1820.] Physical Science during the Year 1819. 15 



loaded point are inversely as the cubes of the lengths, and directly 

 as the cubes of the thickness of the bars. 



The resistance of a square piece, whether placed on a face, or 

 on an angle, is the same. 



The resistance of a round piece is to that of a square piece 

 whose side is equal to the diameter of the former as three-fourths 

 of the circumference of a circle to the contour of the circumscribed 

 square. A consequence of this theorem is that supposmg the 

 volume the same, the resistance of a cylinder to that of a square 

 piece is as 20 to 21 very nearly. 



When a piece supported by its two extremities is left to the 

 effect of its own weight, the bend which it takes is to that which 

 the same weight would produce if concentrated in the middle as 

 5 to 8. 



When a piece supported by the middle is left to its own proper 

 weight, the bend is to that which the same weight would produce 

 if divided into two equal parts, and placed at the two ends as 

 3 to 8. 



The weight capable of bending a piece by pressing it in the 

 direction of its length is proportional to the product produced by 

 multiplying by the length of the piece the resistance which it 

 presents when cliarged perpendicularly to the direction of its 

 fibres.* Hence it follows, that for any piece whatever, this 

 weight is inversely as the square of the length ; and that for a 

 rectangular piece, it is besides directly as the size and as the 

 cube of the thickness. 



When two rectangular pieces of equal dimensions are placed, 

 the one above the other, at a distance a, and connected with each 

 other, so as neither to be able to separate, nor to slide on 

 each other. The resistance of the system of these two pieces is 

 proportional to 



(e + ay — a' 



e denoting the sum of their thickness. 



For a piece having the form of a cylindrical or square tube, 

 the resistance is proportional to the difference between the 

 fourth powers of the outer and inner diameters. It follows from 

 this that a hollow tube, whose thickness is one-twentieth of its 

 diameter, is 9^ times stronger than a solid cylinder of the same 

 weight. 



These are the results of M. Duleau's experiments, upon which 

 the greatest confidence may be placed. The reader is referred 

 for a more complete account of these important experiments to 

 the analysi of his memoir, printed in the Ann. de Chim. et de 

 Phys. xii. 133. 



M. Robiquet has ascertained that octahedral iron ore consists 



♦ This is only true witii regard to an elastic and flexible plate, b\it which is not 

 extensible nor compreesiblc in (he sense of lis length. 



