June 24, 1897] 



NATURE 



189 



velocity in the upper and lower paths, which would be indicated 

 by a displacement of the fringes. No such displacement is 

 observed, and hence we must conclude that either the ether is 

 absolutely at rest everywhere, or that the earth drags it with it 

 up to many thousand miles from the surface, or, lastly, that the 

 length of all bodies is altered by their motion through the 

 ether. 



Bulletin of the American Mathematical Society, May 



Systems of continuous and discontinuous simple groups, by Dr. 

 L. E. Dickson (read at the April meeting of the Society). This 

 paper is in continuation of some results announced at the BuflTalo 

 meeting (August 31, 1896), and consists of four sections. § i 

 enumerates the known systems of discontinuous simple groups ; 

 § 2 the systems of finite continuous transformation groups which 

 are simple ; § 3 gives an elementary deduction of certain groups 

 in § 2, viz. the groups in the /(2/+1) parameters, isomorphic 

 with the general projective group of a linear complex in Roj^i, 

 and a proof of their simplicity ; § 4 discusses the semi-simple 

 linear homogeneous groups whose defining function is the sum of 

 // determinants of order q>2. The contents of §§ 3, 4 were 

 presented by Prof. Lie (February 19) to his class, and he stated 

 that " the interesting result of § 4 was new, and not what one 

 would have expected."— On the number of roots of the hyper- 

 i^eometric series between zero and one by Mr. M. B. Porter 

 read at the March meeting). Klein's solution was published in 

 1S90 {Math. Ann., vol. xxxvii.). Solutions by Hurwitz and 

 (iegenteuer are given in the Math. Ann. (vol. xxxviii.) and the 

 Wiener Sitzungsherichte (vol. c.-«) respectively. The object of 

 the present paper is to apply two theorems of Sturm {Lioiiville's 

 fotirnal, vol. i. ) to the solution of the problem. — Another paper, 

 read at the March meeting, is by Prof. J. Pierpont on modular 

 functions. This treats the subject from the point of view of H. 

 Weber's Memoir, zur theorie der Elliptischen Functionen {.4cla 

 .Math., vol. vi. p. 329; cf. also his Elliptische Functionen und 

 Algebraische Zahlen, 1891).— In the Notes are given the mathe- 

 matical courses for the summer session at the Universities of 

 Chicago, Leipzig, and Munich. 



Bulletin de la SociJtJ des Naturalist es de Moscou, 1896, No. 

 I.— Contributions to the knowledge of the Urticacece and the 

 Moraceje, by M. Golenkin, with one plate. The inflorescence 

 and the disposition of leaves are treated in this second instal- 

 ment (in German). — A preliminary catalogue of the Lepidoptera 

 i)f the province of Kazan, by L. Krulikovski, continued (in 

 Russian). — Study of the embryonal development of Gammarus 

 pulex, by Marie Rossyskaia Kojevnikova, with one plate (in 

 French). — Materials for the mycological fauna of the province 

 of Smolensk, by A. Jaczewski (in French). The author has 

 found in that province 550 species of fungi, out of which 408 

 are new for that region, and he gives the list of these species. — 

 On the structure, function and . evolution of the Nematocysts 

 of Ccelenterata, by N. Iwanzoff, with four plates (in German). 

 .\n elaborate work, made at the zoological laboratories of 

 Naples and Villefranche, to be continued. — On the rotation of 

 the earth, supposed to be fluid in its interior, by Prof. Th. 

 Sloudsky, being a purely mathematical inquiry, continued from 

 a previous number. 



SOCIETIES AND ACADEMIES. 

 London. 



Royal Society, May 13.— "A Dynamical Theory of the 

 Electric and Luminiferous Medium. Part IIL Relations with 

 Material Media." By Joseph Larmor, F.R.S., Fellow of St. 

 John's College, Cambridge. Received April 21. 



This series of papers is mainly concerned with the develop- 

 ment of electrical and optical theory on the basis that electricity 

 is constituted of discrete atomic charges or electrons. It has 

 lieen shown in the previous papers that the facts of electro- 

 dynamics require this hypothesis and are consistent with it. 

 The hypothesis was arrived at from the point of view of the 

 properties of the rether, the conception of the electron as a 

 permanent strain-centre being a necessary feature of a theory of 

 an elastic icther. This idea is here developed and illustrated by 

 aid of a specification, on Lord Kelvin's lines, of a gyrostatic 

 material structure which would possess the rotational elasticity 

 characteristic of the rether, and at the same time contain such 

 strain-centres. The conception of a medium of elastic solid 

 type containing mobile discrete strain-centres is also touched 

 upon, by way of illustration and contrast. 



NO. 1443. VOL. 56] 



In the previous papers the relations of electromotive and 

 optical phenomena in matter at rest had been develoj:)ed on this 

 basis. When the matter is considered as in motion through the 

 a'ther, or when electric forces on matter are treated, we obtain 

 a definite and sufficient basis of connection between matter and 

 aether by assuming that the electrons are attached to the atoms 

 of matter. On this basis the electric and optical relations of 

 moving material media are here developed at length. The 

 more speculative question, as to how far a constitution of the 

 material atom which makes it consist wholly of a system of 

 electrons describing orbits round each other suffices to represent 

 or illustrate the properties of matter, comes under consideration 

 in various respects : this hypothesis in many of its features 

 would agree with the well-known theory of vortex atoms. 



The theory of refraction equivalents is developed, leading to 

 Lorenlz's results. The theory of optical dispersion is treated 

 from the generalised standpoint that the molecule vibrates about 

 a configuration of steady motion instead of one of rest : it 

 appears, also, that the formula usually given for the square of the 

 refractive index must be replaced by a similar formula for the 

 Lorentz refraction equivalent. 



The character of the mechanical forces that are developed in 

 fluid and solid material media by the electric attractions between 

 the polarised molecules of which they are composed, is con- 

 sidered, and expressions are obtained for them. A distinction 

 is here essential between those forces between neighbouring 

 molecules which are compensated locally, and the ones which 

 give rise to transmitted mechanical force which must be 

 compensated by regular mechanical stress in the medium ; 

 somewhat in the manner of the corresponding distinction 

 employed by Young and Poisson in the theory of capillarity. 

 It leads, through the negation of the perpetual motion, to the 

 specification of a function which is the mechanical or organised 

 energy of the material medium : this is different from the 

 available or free energy of thermodynamics, which is also 

 represented by an analytical function on account of the negation 

 of the unlimited availability of diffuse thermal energy : it is, of 

 course, also different from the total or aggi-egate energy of the 

 molecules of the medium, about which little can be known in 

 detail. The theory of osmotic forces is formulated in relation 

 to the available energy with which they are connected, as they 

 are related to the individual molecules sifted by porous partitions 

 and not to the element of matter in bulk : the known general 

 laws of chemical equilibrium are formulated as corollaries to the 

 same principle. On the other hand, the mechanical forces in a 

 fluid molecular medium polarised in any manner are expressed 

 in terms of the distribution of tiiechanical energy of polarisation^ 

 The doctrine oi energetics (including the conception of tempera- 

 ture), which forms a sufficient basis for the descriptive explanatioiv. 

 of the mechanics of statical or steady material systems, thus-. 

 reposes on the negation of the two types of perpetual motion 

 above mentioned, and therefore ultimately on the discrete 

 constitution of matter. 



A thermodynamic application which possesses interest, bolh 

 from the light it throws on the nature of magnetism and from the 

 circumstances that in it the heat supply is calculated indirectly 

 from the magnetic energy that runs down, is the relation between 

 magnetic susceptibility and temperature in substances not in the 

 very susceptible or ferromagnetic condition. According to the 

 Weberian theory, which fits in with the present view, dia- 

 magnetic energy which is not compensated mechanically goes to 

 the induction of Ampercan currents in the molecules ; while 

 paramagnetic energy not thus compensated goes to orientating 

 the molecules, and thus into heat. It follows that the dia- 

 magnetic coefficient is independent of temperature : on the other 

 hand, it is shown that the paramagnetic coefficient should vary 

 inversely as the absolute temperature. These laws were dis- 

 covered experimentally by Curie, who finds from a very extensive 

 investigation that they have the same order of accuracy at 

 sufficiently high temperatures as the ordinary gaseous laws : at 

 lower temperatures and in ferromagnetic substances the control, 

 of the polarised molecules arises in appreciable part from the 

 magnetic interaction of their neighbours, thus vitiating the law 

 as well as introducing effects of hysteresis. The well-known 

 model of Ewing would thus represent an ideal perfect ferro- 

 magnetic in which the control arises wholly from the latter 

 cause. 



In application of the previous results as to how far physical 

 actions can be considered as transmitted across the sether by 

 elastic stress, the conditions are formulated under which the 



