OF ARTS AND SCIENCES. 369 



Tredgold devised a formula, from which tables have been calculated 

 that have gone into general use, and are now in the hand-books used 

 by builders. I have here one of these hand-books, published by "VYeale 

 of London in 1859, and of which these tables form a part. I shall 

 return to them presently. 



The next important step in these investigations, taking the order of 

 time, was made by Mr. Hodgkinson, about the year 1836. Mr. Hodg- 

 kinson was even then most advantageously known for his experiments 

 upon iron in the form of girders, or when exposed to cross-frac- 

 ture. His experiments upon columns or pillars were very numerous, 

 amounting to near three hundred, and were admirably contrived ; and 

 on reading his clear account of them, one only regrets that they were 

 not extended to greater instances, and not confined, as they were, to 

 loads of less than twenty-five tons, although, indeed, this is a greater 

 weight than had ever been used before for experiment. In the account 

 of these experiments, we have the weights required to destroy solid 

 pillars of from 60 inches in length down to 7^ inches, having their 

 diameters from half an inch up to two inches. To state a few of his 

 results in a very general way. He found that pillars 60 inches long, 

 half an inch in diameter, were broken by a weight of 143 pounds ; 30 

 inches long, half an inch in diameter, by 539 pounds ; 15 inches long, 

 half an inch in diameter, by 1,904 pounds. 



These were the breaking weights when both ends of the pillars 

 were rounded so as to bear only upon the centre of the pillar. Now 

 these numbers are to each other as 1, S^, and 134. The squares of the 

 lengths, if taken inversely, would be 1, 4, and 16. These ratios were 

 maintained as well when the ends of the pillars were flat, as when they 

 were rounded ; but when flat, so as to bear upon every part of the 

 end, the actual power of the pillar to sustain pressure was increased 

 about threefold. Again, with pillars of the same length, viz. 60 inches, 

 but of different diameters, he found, that those with a diameter of half 

 an inch broke with a weight of 143 pounds ; those with a diameter 

 of one inch, with 1,902 pounds ; those with a diameter of two inches, 

 with 24,291 pounds. 



These numbers are to each other as 1, 13^, and 170, while the 

 cubes of the diameters are to each other as 1, 8, and 64; the fourth 

 powers or squares of the squares are as 1, 16, and 256. The ratio, 

 therefore, is much above that of the cubes of the diameters, and below 



VOL. IV. 47 



