Conclusion.

51. Although many of the researches mentioned in this report are not unfrequently called dynamical proofs of the Second Law, yet to prove the Second Law, about which we know something, by means of molecules, about which we know much less, would not be in consonance with the sentiments expressed at the end of the last paragraph. The most conclusive evidence for regarding Carnot's principle as a theorem in molecular dynamics lies in the remarkable agreement between the results obtained by the methods described in the three different sections of this report, all of which are based on different fundamental hypotheses. It is worthy of note that the method of Clausius alone is independent of any assumptions regarding the nature of the intermolecular forces.

It has been proved, on each of the various hypotheses, that when a system of molecules undergoes transformations analogous to reversible processes in thermodynamics the molecular kinetic energy T is an integrating divisor of the work dQ communicated to the system through the molecular coordinates. Thus any quantity proportioned to T satisfies the definition of temperature afforded by (2), § 2. The evidence that such a quantity possesses the properties mentioned in § 3 is far less conclusive. These properties have never been investigated by the methods of the first section, while, if the statistical method be adopted, the evidence is confined to the very limited cases in which Maxwell's theorem is valid. The methods of the kinetic theory of gases do not afford a direct proof of any relation between the molecular kinetic energies of two substances which are in thermal contact, but which do not mingle.

In the volume already alluded to in this Report, Prof. J. J. Thomson claims to have deduced certain thermal properties of matter from the generalised equations of dynamics without the use of the Second Law of Thermodynamics, and he further claims that the results thus obtained afford evidence of the connection between the Second Law and the Hamiltonian principle. It would seem, however, that the novelty of this point of view is not fundamentally very great, for the molecular assumptions involved in the proofs are identical with those required in order to deduce the Second Law from dynamical principles. And, moreover, properties of temperature are assumed which, as we have just seen, have not hitherto been satisfactorily deduced from dynamical principles.

If, on the other hand, we decide, for the present at any rate, to regard Carnot's Principle (like Newton's Laws of Motion) as an axiom based on experience, the researches which we have considered show how this principle may be reduced to a theorem in molecular dynamics by making suitable assumptions as to the nature and motion of molecules. In this way the reversible thermal properties of matter may be represented by means of monocyclic or other dynamical systems, and the fundamental equations of thermodynamics may be replaced by particular cases of the ordinary dynamical equations. This is the point of view adopted by Helmholtz in his valuable paper on the physical meaning of the Principle of Least Action.1

In conclusion we may reasonably hope that future researches in the domain of molecular science will still further strengthen the bond of

1 Crelle, Journal, c.

connection which we suppose to exist between the Second Law of Thermodynamics and Newton's Laws of Motion.

My thanks are due to Mr. Larmor for references to many important papers on the present subject and to Mr. C. V. Burton for his most invaluable assistance in revising both the manuscript and proofs and in furnishing many useful suggestions.

Sixth Report of the Committee, consisting of Professors FITZGERALD (Chairman), ARMSTRONG, and O. J. LODGE (Secretaries), Sir WILLIAM THOMSON, Lord RAYLEIGH, J. J. THOMSON, SCHUSTER, POYNTING, CRUM BROWN, RAMSAY, FRANKLAND, TILDEN, HARTLEY, S. P. THOMPSON, MCLEOD, ROBERTS-AUSTEN, RÜCKER, REINOLD, CAREY FOSTER, and H. B. DIXON, Captain ABNEY, Drs. GLADSTONE, HOPKINSON, and FLEMING, and Messrs. CROOKES, SHELFORD BIDWELL, W. N. SHAW, J. LARMOR, J. T. BOTTOMLEY, R. T. GLAZEBROOK, J. BROWN, and JOHN M. THOMSON, appointed for the purpose of considering the subject of Electrolysis in its Physical and Chemical Bearings.

DURING the past year the completed portion of Mr. Shaw's report on our knowledge of electrolysis has been printed and circulated among the members, and has appeared in the annual volume of the Association. So also has the report of the discussion with Professors van t'Hoff and Ostwald and others at Leeds, which was edited by Professor Thorpe.

Papers received from Mr. J. Brown on the subject of the electrification of the spray thrown up from a vessel in which chemical reaction with effervescence was occurring, to which attention has been directed by Mr. Enright, and on the electrolysis of solutions of the chlorides of iodine and bromine, were communicated to the 'Philosophical Magazine.'

The valuable theoretical and experimental work of Professor J. J. Thomson, which has been described in the 'Philosophical Magazine' and in the 'Proceedings of the Royal Society,' on the discharge of electricity through vacuum tubes, has a distinct electrolytic significance; and some researches of Mr. A. P. Chattock on the discharge of electricity from points, which are to be described at the present meeting, are tending in very much the same direction; and showing that all convective passage of electricity, whether in liquids or gases or in partial vacua, are essentially electrolytic, taking place probably by means of a series of Grotthuss chains, and with atomic charges of the same order of magnitude as those concerned in electrolysis proper.

Other interesting work is going on, and a document entailing a great amount of labour which has been drawn up by the Rev. T. C. Fitzpatrick, one of the members of the Committee on Electrical Standards, is nearly complete; it will be published next year.

The Committee suggest that they should be reappointed, and with a grant of 51. to cover printing and postage.

Eleventh Report of the Committee, consisting of Sir WILLIAM THOMSON, Mr. R. ETHERIDGE, Professor JOHN PERRY, Dr. HENRY WOODWARD, Professor THOMAS GRAY, and Professor JOHN MILNE (Secretary), appointed for the purpose of investigating the Earthquake and Volcanic Phenomena of Japan. (Drawn up by the Secretary.)

THE GRAY-MILNE SEISMOGRAPH.

THE first of the above seismographs, constructed in 1883, partly at the expense of the British Association, still continues to be used as the standard instrument. The earthquakes which it has recorded since April 27 of last year are given in the following list.

Catalogue of Earthquakes recorded at the Meteorological Observatory, Tokio, between May 1, 1890, and April 30, 1891, by the Gray-Milne Seismograph.

In the above list eighty earthquakes are recorded, a number comparable with the number of disturbances recorded in previous years. The intensity of these disturbances has, however, been unusually feeble, and without the aid of instruments it is likely that not more than thirty of them would have been noted. Although one earthquake lasted six minutes, the duration has generally been small, whilst only on one occasion did the full range of motion exceed one millimetre.

Notwithstanding the fact that the list of records is as extensive as in previous years, the opportunities for many kinds of observation have been unusually small-so small, in fact, that it is thought better to withhold the results of a certain class of experiments until they have been amplified by the observations of another year.

OBSERVATIONS IN A PIT.

In the Transactions of the Seismological Society,' Vol. X., the present writer, in a paper entitled On a Seismic Survey,' gave examples of observations made in a pit 10 feet in depth. For certain large earth

These

quakes it appeared that the motion at the bottom of the pit was very much less than that observed on the surface, while for small disturbances the difference between the surface and pit records was too small to be measurable. In 1886 a pit 18 feet in depth was sunk through dry compact earth at the Imperial University in Tokio, at the bottom of which seismometers were established on a brick pavement. seismometers and others in the Seismological Laboratory a few yards distant when placed side by side gave records which were identical. The work was commenced by Professor S. Sekiya, and continued by myself, and the records obtained have now been subjected to a careful analysis by Mr. F. Omori, a graduate of the University, who has taken from ten to thirty waves in thirty different earthquakes and for each of these waves calculated its amplitude, period, maximum velocity, and maximum acceleration. Of these thirty disturbances, for each of which diagrams were obtained on the surface and in the pit, three were strong and twenty-seven were feeble. For each set of calculations referring to a particular earthquake average values were obtained, and the average for these average values was as follows:

1. Ratio of Quantities Observed on the Surface to those Observed in the Pit.

From the above it appears that for small disturbances the motion on the surface is slightly greater than it is in the pit; further, from an inspection of the diagrams, it is seen that those from the pit are always smoother than those from the surface. In severe earthquakes Mr. Omori points out that this latter character is strongly marked.

(c) RIPPLES SUPERIMPOSED ON WAVES OF STRONG DISTURBANCES.