OF ARTS AND SCIENCES : FEBRUARY 14, 1865. 411 



In many of the hollow pillars tested, Ilodgkinson found that at the 

 place of fractui'e the metal was much thicker on one side than on the 

 other ; it would be reasonable to expect that this would weaken them 

 sensibly, but such was not generally the case. Thus, in the third ex- 

 periment in Table I., the thickness on one side was 0.55 inch, and on 

 the opposite side, 0.17 inch. In the fourth expei'iment in the same 

 table, the relative thickness on opposite sides was as 2 to 1, nearly. 

 In both of these experiments the breaking weights were above the 

 mean. In the third experiment the direction of the flexure was such 

 that the convex side coincided with the greatest thickness of metal ; in 

 the other experiment the convex side coincided with the least thick- 

 ness. In most cases, however, the convex side coincided with the 

 greatest thickness. 



In experiment 1, Table IX., in Hodgkinson's paper of 1840, the pil- 

 lar was 7 feet 4f inches long, external diameter 1.78 inch, internal 

 diameter 1.21 inch, the ends flat and well fitted. The ratio of the 

 thickness on opposite sides of the ring of metal, at the place of fracture, 

 was as 5 to 1. The convexity was on the thickest side. The break- 

 ing weight by experiment was 17,840 pounds, which is only about ^V 

 less than the breaking weight computed by foi'mula (1). 



The explanation of these remarkable results appears to me to be 

 this : The weight being applied equally on all sides of the pillar, which 

 is supposed to be straight when unloaded, the side having the least 

 metal will be the most compressed ; this will determine the dii'ection of 

 the flexure, so that its convexity will be on the thickest side. When 

 the load is near the breaking weight, the convex side, near the middle, 

 is subject to a tensile force, and the concave side to a crushing force. 

 Hodgkinson found that it required seven or eight times the force per 

 square inch to crush the kind of iron he used that it did to rupture it 

 by a tensile force, and although the sum of the crushing forces, acting 

 on one portion of the horizontal section at the place of fracture, largely 

 exceeds the sum of the tensile forces acting on the other portion of the 

 same section, the difference in the powers of the metal to I'esist the two 

 forces is so great that, in a long pillar, a much less area of section is 

 required to resist the sum of the crushing forces than to resist the sum 

 of the tensile forces. If the iron from being harder on the thm side is 

 less compressible on that side, or if the weight is not equally distributed 

 on all sides, or if the pillar is not straight when unloaded, the direction 

 of the flexure, when loaded, may be such that the convexity is on the 



