The experimental determination of the relation between magnetisation and magnetising force, would be a simple matter if the expression of such relation were not complicated by the fact that the magnetisation depends not alone on the magnetising force at the instant, but also upon previous magnetising forces; in fact, if it were not complicated by the phenomena of residual magnetism. In the absence of any satisfactory theory, we can only experimentally attack particular cases, and the results obtained have only a limited application; for example, we may secure that the sample examined has never been submitted to greater magnetising force than that then operating, and we may determine a curve showing the relation of magnetisation to magnetising force when the latter is always increasing; we may also determine the residual magnetism when after each experiment the magnetising force has been removed. Such curves have been determined by Rowland (Phil. Mag., Aug., 1873) and others. For many purposes a more useful curve is one expressing the relation of the magnetising force and magnetisation when the former is first raised to a maximum and then let down to a defined point; such curves have been called descending curves. One or two descending curves are given in a paper by Mr. Shida (Proc. R. S., 1883, p. 404). It has been shown by Sir W. Thomson and others that the magnetisation of iron depends greatly upon the mechanical force to which the iron is at the time submitted. In the following experiments the samples were not intentionally submitted to any externally applied force. Clerk Maxwell gives in his 'Electricity and Magnetism,' chap. 6, vol. ii., a modification of Weber’s theory of induced magnetism, and from this he deduces, amongst other things, what had been already observed, that iron may be strongly magnetised and then completely demagnetised by a reversed force, but that it will not even then be in the condition of iron which has never been magnetised, but will be more easily affected by forces in one direction than in the other. This I have verified in several cases. The ordinary determinations of residual magnetisation are not applicable to determine the permanent magnetism which a piece of the material of suitable given form will retain after removal of external magnetising force, but, as will be shown, the descending curves which express the relation of magnetisation and force, where these are diminishing, can be a t once used for this purpose. Such curves can also be used, as has been shown by Warburg and by Ewing (Report Brit. Assn., 1883), to determine the energy dissipated when the magnetisation of iron is reversed between given limits. That such dissipation must occur is clear, but some knowledge of its amount is important for some of the recent practical applications of electromagnetism. Probably Professor Ewing has made a more complete experimental study of magnetisation of iron than any one else. The researches of Professor Hughes should be mentioned here, as, although his results are not given in any absolute measure, his method of experiment is remarkable beyond all others for its beautiful simplicity. I have had great doubts whether it was desirable that I should publish my own experiments at all. My reason for deciding to offer them to the Royal Society is that a considerable variety of samples have been examined, that in nearly all cases I am able to give the composition of the samples, that the samples are substantial rods forged or cast and not drawn into wire, and that determinations of specific electric resistance have been made on these rods which have some interest from a practical point of view.