The authors desired their attempt to investigate the laws to which the operation of submerging telegraphic cables were subject, to be considered only as a partial solution of an interesting and somewhat complicated problem. It was evident that much misapprehension existed on the subject, and it had been stated in the journals relating to the proceedings, at tile Meeting of the British Association at Dublin, in the year 1857, that "it seemed to be universally admitted that it was mathematically

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... mpossible, unless the speed of the vessel from which the cable was payed out could be ahnost infinitely increased, to lay out a cable in deep waters, say two miles, or more, in such a way as not to require a length much greater than that of the actual distance, as from the inclined direction of the yet sinking part of the cable, the successive portions payed out, must, when they reach the bottom, arrange themselves in wavy folds, since the actual length is greater than the entire horizontal distance." It was desirable to ascertain how far such a proposition was correct, and, if correct, what amount of "slack," or of surplus cable, should be provided to meet the waste, in varying depths of water. The questions discussed in tlle paper, and of which the mathematical investigations were given in an appendix, were :--1. The possibility of laying out a cable straight along the bottom, in deep water, free from the action of currents. 2. What degree of tension would be required in the process ? 3. What would be the effect, as regarded strain, under the varying circumstances of the depth of water, of the specific gravity of the cable, and of the velocity of the paying-out vessel ? 4. What would be the relative velocities of the cable and of the paying-out vessel requisite to reduce the strain or tension to any given amount, and what would be the consequent waste of cable ? 5. The effect of currents, and the consequent waste of cable. 6. How far it would be necessary, or safe, to check the velocity of paying-out when passing currents, so as to avoid, as far as possible, waste of cable ? 7. Would it be safe, and, if so, under what circumstances, to stop the paying-out, and to attempt to haul in the cable from great depths ? 8. The effect of the pitching of the vessel in a heavy sea. 9. The principal desiderata in the paylng-out apparatus. 10. The.effect of floats or resisters. 11. The best means for saving the cable, in case of fracture. 12. The best mechanical construction of a submarine cable. After investigating the laws of bodies, such as cables, sinking in a resisting medium, the paper proceeded to show the great waste of cable attendant upon paying-out free from tension at the ship. The forrp of the curve assumed by a descending cable was then examined, and the amount of tension at the paying-out vessel requisite to lay the cable * From Newton's London Journal of Arts and Sciences~ March: 1858.