1. In a paper which the Royal Society have printed in their Philosophical Transactions for 1862, I gave a series of curves exhibiting to the eye the diurnal inequalities of Terrestrial Magnetism in the three directions of Westerly Force, Northerly Force, and Nadir Force, as inferred from eye-observations and photographic registers at the Royal Observatory from 1841 to 1857. The paper, or the works to which it refers, exhibits also the secular change and the annual inequality through that period, and the lunar inequalities as inferred from the period 1848 to 1857. These results were obtained by excluding the observations of certain days (of whch a list was given) on which the motions of the magnetometers were so violent that it was difficult to draw a mean curve through the magnetic curve of the day. In the present paper I propose to give the principal results deducible from the days omitted in the former paper. But before entering into the details of the numerical investigations, I think it desirable to explain the principles upon which both parts of the investigations have been conducted. 2. The methods commonly employed in late years for measuring and classifying the effects of magnetic disturbance have been, in my judgment, very valuable to the science, especially in its earlier stages. But familiarity through many past years with magnetic photograms has strongly impressed me with the feeling that a different method ought now to be employed, taking account of relations of disturbances which perhaps could not be known at the introduction of the ancient method. I may thus describe the general ideas which have guided me:—First, that there is no such thing as a day really free from disturbance, and no reason in the nature of things for separating one or more days from the general series. There is abundant reason for such separation on the ground of convenience of reduction; but when the reduction has been effected by suitable process, the results of the separated days ought to be combined with those of the unseparated days in the formation of general means (the numerical necessity for which I propose to consider in the close of this paper),—the reduction of the separated days serving also to throw great light upon the nature of the acting forces on those days, which forces in all probability are acting, though in different degrees, on other days. Second, that, with our present knowledge of the character of magnetic disturbances, I cannot think myself justified in separating any single magnetic indication, or any series of indications defined only by their magnitude; nor do I entertain the belief that any special value could attach to the results which I might derive from observations from which such indications have been removed. The study of the photograms shows clearly that the successive indications at successive moments of the same day are a connected series; there is no such thing as a sudden display of force in any element; the sharpest salience which is exhibited on a generally smooth curve occupies at least an hour in its development (I believe, never less, although the individual saliences in a continued storm are of shorter duration), and during this time the force has been gradually increasing and gradually diminishing. Under these circumstances, I cannot think it right that I should cut off a part of that salienee, with the belief of obtaining results, that can possess any philosophical value, from the part which is left. And I come to the conclusion that each disturbed day must be considered in its entirety, and that our attention ought to be given in the first instance to the devising of methods by which the complicated registers of each of those days, separately considered, can be rendered manageable, and in the next place to the discussion of the laws of disturbance which they may aid to reveal to us, and to the ascertaining of their effects on the general means in which they ought to be included.
General Series Solutions for Stresses and Displacements in an Inner-fixed Ring
