The numbers in the last column show very clearly : (1) That the loss of silver is never even distantly equivalent to the amount of hydrogen developed ; (2) That the knobs suffer greater losses, under otherwise like conditions, the oftener they have already served for experiments -that is, the more their form has been already broken up and become adapted to the passing arc of light; (3) That in experiments of longer duration (where of course a brief interruption was always made when the knobs began to approach the temperature of fusion) the losses are more considerable; that is, higher temperature of the knobs determines greater losses; (4) That the positive electrode of silver suffers smaller losses when the opposite parts of the negative plate are dissimilar in constitution; for the experiments marked with an asterisk were made with a copper plate which had been first prepared at the turning-lathe, and presented concentric higher and deeper portions. In the commencing experiments the silver knobs were frequently carried transversely over these unevennesses. (5) That the knobs taken for the positive electrode give greater losses. It does not, then, depend exclusively on the chemical nature of the electrodes and the intensity of the current, but much more on manifold circumstances, how great the quantity of the disintegrated material shall be. For these experiments, if they are to be performed in the preceding simple form, only non-oxidable electrodes can with advantage be used. I have not on this account deemed it necessary to follow up the experiments further with expensive metals of this sort, because those communicated are quite sufficient to definitively cut off all supposition of any simple connexion between the intensity of the current and the disintegration of the electrodes. Aachen, April 4, 1873. Τ III. A Theory of the Source of Terrestrial Magnetism. By Professor CHALLIS, M.A., F.R.S., F.R.A.S.* IT may facilitate the understanding of the theory which is the subject of this communication if I begin with indicating the writings in which I have already discussed the theory of magnetism generally, and make some remarks on the views included therein as to the specific character of the earth's magnetism. * Communicated by the Author. My first researches relative to a theory of magnetic force were published in a communication consisting of Parts I. and II. contained in the Numbers of the Philosophical Magazine for January and February 1861. The account of the source of terrestrial magnetism given in articles 27-30 of that communication agrees for the most part with the views I hold at the present time, especially as regards the explanation in art. 27 of the generation of magnetic streams of the æther by the impulses it receives from the component atoms of the earth in their rotation about the earth's axis. Also I consider it to be correctly asserted in art. 33 that no recognizable magnetic current results either from the motion of the earth in its orbit, or from that due to the motion of translation of the solar system in space. This assertion, however, is partly dependent on facts of observation, no independent theoretical reason being there given for it. Some discussion of the essential principles of the hydrodynamical theories of magnetic force, and of other physical forces, will be found in the Philosophical Magazine for April 1861 (p. 250). Two papers in the Numbers of the Philosophical Magazine for February and March 1863 treat (1) of the zodiacal light; (2) of the analogous phenomenon of a uniform luminous arch seen at night across the sky, and symmetrically disposed about the ecliptic; (3) of diffused nocturnal luminosity. These phenomena are considered to give ocular evidence of the existence of solar and terrestrial magnetic streams. In my work On the Principles of Mathematics and Physics (published in 1869), the Theory of Magnetic Force occupies pages 604-676, including, in pages 613-618, a theory of terrestrial magnetism. In discussing the source of the earth's magnetism I have there maintained, in contradiction to an unsustained assertion in art. 28 of the before-cited communication, that the earth by its motion does not carry with it any sensible amount of the æther. It is, however, to be said that no distinct account is given in that work of the respective effects of the orbital and rotatory motions of the earth in generating magnetic streams. With the view of making the hydrodynamical theory of magnetism more complete, I subsequently went through a new discussion of its mathematical principles, which is published in the Philosophical Magazine for June 1872. Lastly, in a work entitled "An Essay on the Mathematical Principles of Physics," produced in the present year, I have brought under review the whole of the hydrodynamical theory of magnetism, and in such manner that as little use as possible is made of analytical symbols. In arts. 120-122 and 130-132 of this publication, theoretical reasons are given for concluding that little or no magnetic effect is attributable to the earth's motion of translation, and that terrestrial magnetism is almost wholly due to streams generated by the rotation about its axis. For the sake of convenience, I propose to reproduce here the reasoning by which these conclusions are there arrived at, previously to adding other considerations confirmatory of them. As the writings above enumerated sufficiently indicate the way in which the hydrodynamical theory of magnetism accounts generally for magnetic force by the action of steady streams of the æther, it will only be necessary for the present purpose to investigate the mode of generation of those steady streams by the agency of which the principal facts of the proper magnetism of the earth may admit of explanation. It must first be mentioned that the philosophical principles I have so long advocated forbid making any other hypotheses respecting atoms and the æther than those I have frequently had occasion to enunciate in this Journal. Accordingly it will be supposed that the earth consists wholly of inert spherical atoms of constant form and magnitude-that they are held in positions of equilibrium by atomic and molecular forces, which are only modes of action of the æther itself, which is assumed to be the source of all active force, and to press always and everywhere proportionally to its density-and that consequently the æther at rest has the same density within the earth as in the space outside. Moreover it is supposed that the occupation of space by the finite atoms is very small compared with the intervening spaces, even at the earth's centre, where the atomic density is greatest. Considering, first, the motions which the atoms impress on the æther by reason of the earth's orbital motion, we may at once infer from Poisson's solution of the problem of the simultaneous movements of a ball-pendulum and the surrounding air, the motions of the æther which will be produced by any single atom; and since the motions due to different atoms, as being steady relatively to the positions of their centres, may coexist, we may conclude, on the hypothesis that the proportion of space occupied by the atoms is very small, that the total motion is quam proxime the sum of all the motions caused by individual atoms. Also since, according to that solution, just as much fluid flows backwards as the atom displaces by its forward motion, it follows that during the time the earth is moving over a portion of its orbit equal to its diameter, a quantity of fluid crosses the transverse plane which is tangential to its surface in the first and last positions, equal to the quantity which would just fill the space occupied by the atoms. Hence, if we supposed this quantity to flow in that interval in a uniform concentrated stream through a circular aperture of radius equal to that of the earth, it might readily be shown that the ratio of its velocity to the velocity of the earth is two thirds of the ratio of the space occupied by the atoms to the earth's volume. This ratio, by hypothesis, is extremely small; and therefore it would not be contradictory to the theory to find that but little magnetic effect is due to ætherial currents at the earth's surface produced by the orbital motion. The motions resulting from the composition of all those severally impressed by the atoms will evidently be symmetrical with respect to an axis passing through the earth's centre in the direction of the motion, and fulfil at the same time the condition that just as much fluid enters at the following hemispherical surface as issues at the preceding one. The total motion relative to the position of the earth's centre at any time will consequently be a circulating motion; and a plane through the centre transverse to the direction of the earth's motion will be crossed by the refluent streams at right angles. The disturbances of a magnet's declination by these currents would have two maxima and two minima in the course of a revolution of the earth about its axis. Like effect would result from the earth's motion of translation due to the motion of the solar system in space. But no variations of magnetic declination subject to a regular law of this kind have been detected by observation, excepting one of very small amount traceable to the influence of the moon. It follows, therefore, that experience confirms the foregoing theoretical inference, that the currents generated by the earth's motions of translation have little or no magnetic effect. It will appear from a consideration of the foregoing argument that the earth, conceived to consist of discrete atoms, is incapable, by reason of the resistance arising from the inertia of the unlimited mass of the æther, to impress either in its interior or its immediate neighbourhood, motions whereby any portion of the æther could be permanently transported across a given fixed plane. The only possible motions are those necessary for vacating and filling up the spaces successively occupied by the atoms in their onward course, which motions, as we have scen, are not recognizable by any magnetic effects, and may therefore be supposed to be extremely small compared with the earth's velocity. The case is otherwise with respect to the streams due to the earth's rotation, the generation of which may be conceived of as follows. As the resultants of the movements immediately impressed on Phil. Mag. S. 4. Vol. 47. No. 309. Jan. 1874. C the æther by the revolution of the atoms about the earth's axis are circular, there will be no such refluent streams due to the inertia of the general mass of the æther as those produced by the earth's motion in its orbit. In fact, so long as there is any relative circular motion between the æther and the atoms, the latter will continually impel the æther, till the relative motion is reduced to zero. It may therefore be inferred that in the ultimate or steady state of the 'motion, the circular motion of the æther within the earth is the same as that of the atoms by which it is immediately impressed. This circular motion will, by reason of the centrifugal force, operate upon the æther external to the earth; and the condition of steadiness requires that the external æther should partake of a certain amount of circular motion decreasing with the distance from the axis of revolution, in order that the whole tendency of the centrifugal force transversely to the axis may be counteracted by the inertia of the surrounding mass of the æther. In short, if we conceive to be impressed on the earth and the æther a motion equal and contrary to the earth's orbital motion, the result of combining this motion of progression with the circular motion would be a composite spiral motion of the æther having always at the same points the same relations to the fixed centre of the earth. Hence, the earth being now supposed to move, this spiral form of steady motion would be capable of travelling uniformly through space in company with the earth. (See a discussion of this kind of motion in the article on the theory of magnetism in the Philosophical Magazine for June 1872.) But it is evident that this rotatory motion will tend to draw the æther from the axis equally in all directions in any given transverse plane, and thus to cause the external æther to rush in at the polar parts to supply any partial vacancy which the centrifugal force might produce. If, however, the circumstances of the earth were in all respects symmetrical with respect to the equatorial plane, these tendencies would just counteract each other, and no currents, other than the circular movements, would be generated; for the circulating currents which the influx at one pole would produce of itself would be just neutralized by those due to the influx at the other, and in consequence the influx at each would be stopped. But because the circumstances of the solid and fluid parts of the earth are not symmetrical with respect to the equatorial plane, there will be a differential action due to the centrifugal force, whereby streams will be produced which, as satisfying the necessary condition of circulating, will be permanent relatively to the earth. The direction of the flow will be determined by the circumstances which violate the condition of symmetry; and it is therefore reasonable to suppose, |