160 OUTLINES OF NATURAL PHILOSOPHY. 



In like manner, in a cylindric beam, of which the ra- 



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dius is r, W =s 



I 



In a cylindric tube, the radius of the external surface 

 being r, and of the internal r', 



w= vsrW 



The strength of the tube is therefore to the 

 strength of the same quantity of matter, formed 

 into a solid cylinder of the same length, as r to 



A tube may, therefore, be much stronger than the same 

 quantity of matter in a solid form. This is known 

 to be agreeable to experience. But it is also said, 

 that a tube of metal has been found to support a 

 greater transverse strain than a solid cylinder, of 

 the same diameter ; or that a solid cylinder, when 

 bored in the direction of the axis, and a considerable 

 part taken away, was stronger than before. 



This must undoubtedly arise from a change taking 

 place in the position of the fulcrum or hinge round 

 which the fracture is made. In the case of a cylin- 

 der, and, indeed, of all solids, the fulcrum is not the 

 mere outward wedge, but a point in the interior ; on 

 the one side of which the fibres are elongated, and 

 on the other crushed together. The point, then, 

 which serves as the fulcrum, will be found within 

 the solid, at a greater or less distance, as the parts 

 3 resist 



