feet long, 3.36 inches in external diameter, and .36 of 

 an inch thick, being on round or hemispherical ends, bi'oke only under 

 a load of 50,477 pounds, or 22^ tons. Now, we have in the tables no 

 length under ten feet. Taking this height and the diameter at 3^ inches, 

 with a thickness of half an inch, and to this is assigned a breaking weight 

 of 3 tons 15 cwt., or 75 cwt. But according to Hodgkinson's formula, 

 carried but a very little way from his actual example, such a pillar will 

 sustain a weight of 18.9 tons or 379 cwt. with round ends, or 56.7 tons 

 or 1,138 cwt. with flat ends. Again, to find from the tables a hollow 

 column 10 feet long that will bear a weight of 18.9 tons, I find that it 

 should be 8 inches in diameter and f inch thick, and to bear 56 tons 

 it should be 11 inches in diameter and 1^ inches thick. 



We see, therefore, that whatever discrepancies and incongruities 

 these tables may contain, they are all, most probably, within the limits 

 of safety, though the longest and smallest solid pillars ai*e but just 

 Avithin those limits ; while certainly the large and short ones are safe 

 to a somewhat prodigal use of iron. But ought these incongruous rules 

 to be followed ? Safety, absolute safety, against all ordinary, and some 

 even extraordinary cii'cumstances, should first be provided for ; beyond 

 that, weight of iron is almost waste of iron ; and it seems to me that 

 it would be a good service to mark out where this line is, under differ- 

 ent conditions, and to give rules for keeping safely within it, — rules 



