Lord Kelvin. Nineteenth-Century Clouds over the Dynamical Theory of Heat and Light. // Phil. Mag. S. 6. Vol. 2. No. 7. July 1901.

Lord Kelvin. Nineteenth-Century Clouds over the Dynamical Theory of Heat and Light. // Phil. Mag. S. 6. Vol. 2. No. 7. July 1901.

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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, maybe found in a brilliant suggestion made independently by FitzGerald t and by Lorentz J 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 one-hundred-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:

u 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 4* SO3. The authentic mean of 13 values determined by the methods of Argelander or Airy gives 274° and + 35° (Andrl, TraitS dy Astronomic Stellaire

* Phil. Mag., December 1887.

f Public Lectures in Trinity College, Dublin.

J Versuch einer Theorie der electrischm tmd optischen Er&cheinungen in bewegten Korpem.

§ 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.).

rescued from oblivion by Lord Rayleigh and published, with an introductory notice of great interest and importance, in the Transactions of the Royal Society for 1892), enunciated the following proposition: “ In mixed media the mean square “ molecular velocity is inversely proportional to the specific <( weight of the molecule. This is the law of the equilibrium a of vis viva/’ Of this proposition Lord Rayleigh in a footnote * says, “ This is ihe first statement of a very “ important theorem (see also Brit. Assoc. Rep., 1851). “ The demonstration, however, of § 10 can hardly be de-*c fended. It bears some resemblance to an argument a indicated and exposed by Professor Tait (Edinburgh a Trans., vol. 33, p. 79, 1886). There is reason to think “ that this law is intimately connected with the Maxwellian u distribution of velocities of which Waters ton had no know-“ ledge "

§ 13. In Waterston’s statement, the “ specific weight of a molecule" means what we now call simply the mass of a molecule ; and u molecular velocity ” means the translational velocity of a molecule. Writing on the theory of sound in the Phil. Mag. for 1858, and referring to the theory developed in his buried paper t> Waterston said, “ The theory “ . . . . assumes .... that if the impacts produce rotatory

motion the vis viva thus invested bears a constant ratio to u the rectilineal vis viva.” This agrees with the very important principle or truism given independently about the same time by Clausius to the effect that the mean energy, kinetic and potential, due to the relative motion of all the parts of any molecule of a gas, bears a constant ratio to the mean energy of the motion of its centre of inertia when the density and pressure are constant.

§ 14. Without any knowledge of what was to be found in Waterston's buried paper, Maxwell, at the meeting of the British Association at Aberdeen, in 1859 } gave the following proposition regarding the motion and collisions of perfectly elastic spheres: “ Two systems of particles move in the same u vessel; to prove that the mean vis viva of each particle “ will become the same in the two systems.” This is precisely Waterston’s proposition regarding the law of partition of energy, quoted in § 12 above ; but Maxwell's 1860 proof was certainly not more successful than Waterston’s. Max

* Phil. Trans. A, 1892, p. 16.

t “ On the Physics of Media that are composed of Force and Perfectly Elastic Molecules in a State of Motion.” Phil. Trans., A, 1892, p. 13.

{ “ Illustrations of the Dynamical Theory of Gases,” Phil. Mag., January and July 1860, and collected works, vol. i. p, 378.

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