232 Proceedings of the British Association. 



times the side of its square, that the strength may be considered 

 as uniform, the mean being 10,000 lbs. per square inch, or upwards. 

 From the experiments on the columns one inch square, it appears that 

 when the height is 15 times the side of the square, the strength is 

 slightly reduced ; when the height is 24 times the base, the falling 

 off is from 138 to 96 nearly ; when it is 30 times the base, the 

 strength is reduced from 138 to 75 ; and when it is 40 times the base, 

 the strength is reduced to 52, or to little more than one-third. These 

 numbers will be modified to some extent by the experiments in 

 progress. In all columns shorter than 30 times the side of the square, 

 fracture took place by one of the ends failing ; showing the ends to 

 be the weakest parts; and the increased weakness of the longer 

 columns over that of the shorter ones seemed to arise from the former 

 being deflected more than the latter, and therefore exposing a smaller 

 part of the ends to the crushing force. The cause of failure is the 

 tendency of rigid materials to form wedges with sharp ends, these 

 wedges splitting the body up in a manner which is always pretty 

 nearly the same ; some attempts to explain this matter theoretically 

 were made by Coulomb. As long columns always give way first 

 at the ends — showing that part to be the weakest — we might econo- 

 mize the material by making the areas of the ends larger than that of 

 the middle, increasing the strength from the middle both ways to- 

 wards the ends. If the area of the ends be to the area in the middle 

 as the strength of a short column is to that of a long one, we should 

 have for a column whose height was 24 times the breadth, the area of 

 the ends and middle as 13,766 to 9,595 nearly. This, however, 

 would make the ends somewhat too strong ; since the weakness of 

 long columns arises from their flexure, and increasing the ends would 

 diminish that flexure. Another mode of increasing the strength of the 

 ends would be that of preventing flexure by increasing the dimensions 

 of the middle. From the experiments it would appear that the 

 Grecian columns, which seldom had their lengths more than about 

 10 times the diameter, were nearly of the form capable of bearing the 

 greatest weight when their shafts were uniform ; and that columns 

 tapering from the bottom to the top were only capable of bearing 

 weights due to the smallest part of their section, though the larger 

 end might serve to prevent lateral thrusts. This last remark applies, 



