## Abstract

LONDON.

Physical Society, November 11.—Mr. Walter Baily, M.A., Vice-President, in the chair.—The discussion on Mr. Williams's paper, the dimensions of physical quantities, was resumed by Burton. He remarked that the idea that so-called “specific quantities,” such as specific gravity, are pure numbers was an erroneous one, and liable to lead to difficulties. The specific gravity of a substance was of the nature of density, and was a simple number on the convention that the density of water was taken as unity. If dimensions be given to specific quantities their interpretation would, he thought, be easy when rational dimensional formuæ were found. Referring to Fitzgerald's comments, he said, although the contention all energy is ultimately kinetic could not be gainsaid, the distinction commonly drawn between kinetic and potential energy involved nothing contrary to this view, and was useful convenient in many cases. As to the dimensions of s and k was inclined to favour Mr. Williams's views, for several considerations suggest that the two capacities of the medium are essentially different. Arguments to show that was probably absolutely constant in the ether, whilst Ze might be variable, brought forward. Of the two systems of dimensions for and k suggested by Mr. Williams, that which made r a density seemed preferable.—Prof. A. Lodge said he was greatly interested in propagating the idea that physical quantities are concrete, and therefore welcomed Mr. Williams's paper. He thought it desirable to keep some names for abstract numbers, “specific gravity” should be one. If another name involving dimensions was required “specific weight,”or "weight per unit volume,"might be used. Speaking of the dimensions of the various terms of an equation he did not think was usually recognized that in ordinary algebra or Cartesian geometry the principle of directed terms was rigidly adhered to, for if directed at all every term of such an equation directed along the same line. In this respect ordinary algebra was more rigid than vector algebra. Even if circular functions were involved, as in polar co-ordinates, they had the effect of making the directions of the terms the same. Other instances of problems bringing out the same fact were men- tioned. Mr. Boys thought Mr. Madden had been arguing in a circle when he spoke of the astronomical unit of mass, and deduced he dimensions of mass as L3/T2 from the equation MLT'2=M2/L2, for it was quite impossible that this equation could be true unless y, the gravitation constant, was intro- duced on the right-hand side. Mr. Williams's method was quite the reverse, for he maintained that unless k and i were introduced in the dimensions of electric and magnetic quantities, their dimensional formulte could not indicate the true - nature of those quantities, and hence were open to objection. Mr. W. Baily, whilst agreeing with Mr. Williams on most essential points, thought the total omission of L from dimensional formuize made the expressions more complicated and less symmetrical. For example, such expressions as XY/Z, X2 and xYz, which respectively represent undirected length, area, and volume, might with advantage be written L, L2, and L3 respectively. The restriction of the dimensions of r and k to those which give interpretable dimensional formulze for electrical and magnetic quantities seemed scarcely justified. Both the systems proposed could not be right, and he thought it would be more in accordance with our present want ofkrrowledge, if a quantity U of unknown dimensions were introduced such that r or k= U. density and k' or = U2. rigidity. This would keel) in view the fact that the absolute dimensions of quantities involving U were unknown. A list of the dimensions of the various quantities based on this arrangement was given. Mr. Swinburne, referring to the conventional nature of many units, said great differences exist between the ideas held by different persons about such units. Starting with the convention that unlike quantities could be multiplied together, he might have six amperes flow- ing in an electric circuit under a pressure of ten volts, and he might say he had sixty volt-amperes. The term "volt-ampere"could be regarded as indicating that the sixty was the numerical result of multiplying a number of volts by a number of amperes, or on the other hand it might be understood as a new unit, a wait, compounded of a volt and an ampere. Before Prof. Riicker's paper on suppressed dimensions was published, an electrician might have suggested measuring the length of a bench by sending an alternating current through it and deter- mining its self-induction, which he regarded as a length. Prof. Rbcker, however, would say that this could not give the right result, for s must be taken into account. He was inclined to think that dimensions were liable to mislead. Referring to scientific writers as authorities, he said Maxwell had been careless in some cases, for he had sometimes given dimensional formulre as zero, which really ought to have been L W T, or unity. In French text-books the errors had been corrected. Mr. Williams, in reply to Mr. Madden's remarks about self. induction being a length, pointed out that the subject might be looked at in two different ways, depending on whether one thinks of the standarciof self-induction as the practical standard of measurement, or the unit of self-induction as a physical quantity. In the former case the standard was a length, but in the latter the unit was a quantity of the same shecies as self-induction, the nature of which was as yet unknown. If its dynamical nature was known, then the absolute dimensions of all other magnetic and electric quantities would also be determined. In answer to Prof. Fitzgerald's remarks he said it was hardly likely that he should be unacquainted with the common view that kinetic and potential energies were ultimately quantities of the same kind, for it was a view with which he was quite familiar. The fact that they have the same dimensions was sufficient to show their identity, and the idea that all energy is ultimately kinetic was fundamental to his paper. This, however, did not imply that electrification and magnetization are of necessity the same, and the suggestion that they may be the same was only one of several "probable suggestions,"all of which were entitled to consideration. His chief reason for regarding Prof. Fitzgerald's suggestion as probably incorrect was that it led to a system of dimensional formulie incapable of rational mechanical interpretation, and containing fractional powers of the fundamental units. Prof. Fitzgerald's system would make resistance an abstract number, and.r and k directed quantities, whereas the former was a concrete quantity and the two latter must be scalar in isotropic media. If he (Mr. Williams) had erred in treating electrification and magnetization as different phenomena he could only plead that he had done nothing more than follow such authorities as Lord Kelvin, Dr. Lodge, and Mr. 0. Heaviside in the matter-The discus- sion on Mr. Sutherland's paper, on the laws of molecular force, was reopened by Prof. Perry reading a communication from the President, Prof. Fitzgerald. He objected to discontinuous theories, especially when Clausius had given a continuous formulae much more accurate over a very long range than Mr. Sutherland's discontinuous ones. The introduction of Brownian motions without carefully estimating the rates required and energy represented, and without giving any dynamical explanation of their existence, was not satisfactory. It would, he said, be most interesting if Mr. Sutherland would calculate the law of variation of temperature with height of a column of convectionless gas, under conduction alone (for Maxwell thought the inverse fifth power law ofmolecular attraction was the only one that gave uniformity of temperature under these conditions), and if necessary make tests with solid bars. Referring to the statement that molecular attraction at one cm. was comparable with gravitation at the same distance, he thought Mr. Boys would question this, and he suggested an exj5erimcnium crucis of the inverse fourth power law. Both the inverse fourth and inverse fifth power laws, assumed symmetry which did not exist. He also took exception to other parts of the paper. Dr. Glad- stone, referring to the relative dynic and refraction equivalents given in Table XXVIII. ofthepaper,said hethought it interesting to make a similar comparison between dynic and dispersion and magnetic rotation equivalents. The result as exhibited in a complete table showed a certain proportionality between the four columns but the differences were beyond the limits of experimental error. Mr. Sutherland, however, sometimes reckoned the dynic equivalent of hydrogen as o2I5, and at other times looked upon it as negligible. The analogies be- tween the optical equivalents did not depend on the propor. tionality of the numbers so much as upon the fact that the refraction, dispersion, and magnetic rotation equivalents of a compound was the sum of the corresponding equivalents of its constituent atoms, modified to some extent by the way in which they were combined. Whilst a somewhat similar relation held true for the dynic equivalents, the effect of "double-linking"of carbon atoms, so evident in the optical properties, was scarcely perceptible. The result of calculating the constants from Mi instead of from M2? was next discussed, the effect of which was to quite upset the proportionality before noticeable. Mr. S. H. Burbury said that on referring to the author's original paper, on which the present one was based, he found that a uniform distribution of molecules was assumed. On this supposition the demonstrations given were quite correct, and the potential was a maximum. If, however, the molecules were in motion the average potential must be less than the maximum, and the deductions in the present paper being based on wrong assumptions were liable to error. Prof. Ramsay remarked that many statements in the paper, on the subject of critical points, were very doubtful. Separate equations for the different states of matter were not satisfactory, neither was the artificial division of substance into five classes. The predicted differences in the critical points due to capillarity, had not been found to exist. Speaking of the virial equation, he said that hitherto R had been taken as constant. Considerations he had recently made led him to believe that R was not constant. The whole question should be reconsidered regarding R as a variable. Mr. Macfarlane Gray said he had been working at subjects similar to those dealt with in Mr. Sutherland's paper, but from an opposite point of view, no attraction being supposed to exist between molecules. In the theoretical treatment of steam he found that no arbitrary constants were required, for all could be determined thermo-dynamically. The calculated results were in perfect accord with M. Cailletet's exhaustive experiments except at very high pressures, and even here, the theoretical volume was the mean between those obtained experimentally by Cailletet and Battelli respectiyely. Prof. Herschel pointed out that Villar §eau had discussed the equation of the virial, where the chemical and mechanical energies were not supposed to balance each other. Mr. Sutherland's paper all turns on the existence of such a balance, and he (Prof. Herschel) could not understand why this balancing was necessary. The discussion was then closed, and the meeting adjourned.

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Societies and Academies.
*Nature* **47**, 116–120 (1892). https://doi.org/10.1038/047116b0

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DOI: https://doi.org/10.1038/047116b0