MECHANICS.

153

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

.« « .if_ ^ s

dius is r, W =-

/

In a cylindric tube, the radius of the external surfacebeing r, and of the internal /,

The strength of the tube is therefore to thestrength of the same quantity of matter, formedinto a solid cylinder of the same length, as r to

v'r' — r'

A tube may, therefore, be much stronger than the samequantity of matter in a solid form. This is knownto be agreeable to experience. But it is also said,that a tube of metal has been found to support agreater transverse strain than a solid cylinder, ofthe same diameter; or that a solid cylinder, whenbored in the direction of the axis, and a considerablepart taken away, was stronger than before.

This must undoubtedly arise from a change takingplace in the position of the fulcrum or hinge roundwhicli the fracture is made. In the case of a cylin-der, and, indeed, of all solids, the fulcrum is not themere outward edge, but a point in the interior; onthe one side of which the fibres are elongated, andon tbe other crushed together. The point, then,which serves as the fulcrum, will be found withinthe solid, at a greater or less distance, as the parts

resist