With the progress of modern mining engineering, one of the features of which is the mining from greater depths and the hoisting of greatly increased loads, it becomes a matter of increasing importance that the engineer should be able to determinewith some degree of precision the character of the strains on the hauling rope. But a wire rope is a complex structure; it is made up of spirally-twisted strands, which in turn are composed of spirally-twisted wires, and it is not particularly easy to say exactly what happens when this "doubly-twisted structure is wound round a drum or over a pulley.. The difficulty has been generally evaded in ordinary practice by the simple device of adopting a large factor of safety for the rope-usually from 8 to 10-a factor which experience has shown is sufficiently large to cover the bending strains set "up when the rope is passed over pulleys of the sizes commonly considered appropriate.When, however, we add the stress due to the bending of the rope to the stress produced by" the direct pull, we find that the actual factor of safety is usually more nearly 4 than 10, and frequently the bending stresses in the rope are so large compared with the simple tensile stresses that their neglect may easily lead to disastrous results when dealing with problems a little out of the common run. Common Empirical Rules.-It is always "recognized that the bending of a wire rope round too small a pulley is likely to do the rope serious injury, but as it is desirable in ordinary winding operations to reduce the inertia of the moving parts to a minimum...