grasped this idea, they must have noticed the enormous difficulty presented by the laceration which the ether must experience if it moves through pores or interstices among the atoms of matter. §3. It has occurred to me that, without contravening anything we know from observation of nature, we may simply deny the scholastic axiom that two portions of matter cannot jointly occupy the same space, and may assert, as an admissible hypothesis, that ether does occupy the same space as ponderable matter, and that ether is not displaced by ponderable bodies moving through space occupied by ether. But how then could matter act on ether, and ether act on matter, to produce the known phenomena of light (or radiant heat), generated by the action of ponderable bodies on ether, and acting on ponderable bodies to produce its visual, chemical, phosphorescent, thermal, and photographic effects? There is no difficulty in answering this question if, as it probably is, ether is a compressible and dilatable solid. We have only to suppose that the atom exerts force on the ether, by which condensation or rarefaction is produced within the space occupied by the atom. At present I confine myself, for the sake of simplicity, to the suggestion of a spherical atom producing condensation and rarefaction, with concentric spherical surfaces of equal density, but the same total quantity of ether within its boundary as the quantity in an equal volume of free undisturbed ether. * § 4. Consider now such an atom given at rest anywhere in space occupied by ether. Let force be applied to it to cause it to move in any direction, first with gradually increasing speed, and after that with uniform speed. If this speed is anything less than the velocity of light, the force may be mathematically proved to become zero at some short time after the instant when the velocity of the atom becomes uniform, and to remain zero for ever thereafter. What takes place is this: § 5. During all the time in which the velocity of the atom is being augmented from zero, two sets of non-periodic waves, one of them equi-voluminal, the other irrotational (which is therefore condensational-rarefactional), are being sent out in To deny this property is to attribute to ether infinitely great resistance against forces tending to condense it or to dilate it-which seems, in truth, an infinitely difficult assumption. † Further developments of the suggested idea have been contributed to the Royal Society of Edinburgh, and to the Congrès International de Physique, held in Paris in August. (Proc. R.S.E. July 1900; vol. of reports, in French, of the Cong. Inter.; and Phil. Mag., Aug., Sept., 1900.) all directions through the surrounding ether. The rears of the last of these waves leave the atom, at some time after its acceleration ceases. This time, if the motion of the ether outside the atom, close beside it, is infinitesimal, is equal to the time taken by the slower wave (which is the equivoluminal) to travel the diameter of the atom, and is the short time referred to in § 4. When the rears of both waves have got clear of the atom, the ether within it and in the space around it, left clear by both rears, has come to a steady state of motion relatively to the atom. This steady motion approximates more and more nearly to uniform motion in parallel lines, at greater and greater distances from the atom. At a distance of twenty diameters it differs exceedingly little from uniformity. § 6. But it is only when the velocity of the atom is very small in comparison with the velocity of light, that the disturbance of the ether in the space close round the atom is infinitesimal. The propositions asserted in § 4 and the first sentence of § 5 are true, however little the final velocity of the atom falls short of the velocity of light. If this uniform final velocity of the atom exceeds the velocity of light, by ever so little, a non-periodic conical wave of equi-voluminal motion is produced, according to the same principle as that illustrated for sound by Mach's beautiful photographs of illumination by electric spark, showing, by changed refractivity, the condensational-rarefactional disturbance produced in air by the motion through it of a rifle bullet. The semi-vertical angle of the cone, whether in air or ether, is equal to the angle whose sine is the ratio of the wave velocity to the velocity of the moving body *. *On the same principle we see that a body moving steadily (and, with little error, we may say also that a fish or water-fowl propelling itself by fins or web-feet) through calm water, either floating on the surface or wholly submerged at some moderate distance below the surface, produces no wave disturbance if its velocity is less than the minimum wave velocity due to gravity and surface tension (being about 23 cms. per second, or 44 of a nautical mile per hour, whether for sea water or fresh water); and if its velocity exceeds the minimum wave velocity, it produces a wave disturbance bounded by two lines inclined on each side of its wake at angles each equal to the angle whose sine is the minimum wave velocity divided by the velocity of the moving body. It is easy for anyone to observe this by dipping vertically a pencil or a walking-stick into still water in a pond (or even in a good-sized hand basin), and moving it horizontally, first with exceeding small speed, and afterwards faster and faster. I first noticed it nineteen years ago, and described observations for an experimental determination of the minimum velocity of waves, in a letter to William Froude, published in Nature' for October 26, and in the Phil. Mag. for November 1871, from which the following is extracted. "[Recently, in the schooner yacht Lalla § 7. If, for a moment, we imagine the steady motion of the atom to be at a higher speed than the wave velocity of the condensational-rarefactional wave, two conical waves, of angles corresponding to the two wave velocities, will be steadily produced; but we need not occupy ourselves at present with this case because the velocity of the condensational-rarefactional wave in ether is, we are compelled to believe, enormously great in comparison with the velocity of light. § 8. Let now a periodic force be applied to the atom so as to cause it to move to and fro continually, with simple harmonic motion. By the first sentence of $5 we see that two sets of periodic waves, one equi-voluminal, the other irrotational, are continually produced. Withou athematical investigation we see that if, as in ether, the condensationalrarefactional wave velocity is very great in comparison with the equi-voluminal wave velocity, the energy taken by the condensational-rarefactional wave is exceedingly small in comparison with that taken by the equi-voluminal wave; how small we can find easily enough by regular mathematical investigation. Thus we see how it is that the hypothesis of §3 suffices for the answer suggested in that section to the question, How could matter act on ether so as to produce light? § 9. But this, though of primary importance, is only a small part of the very general question pointed out in §3 as needing answer. Another part, fundamental in the "Rookh], being becalmed in the Sound of Mull, I had an excellent opportunity, with the assistance of Professor Helmholtz, and my "brother from Belfast [the late Professor James Thomson, of deter"mining by observation the minimum wave-velocity with some approach "to accuracy. The fishing-line was hung at a distance of two or three "feet from the vessel's side, so as to cut the water at a point not sensibly "disturbed by the motion of the vessel. The speed was determined by "throwing into the sea pieces of paper previously wetted, and observing "their times of transit across parallel planes, at a distance of 912 centi"metres asunder, fixed relatively to the vessel by marks on the deck and "gunwale. By watching carefully the pattern of ripples and waves which "connected the ripples in front with the waves in rear, I had seen that "it included a set of parallel waves slanting off obliquely on each side "and presenting appearances which proved them to be waves of the "critical length and corresponding minimum speed of propagation." When the speed of the yacht fell to but little above the critical velocity, the front of the ripples was very nearly perpendicular to the line of motion, and when it just fell below the critical velocity the ripples disappeared altogether, and there was no perceptible disturbance on the surface of the water. The sea was "glassy"; though there was wind enough to propel the schooner at speed varying between mile and 1 mile per hour. undulatory theory of optics, is, How is it that the velocity of light is smaller in transparent ponderable matter than in pure ether? Attention was called to this particular question in my address, to the Royal Institution, of last April; and a slight explanation of my proposal for answering it was given, and illustrated by a diagram. The validity of this proposal is confirmed by a somewhat elaborate discussion and mathematical investigation of the subject worked out since that time and communicated under the title, "On the Motion produced in an infinite Elastic Solid by the Motion through the Space occupied by it of a Body acting on it only by Attraction or Repulsion," to the Royal Society of Edinburgh on July 16, and to the Congrès International de Physique for its meeting at Paris in the beginning of August *. § 10. The other phenomena referred to in § 3 come naturally under the general dynamics of the undulatory theory of light, and the full explanation of them all is brought much nearer if we have a satisfactory fundamental relation between ether and matter, instead of the old intractable idea that atoms of matter displace ether from the space before them, when they are in motion relatively to the ether around them. May we then suppose that the hypothesis which I have suggested clears away the first of our two clouds? It certainly would explain the "aberration of light" connected with the earth's motion through ether in a thoroughly satisfactory manner. It would allow the earth to move with perfect freedom through space occupied by ether without displacing it. In passing through the earth the ether, an elastic solid, would not be lacerated as it would be according to Fresnel's idea of porosity and ether moving through the pores as if it were a fluid. Ether would move relatively to ponderables with the perfect freedom wanted. for what we know of aberration, instead of the imperfect freedom of air moving through a grove of trees suggested by Thomas Young. According to it, and for simplicity neglecting the comparatively very small component due to the earth's rotation (only 46 of a kilometre per second at the equator where it is a maximum), and neglecting the imperfectly known motion of the solar system through space towards the constellation Hercules, discovered by Herschel †, * Phil. Mag., Aug. 1900. †The splendid spectroscopic method originated by Huggins thirtythree years ago, for measuring the component in the line of vision of the relative motion of the earth, and any visible star, has been carried on since that time with admirable perseverance and skill by other observers, who have from their results made estimates of the velocity and direction of the motion through space of the centre of inertia of the solar system. there would be at all points of the earth's surface a flow of ether at the rate of 30 kilometres per second in lines all parallel to the tangent to the earth's orbit round the sun. There is nothing inconsistent with this in all we know of the ordinary phenomena of terrestrial optics; but, alas! there is inconsistency with a conclusion that ether in the earth's atmosphere is motionless relatively to the earth, seemingly proved by an admirable experiment designed by Michelsen, and carried out, with most searching care to secure a trustworthy result, by himself and Morley *. I cannot see any flaw either in the idea or in the execution of this experiment. But a possibility of escaping from the conclusion which it seemed to prove, may be found in a brilliant suggestion made independently by FitzGerald † and by Lorentz of Leyden, to the effect that the motion of ether through matter may slightly alter its linear dimensions, according to which if the stone slab constituting the sole plate of Michelsen and Morley's apparatus has, in virtue of its motion through space occupied by ether, its lineal dimensions shortened one onehundred-millionth § in the direction of motion, the result of the experiment would not disprove the free motion of ether through space occupied by the earth. § 11. I am afraid we must still regard Cloud No. I. as very dense. §12. CLOUD II.-Waterston (in a communication to the Royal Society, now famous; which, after lying forty-five years buried and almost forgotten in the archives, was My Glasgow colleague, Professor Becker, has kindly given me the following information on the subject of these researches: "The early (1888) Potsdam photographs of the spectra of 51 stars brighter than 2 magnitude have been employed for the determination of the apex and velocity of the solar system. Kempf (Astronomische Nachrichten, vol. 132) finds for the apex: right ascension, 206° ± 12°; declination, 46° +9°; velocity, 19 kilometres per second; and Risteen (Astronomical Journal, 1893) finds practically the same quantities. The proper motions of the fixed stars assign to the apex a position which may be anywhere in a narrow zone parallel to the Milky-way, and extending 20° on both sides of a point of Right Ascension 275° and Declination +30°. The authentic mean of 13 values determined by the methods of Argelander or Airy gives 274° and + 35° (André, Traité d' Astronomie Stellaire).” * Phil. Mag., December 1887. + Public Lectures in Trinity College, Dublin. Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern. § This being the square of the ratio of the earth's velocity round the sun (30 kilometres per sec.) to the velocity of light (300,000 kilometres per sec.). |