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Resistance of the Fibrec of Solid Bodies

weight, cylinder, base, length, break and fixed

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RESISTANCE OF THE FIBREC OF SOLID BODIES, Theory of the. To form an idea of this resistance or reniteney of the parts, suppose a cylindrical body suspended vertically by one end. Here all its parts, being heavy, tend downwards, and endeavour to separate the two contiguous planes, where the body is the weakest ; but all the parts resist this separa tion by the force with which they cohere, or are bound together. Here, then, are two opposite powers ; viz., the weight of the cylinder, which tends to break it ; and the force of cohesion of the parts, which resists the fracture. If the base of the cylinder be increased, without increasing its length, it is evident the resistance will be increased in the same ratio as the base ; but the weight also increases in the same ratio : whence it is evident, that all cylinders of the same matter and length, whatever their bases may be, have an equal resistance, when vertically suspended.

But if the length of the cylinder be increased, without increasing its base, its weight is increased, while the resist ance, or strength, remains the same : consequently, it is weakened by its additional length, and has a greater tendency to break.

Hence, to find the greatest length a cylinder of any matter may have to break with its own weight, it is only necessary to know what weight is just suflieien't to break another cylinder of the same base and matter : for the length of the required cylinder must be such, that its weight may be equal to the weight of the first cylinder, together with the addi tional weight that was employed in producing the separation.

If one end of the cylinder were fixed horizontally into a wall, and the rest suspended thence, its weight and resistance would then act in a different manner ; and if' it be broke by the action of its weight, the rupture would be at the end fixed into the wall. A circle, ur plane, contiguous to the wall, and parallel to the base, and consequently vertical, would be detached from the contiguous circle within the plane of the wall, and would descend. All the motion is

performed On the lowest extremity of the diameter, which remains immovable, while the upper extremity describes a quadrant of it circle, and till the circle, which before was vertical, become horizontal, i. c. till the cylinder be entirely broken.

In the fracture of the cylinder, it is visible, two forces have acted, and the one has overcome the other : the weight of the cylinder, which arose from its whole mass, has over come the resistance which arose from the largeness of the base ; and, as the centres of gravity are points in which all the forces, arising from the weight of the several parts of the same bodies, are conceived to be united, one may con ceive the weight of the whole cylinder applied in the centre of gravity of its mass, i. e. in a point in the middle of its axis : and the resistance of the cylinder applied in the centre of gravity of its base i. e. in the centre of the base ; it being the base which resists the fracture.

When the eylinder breaks by its own weight, all the motion is on an immovable extremity of a diameter of the base. This extremity, therefore, is the fixed point of a lever, whose two arms are the radius of the base, and half the axis ; and, of consequence, the two opposite forces do not only act of themselves, and by their absolute force, but also by the relative force they derive from their distance with regard to the fixed point of the lever.

Hence it evidently follows, that a cylinder, e. gr. of copper, which, vertically suspended, will not break by its own weight, if less than four hundred and eighty fathoms long, will break with a less length in an horizontal situation ; because the length, in this latter ease, contributes two ways to the frac ture; both as • makes it of such a weight, and as it is an arm of a lever to which the weight is applied. Hence, also, the smaller the base is, the less length or weight will suffice to break it; both because the resistance is really less, and because it acts by a less arm of a lever.

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