of small gyrostats, having the undisturbed positions of their axes in the common direction of the magnetic force and the propagation of the beam, and all vibrating in the same sense. When in consequence of the vibrating motion each gyrostat has its axis of rotation displaced from this direction, it reacts on the surrounding medium with transverse force at right angles to the plane through the axis of rotation and the direction of motion. By compounding this stress with the elastic forces of displacement of the ether, differential equations of motion are obtained which are of precisely the form necessary to account for the difference in rate of propagation of the two circularly polarised rays constituting the plane polarised ray. It is obviously suggested by the gyrostatic investigation that it ought to be possible to explain the magneto-optic rotation on the electromagnetic theory of light as a consequence of the existence of the small magnets which are supposed imbedded in the medium with their axes in the direction of propagation of the ray, and therefore producing the magnetisation which the medium has in that direction. In consequence of the motions of the ether, the direction of the chains of magnetised molecules which are supposed to exist along the direction of magnetisation (here taken as axis of ≈) in the undisturbed state of the medium is continually undergoing change at every point, and thus the direction of the axial magnetic force along each chain also undergoes alteration. It is obvious that if the displacements be everywhere small, the actual magnitude of this force will sustain only a very small percentage of alteration, but that each small change of direction will produce a component magnetic force in each of the two directions at right angles to the axis. The calling into existence of these components will produce corresponding electromotive forces tending to increase the displacements. The electromotive force in the direction of y is given by where dG/dt stands for the total time rate of change of G, the component of vector potential in the direction of y. Also since H, the component along does not perceptibly vary along .r, if the direction of propagation be as taken here along ≈, -Goz denotes magnetic induction through unit of area in the plane of yz. Hence any part of the total time-rate of variation of -G/Oz will denote the space-rate of variation in the direction of z of an electromotive force parallel to y, provided the time and space differentiations of the part are commutative. Now if the displacement of the ether particles from the undisturbed positions be taken as parallel and proportional to the electric displacement, and C be the component of magnetisation of the substance in the direction of z due to the existence of the molecular magnets, then considering the electric displacement f in the direction of x, we see that the component magnetic force in the direction of r is eCoroz, and thus the magnetic induction through unit of area in the plane of yz is eCofoz, where e is a coefficient of proportionality. The time-rate of variation of this is мера да Further, by the relation of magnetic force to vector potential, B = (ƏF/dz)|μ, and therefore the last equation becomes Now, since the differentiation of ƒ with respect to t is partial only, we may use the substitution a of a af which gives an electromotive force in the direction of y of amount But the displacement current in the direction of y is dg dt, and thus is K'4. Qat. Also, by the equations of currents dy/dt = −14πμ.d2G/02. Therefore we have the equation 1 02G K dQ dg = = which would in the equation already found for Qot yield Similarly for the other component in the case of circularly polarised light we find the equation These two equations are identical in form with those given by the gyrostatic theory, and of course lead to the same results; that is to say, the plane of polarisation of an electromagnetic beam will show a turning effect when the beam is transmitted along the lines of force in a magnetised medium.1 3. On an Experiment on the Velocity of Light in the neighbourhood of Rapidly-moving Matter. By Professor OLIVER J. LODGE, F.R.S. An apparatus was described which had been constructed to apply Michelson's interference method to a beam of light sent round and round by mirrors between a pair of circular saws clamped together and rotating rapidly. The results were, at present, negative. 4. The Action of Electrical Radiators, with a Mechanical Analogy. By J. LARMOR. In an electrical vibrator of rapid period the currents in the metallic parts are confined to the surface; the periodic times are therefore independent of the metals It ought to be stated that I understand from a reference in M. Poincaré's · Thé ories de Maxwell' that a similar theory has been proposed by M. Potier in a note to his French translation of Maxwell's Electricity.' I have not seen M. Potier's investigations, which may have completely anticipated the present note. of which the vibrators are made, being determined only by their forms, and there is no considerable loss due to degradation into heat in these conductors. The question occurs, what are the surface conditions that must be imposed under these circumstances at the boundaries of the dielectric, in order that the vibrations may be discussed with reference only to the dielectric in which they exist and are propagated? It appears that the vibrations are analogous to those of an elastic solid, when elastic displacement is made the analogue of the electric displacement in the dielectric. It is demonstrable that if the velocity of propagation is the inverse square root of the specific inductive capacity, this auxiliary solid must be considered as incompressible, and the scheme of electrodynamics must be that of Maxwell. The surface condition will then be absolute stiffness in the surface layer for all tangential displacement, and freedom for normal displacement. The mathematical examination of a typical case shows that this way of presenting the phenomena is practically exact for all wave-lengths greater than a centimetre for copper or other good conducting metal. For very minute waves the circumstances are not independent of the material of the conductor, but are similar to those which actually exist in the case of the metallic reflexion of light-waves. By aid of this representation a qualitative view of the possible modes of vibration is rendered feasible in cases where the mathematical analysis would be difficult or impossible. 5. On the Measurement of Stationary Hertzian Oscillations along Wires, and the Damping of Electric Waves. By Professor D. E. JONES, B.Sc. An account was given of preliminary experiments made in Bonn (at the suggestion of Professor Hertz) on electric waves in wires. The first object was to find a simple method of measuring the disturbance at different points of a wire (or pair of wires) along which are sent waves which interfere after reflection at the ends. It was found that satisfactory measurements could be made by inserting a very small thermo-junction in the circuit at different points, and noting the deflection of a low-resistance galvanometer connected up to it. The method is delicate enough to detect and measure exceedingly small currents, such as those produced by telephones. The method was applied to measure disturbances along a pair of parallel wires about 8 cm. apart and each about 130 metres in length. One end of each wire was connected to a (secondary) metallic plate 40 cm. in diameter. In the first set of experiments the other (far) ends of the wires were left free. The vibrator was of the usual type, provided with plates of the same size as those on the near ends of the wires and facing them. The wave-length of the disturbance along the wires was about 4:3 metres. On plotting curves with distances from the (far) ends of the wires as abscissæ and galvanometer deflections as ordinates the following results were obtained: I. The disturbance was zero at the end (0) rising to a maximum (51) at 2·2 m. There was no further absolute minimum, i.e. the disturbance did not fall to zero Proc. Roy. Soc. May 1891. 1891. 2 Proc. Camb. Phil. Soc. May 1891. 00 at any point. At about 4.6 m. there was a minimum deflection of 11, at 6.7 m. a maximum of 46, at 9 m. a minimum of 13, at 11 m. a maximum of 23, and so on. Thus the waves tail off rapidly. There are two complete strongly-marked waves and indications of a third, after which the disturbance tends to become steady along the wire. II. When the far ends of the wires were joined together similar results were obtained, excepting that the positions of maxima and minima were interchanged, the disturbance, e.g., being a maximum at the ends. The results indicate that only a small number of waves are sent out by the primary vibrator, and that these are rapidly damped. In both the above sets of experiments the primary and secondary plates were 30 cm. apart. III. (Ends joined). On bringing the secondary and together the damping became more and more rapid, as quickly absorbed the energy radiated out by the primary. 5 cm. apart only one wave could be detected. primary plates nearer if the secondary more When the plates were The curves (I, II, III) given above were measured on different days and under different circumstances. They cease where the errors of observation become comparable with the variations to be measured. The author's method has the advantage of requiring only the simplest apparatus. The only other published method which has been used for such measurements is Dr. Rubens' bolometric method, but Mr. Bjerknes has obtained similar results to those of the author with an electrometer instead of a thermo-junction. In order to find whether the junction produced any disturbance, loops of wire of varying lengths were inserted at 17 m. from the far end; but loops up to 1 m. long did not appear seriously to affect the positions of the maxima and minima. 6. On the Propagation of Electromagnetic Waves in Wires. The following is an account of some experiments made in the physical laboratory at Trinity College, Dublin, with apparatus kindly placed at the author's disposal by Professor Fitzgerald. The experiments are incomplete, inasmuch as Mr. Trouton's value (0.68 metre) of the wave-length in air is assumed for the resonating circle which the author used. The author's determinations of this wave-length agree with Mr. Trouton's, but they were few in number, and made at the very commencement of the work. These experiments were undertaken with the hope of throwing some light upon the results previously obtained by Professor Hertz. He found the ratio of the velocity of propagation of electromagnetic waves in air to the velocity in copper wires to be as 75 47, or 1.6. His wave-length in air was 7.5 metres. Using much shorter waves (0 68m.) and wires of different diameters, the author obtained a ratio varying from 177 for very fine wires to very near unity for thick wires. The apparatus has been fully described by Mr. Trouton. The wire used was soldered at one end to a piece of iron plate (9 × 4cm, and 0·3cm. thick), which was attached by means of silken cord to the vertical wooden support of the oscillators. the plate being fixed opposite one of the cylindrical oscillators. The wire was supported horizontally along the axis of the parabolic cylinder used to concentrate the radiations. In the first few experiments the further end of the wire was bent into a very small hook, to which a piece of string was attached to keep the wire taut; but this minute hook was found to cause considerable disturbance at the end which was never a node, and the distance from the end to the first node along the wire was always less than the other internodes. The hook was therefore removed, and the end of the wire kept straight. The resonating circle was 7.5cm. diameter, and was held with its plane parallel to the wire, and with the spark gap at its greatest distance from the wire. Wiedemann's Annalen, vol. 34, p. 551. The method of experiment was to adjust the gilt knobs of the oscillators about 5mm. apart, and, starting from the most distant end of the wire, pick out nodes by careful adjustment of the length of the spark gap in the resonating circle. Two internodal distances were usually measured, but sometimes three or four. The lengths of the internodal distances were found to agree well for the same wire and receiver. The mean of thirteen measurements with a wire 49 metres long and 1.57mm. diameter gave a wave-length of 0.605 metre. Five experiments with a wire 4 metres long and 2.9mm. diameter showed the wave-length 0·65 metre. A brass gas-pipe was next tried. This was 36 metres long and 11mm. diameter and gave a wave-length of 0.62 metre, as a mean of fourteen experiments. A thin wire, 5 metres long and 0.36mm. diameter, gave a wave-length of 0.476 metre (mean of ten experiments). A very fine wire, 4 metres long and 0078mm. diameter, gave as a mean of twelve experiments a wave-length of 0.384 metre. The author thinks that these experiments show that Professor Hertz's results were due to the comparative thinness of the wire he used as judged by the length of his waves. 7. On Reflection near the Polarising Angle from the Clean Surfaces of Liquids. By Lord RAYLEIGH, Sec. R. S. If the image of the sun, reflected at the polarising angle from the surface of ordinary water, be examined through a good nicol, no complete extinction can be observed. At most a dark nebulous patch is seen upon the face of the sun. If, however, the surface of the water be free from contamination, a well-defined band crosses the solar disc, coloured above and below, and to all appearance black, or nearly so, at its centre. The width of this band may be estimated at about onefifth of the solar diameter. A trace of olive-oil, decidedly short of what is required to stop the camphor movements, practically obliterates the band. The colour seen from clean water, which is due to the variation of the polarising angle with wave-length, may be compensated by holding a 20° water prism between the eye and the nicol. The band is thus achromatised, but colour is of course introduced at the upper and lower limbs of the sun. The deterioration of the band by contamination is not measured by the decrement of surface tension. A strong solution of oleate of soda or a saturated solution of camphor may give a much better band than distilled water with a somewhat greasy face. Moreover, different parts of the same surface (over which the tension is constant) are often observed to produce very different effects. Precise measures of the ellipticity abundantly confirm these preliminary results. Sunlight passing through a round hole fitted with cross-wires falls upon a collimating lens, thence after reflection from an adjustable mirror traverses the polarising nicol, and after reflection from the horizontal liquid surface passes a quarter-wave mica and an analysing nicol. The latter is set alternately to a deviation of 30° from the plane of incidence, and the azimuth of the polariser required to bring the dark spot upon the cross-wires in each case is recorded. If 2a be the difference of readings, tan 30° tan a, denoted by K, represents the ellipticity, measuring as it does the ratio of reflection of amplitudes of the two principal components. Jamin found for water K = - -00577, and for alcohol K = +'00208. In my apparatus, which worked remarkably well, a change of setting of the polariser of about two minutes was directly apparent when the analyser stood at +30°, and very early experiments showed that the ellipticity of clean water could barely be measured. While in the ordinary water 2a might lie between 0 and 1°, the value for clean water seemed not to exceed 2'. Usually no error could be perceived by mere inspection when the analyser was put over from +30° to -30°; and the mean of long series of alternations gave a difference sometimes in one direction and sometimes in the opposite. These discrepancies could only be attributed to real changes in the purity of the surfaces, and evidence gradually accumulated that the value for a clean surface was not zero, as had been expected, |