OF ARTS AND SCIENCES. 867 



"We have no record of any experiments to determine the power of 

 iron to resist a force applied, in any of the four or five ways in which 

 it may be applied, to break it, until about a hundred years ago, al- 

 though such experiments might have been made and kept as secrets, 

 or passed as traditions in the trade. About a hundred years ago, 

 Musschenbroek made numerous experiments upon the direct tensile 

 or cohesive strength of both wrought and cast iron ; and, although the 

 experiments were numerous, the results obtained gave much more 

 strength to iron than later experimenters have been able to obtain. 

 But neither Musschenbroek, nor, as far as I have found, any other 

 experimenter, attempted to determine the power of cast-iron to resist 

 a compressing force, like that to which columns are subjected, until 

 near the commencement of the present century. As early as the year 

 1757, however, Euler published a paper in the Berlin Memoirs, which 

 seems to be a sequel to some previous work of his upon the subject 

 that I have not seen. This paper consists of an elaborate geomet- 

 rical investigation of the comparative strength of columns of the same 

 materials, but of different diameters and lengths, without, however, 

 determining the absolute strength of any one material, or any one size 

 of column, as this indeed could be done only by experiment. No 

 proper and useful practical rules, applicable to cast-iron or stone, could 

 therefore be drawn from the conclusions arrived at. But the theoreti- 

 cal conclusions of Euler deserve to be noticed, both on account of the 

 great mathematical power of the man, and the somewhat near con- 

 formity which his formula bears to the truth, as derived from the 

 latest and best experiments. Euler's results may be summed up in 

 a very few words. They were these : — With columns of the same 

 material and of equal diameters, but of different lengths, the strength 

 must be inversely as the squares of the lengths. If the lengths be 

 equal and the diameters unequal, the strength must be as the fourth 

 powers of the diameters directly. Thus, let A and B be two columns 

 of equal diameters, B being twice as tall as A. A will bear four 

 times the load carried by B. And if C and D be two columns of 

 equal height, D being twice the diameter of C, then D will bear 



sixteen times the load borne by C, or, in general, P = — . 



Here the application of science to columns, or at least to cast-iron 

 columns, rested, until some time near the commencement of the present 



