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The subject of oscillations in chains suspended at two points, has recently been discussed in a paper by J. H. Rohrs, published in the Philosophical Magazine. The object is to explain the causes of fracture in suspension bridges arising from the tramping of troops, gusts of wind, etc. The following are the principal conclusions arrived at:— 1st. That if the tension at the ends of the chain where it is suspended be kept constant by allowing play at those points, the variation of tension due to vibration at any other point of the chain will be but small. 2nd. That it the chain be tied at the points of suspension so that it can have no motion there, a slight extent of vibration will produce comparatively a great increase ot tension. 3d. That periodic forces, such as may be taken, for instance, to represent the effect of tramping in time of troops moving across the bridge, are dangerous in the extreme, as if they happen to coincide in period with any of the possible types of vibration, the extent of vibration will increase continuously, till it ceases to be represented approximately by a linear or even an equation of the second order ; in this case, the chain will be divided by nodal points where there is no vertical motion. 4th. That the mere transit without tramping, of ordinary loads at an ordinary pace would not cause sensible vibration in a bridge of wide span; but that terms not periodic might be introduced by the variable pressure of wind sweeping in rapid gusts along the platform.
