May 17, 1894J 



NA JURE 



69 



advocacy of its aims the Association for the Improvement of 

 Geometrical Teaching owes so much as late secretary, hopes, 

 through the agency of its columns, to extract from experienced 

 teachers MSS. which have long been lurking in desk or pigeon- 

 hole for want of a suitable organ for making them known. 

 This new venture, which has been started in consequence of a 

 resolution passed at the association's annual meeting in January 

 'last, is proposed to be "a terminal journal for students and 

 teachers." The editor has to feel his way : words of encourage- 

 ment have come from the far East and West, as well as from 

 many teachers in this country. The number before us opens 

 with a short paper, by the editor, on the eccentric circle of 

 Boscovich. We borrow from Dr. C. Taylor's classical book on 

 'Conics the following verdict on Bosovich's work : — It is "a 

 [clear and compact treatise, which for simplicity, depth, and 

 jsuggestiveness will not readily be surpassed." Dr. J. S. Mackay 

 abstracts the first book of Gino Loria's treatise on " the exact 

 Isciences in ancient Greece," viz. that on the Greek geometers 

 before Euclid. In addition to the works cited by Dr. Mackay, 

 we may call attention to three notes on the history of mathe- 

 matics by the Danish mathematician, H. G. Zeuthen (which 

 have recently been published in the Bulletin de I' Acadcmie 

 Royalc Jes Sciences de Danemari (\&<)t,). Prof A. Lodge gives 

 some usefal approximations and reductions. Then follov some 

 elegant solutions of examination questions, and a select number 

 of questions for solution. A commendation of the new French 

 journal, l' fntermediare des Mathematiciens closes this No. I. 

 The size of the page, the clear type, and the excellent paper, 

 ■should secure for the Gazette far more than a mere succis d'estime. 

 The figures are lith'graphed on a separate sheet. We note one 

 little slip — Adam's property for Adams' (p. S. ) 



American 'Journal of Mathematics, vol. xvi. 2. (Johns Hop- 

 ikins University, April, 1S94.) — W. H. Metzler in compound 

 determinants (pp. 131-150) shows how to express certain minors 

 of a compound determinant A(,„) in terms of the minors of various 

 orders of A. The paper is divided into two parts, one relating 

 to determinants, ihe other to matrices. A short note follows 

 on the order of terms in a semi-convergent series, by II. P. 

 Manning (pp. 151-155). Writing on the addition theorems of 

 [acobi and Weierstrass (pp. 156-163), E. Study gives a new 

 presentation of results connected with an investigation of the 

 addition theorems given in Hirzel's paper, " Sph.Trische 

 Trigonometrle, orthogonale Substitutionen und Elliptische 

 iKunclioneu " (1S93). Two articles follow by A. Chessin. The 

 first is summaiion of logarithmic and exponential series (pp. 

 164-1S5), the second a note on the general solution of Bessel's 

 pqualion (pp. 186-7). '" an article on adjustable cycloidal and 

 irochoidal curves (pp. 188-204) Prof. F. Morley gives many 

 interesting results in connection with these curves. The text is 

 illustrated wiih several carefully drawn figures. A two-page 

 lole on induced linear substitutions, by Prof. F. Franklin, 

 :loses the number. 



SOCIETIES AND ACADEMIES. 



London. 



Royal Society, April 19. — "Electrical Interference 

 Phenomena somewhat analogous to Newton's Rings, but 

 :xhibited by Waves along Wires." By Edwin H. Barton, 

 B.Sc, late "1851 Exhibition" Science Scholar. 



(1) The preliminary paper (Roy. Soc. Proc, vol. liv. 

 jp. 85-96, 1893) on this subject gave the results of a single 

 !xperiment, and approximately accounted for them by a 

 nathematical theory of the phenomena involved. 



(2) The present paper discus^es the question of disturbances,' 

 md gives nine experiments. Two of these are similar to the 

 irst experiment, but were made under better conditions ; the 

 Jthers were made either to lead to these improved conditions or 

 n confirmation of the original fundamental conclusions. 



(3) The disluibances alluded to arise from the fact that the 

 decirical waves are not suddenly lost after their first incidence 

 ipon Ihe abnormal part of the secondary, but course to and fro 

 intil they die out. A method of avoiding the greatest dis- 

 urbance due to this cause is pointed out and adopted. A 

 :orrection is also calculated and applied for another disturbance 

 vhich still remains. 



(4) The chief experiment (Expt. v. arts. 42-48) is on inler- 

 erence phenomena, som?what an.ilogous to Newton's rings, I y 

 ransmission. 



NO. 1281, VOL. 50] 



(5) The experiments conclude with two exampl^ (Expts. viii. 

 and ix. arts. 51-62) of modifications of the secondary which 

 produce no reflexion. These consisted respectively of thinner 

 wires near together, and of thicker wires further apart, than the 

 normal spacing. In each case the capacity was practically 

 unaltered by the change in the wires ; hence, as anticipated 

 from the theory, no reflexion occurred. 



(6) The systematic comparison of theory and experiment, 

 made (Arts. 63-77) near the end of the paper, does not 

 exhibit an absolute quantitative agreement. Nevertheless, the 

 two are so far concordant in all their general features as to be 

 mutually confirmatory, and were approved by Prof. Hertz 

 (under whose able guidance the work was carried out in Bonn, 

 1892-93) as close approximations. 



" On Rocks and Minerals collected by Mr. W. M. Conway 

 in the Karakoram- Himalayas." By Prof. T. G. Bonney, F.R.S., 

 and Miss C. A. Raisin. 



Physical Society, April 27.— Prof. A. W. RUcker, F.R.S., 

 President, in the chair. — A paper on the mechanism of electrical 

 conduction (Part I. Conduction in MetaU) was read by C. V. 

 Burton. Considering a body not at absolute zero of tem- 

 perature, the author shows that electromagnetic radiation 

 would result in heat being degraded into a lower form of 

 energy, if any parts of finite electric conductivity were present, 

 and from the fact that our planet is not devoid of heit, deduces 

 the following Theorem I. : — " In a region contaii.ing matter 

 there may be (and probably always are) some parts which are 

 perfect insulator-', and some parts which are perfect conductors, 

 but there can be no parts whose conductivity is finite, unless 

 every finitely conductive portion is enclosed by a perfectly con- 

 ductive envelope." This conclusion is in accordance with 

 Poisson's theory of dielectrics, and with Ampere's and Weber's 

 theories of magnetism and diamagnetism respectively. Theorem 

 II. is enunciated as fellows : — "In metals, and in other non- 

 electrolytes whose conductivity is finite, the transmission of 

 currents must be afi'ected by the intermittent contact of per- 

 fectly conductive particles " ; and as a corollary. Theorem lit. 

 is given : — " If we suppose that in a substance at the absolute 

 zero of temperature there is no relative motion amongst the 

 molecules or amongst their appreciable parts, it follows that 

 every substance at this temperature must have either infinite 

 specific resistance (which does not imply infinite dielectric 

 strength) or infinite conductiviiy.'' Fleiring and Dewar's ex- 

 periments on pure metals tend to confirm this. The aulhoc 

 then shows why, on the intermittent contact hypothesis, a 

 conductor is heated when a current flows through it. On the 

 assumption that in ordinary conductors the relation between 

 the eleccromotive intensity in the intermolecular spaces and 

 electric displacement is a linear one, and that the electric . forces 

 lire small in comparison with theordinary intermolecular forces. 

 Ohm's Law is deduced. A model is next described by means 

 of which contact E.M.F. and the Peltier effect can be repre- 

 sented and explained, and in considering V'olta E.M.F. 's, (he 

 author points out that it is doubtful whether experiments in a 

 perfect vacuum could decide the questions at issue in the con- 

 tact-force controversy. The fact that the transparency of metals 

 is much greater than Maxwell's theory indicates might be ex- 

 plained without attributing any new properties lo the electro- 

 magnetic field by supposing the dimensions of molecules not 

 quite negligible in comparison with the wave-length of light 

 Prof. S. P. Thompson thought the paper had an important 

 bearing on the kinetic theory of solids. He saw no reason 

 why Ohm's Law should be proved, for he regarded it as a 

 definition. The President said the author represented all 

 actions as being due to collisions, thereby introducing the same 

 difficulties as were felt in the kinetic theory of gases, viz. that 

 collisions would give rise to mechanical oscillations in the 

 molecules of shriller and shriller pitch. Prof. J. J. Thomson 

 had recently given an explanation of electrical phenomena by 

 vortex filaments. After some remarks on the visibility of 

 molecules by Mr. Hovenden, Dr. Burton, in reply lo Prof. 



Thompson, said Ohm's Law, when expressed .as . = a con- 

 stant, was really a law, and not a mere definition. — A com- 

 munication on the design and winding allernatecurrcnt electro- 

 magnets, by Silvanus P. Thompson, F. R.S., and Miles 

 Walker, was read by the former. The paper describes ex- 

 periments showing that when the magnetic induction does not 

 exceed 4000 (C.G.S.), the pull exerted by a laminated electro- 



