382 



NA TURE 



[February 20, 1896 



operations rationnelles ramener le probleme au cas ou le groupe 

 est seiiii-simph, et meme reconnait'^e d'avance la nature des sous- 

 groupes invariants simples qui tW-v/^^-fr^/ le groupe. . . . Quant 

 a la reduction a sa forme canonique de la structure d'un groupe 

 simple, elle depend d'une certaine equation algebrique dont le 

 groupe de substitutions, au sens de Galois, est connu ; cette 

 equation s'appelle Pequation caracth-istiqtie du groupe. Les 

 differents groupes de substitutions qui s'introduisent ainsi ne 

 presentent rien d'interessant et se relient immediatement aux 

 groupes symetriques de n lettres. Neanmoins trois d'entre 

 eux oflfrent un interet particulier et sont isomorphes, I'un 

 avec le groupe des 27 droites dune surface du 3* ordre, 

 I'autre avec le groupe des 28 tangentes doubles d'une courbe 

 du 4« ordre, le dernier avec le 7« groupe hypoabdlien de 

 120 lettres. Ce n'est pas un des resultats les moins 

 interessants et les moins inattendus de cette etude, que d'etablir 

 une relation entre ces groupes de substitutions de Galois et les 

 groupe* de transformations de M. Lie." — Mr. A. L. Baker 

 writes upon algebraic symbols. The symbols considered are 

 + , - , ?■( n/- i), and - i. The closing sentences will indicate 

 the line of reasoning. " In tri-dimensional domains we have 

 V V - ) °°x ::= X + iy + jv + ku, a quaternion. Is this a hint 

 that in the Calculus of Reals, Complex Functions and Quater- 

 nions, we have run the gamut of the Algebraic Calculi ? " There 

 is some (to us) novel notation in this article. To express the 

 roots of the Solvable Quantics as symmetrical functions of homo- 

 logues, is the title of an interesting algebraic article by C. H. 

 Kummell. There is, it may be inferred, some stiff reading in 

 these three articles. — Two sliort notes on singular solutions by 

 J. M. Page, and on a point of the theory of functions by A. S. 

 Chessin, close the number, which is adorned with a fine portrait 

 of the French mathematician, M. Paul Appell. 



Bulletin of the Mathematical Society, vol. ii. No. 4, January. 

 — On the convergence of the series used in the subject of 

 perturbations, by Dr. G. W. Hill. M. Poincare (" Les Methodes 

 nouvelles de la Mecanique celeste") has recently insisted that 

 certain series, in this subject, under a certain condition, are, in 

 the rigorous mathematical sense, divergent. Dr. Hill thinks 

 that the reasons brought forward to sustain this opinion are 

 scarcely convincing, and so, without attempting to find a flaw 

 in M. Poincare's logic, he aims at pointing out a class of cases 

 where the convergency can be shown in spite of the incommen- 

 surability of the component arguments. — Mr. R. A. Roberts 

 contributes an article on the locus of the foci of conies having 

 double contact with two fixed conies. — Note on the common 

 tangents of two similar cycloidal curves, by Prof. F. Morley. 

 This is the application of a new method, given by the writer in 

 vols. XV. and xvi. oi \h& A/nerican Jou) tial of Mathematics, to a 

 question proposed by Prof. Aiyar, in the Educational Times for 

 November 1895. — The list of new publications is an extended 

 one, and the notes, as usual, are of interest. There is, however, 

 an error in the quotation from our pages. On p. 651 (vol. Hi.) 

 is given a list of names proposed for the Council of the London 

 Mathematical Society, and at the end of the note it is stated that 

 Mr. Jenkins and the late G. C. De Morgan were elected joint 

 secretaries (in January 1866). The Bulletin says, "the late 

 Prof De Morgan." It is a matter of common knowledge 

 that Prof. Augustus De Morgan was the first President. The 

 Secretary was his son. 



SOCIETIES AND ACADEMIES. 

 London. 



Royal Society, January 23.—" An Attempt to Determine 

 the Condition in which Helium and the Associated Gases exist 

 in Minerals." By Prof W. A. Tilden, F.R.S. 



From the results of the experiments recorded in this paper, it 

 seems that helium exists in the minerals in which it is found in a 

 condition comparable with that in which hydrogen is associated 

 with many metals, and carbonic oxide especially with iron. 

 Whether this condition is rightly distinguished from ordinary 

 chemical combination isa question which admits of debate. The 

 stability of all dissociable compounds is influenced by pressure 

 and by temperature in the same kind of way as "occlusion," 

 which, like ordinary chemical combination again, is a 

 phenomenon in which the bodies concerned exercise a power of 

 selection. 



The presence of hydrogen as well as carbon dioxide in granite, 



NO. 1373, VOL. 53] 



if already observed, is not known to geologists generally. From 

 observation on variations in the critical point of carbon dioxide 

 in minerals (Journ. Chem. Soc, 1876, ii. 248), Hartley seems 

 to infer that the incondensable gas present with carbon dioxide, 

 is usually nitrogen. A passage in Geikie's "Text-Book of 

 Geology," third edition, p. 1 10, refers to the presence of 

 hydrogen in cavities ; but no information is given as to the 

 evidence upon which this statement is based. The presence of 

 hydrogen in such a rock as granite must be attributed to the 

 existence of this gas in large proportion in the atmosphere in 

 which the rock was crystallised. Whether this was the primeval 

 atmosphere of the earth before the hydrogen had escaped or had 

 been oxidised into water, or whether it resulted from the local 

 action of water upon unoxidised metals or other materials in the 

 interior of the earth, is a question which may be of some interest 

 to the geologist. If the former hypothesis were adopted, it 

 would perhaps be difficult to explain the absence of helium from 

 the gas included in the rock ; and, on the whole, the latter view 

 appears to afford the more probable explanation. 



Experiments show that hydrogen is present in even larger 

 proportion in the granite from the neighbourhood of Dublin, 

 and it is proposed to examine some other examples of the 

 ancient crystalline rocks in order to determine the nature of the 

 gases enclosed in them. 



Physical Society, February 14. — Annual General Meeting. 

 — Captain W. de W. Abney, President, in the chair. — The 

 Chairman, after referring to the position of the Society, called 

 upon the Treasurer to read the balance-sheet. After a discussion 

 on the financial status of the Society, in which a number of 

 members took part, the ballot was held for the election of a 

 President and Council for the ensuing year. The following 

 gentlemen were declared duly elected : President — Caotain 

 W. de W. Abney, C.B., F.R.S. Vice-Presidents— Shelford 

 Bidwell, F.R.S. ; Major-General E. R. Festing, F.R.S. ; 

 Prof J. Perry, F.R.S. ; G. Johnstone Stoney, F.R.S. Secre- 

 taries — T. H. Blakesley, 3 Eliot Hill, Lewisham, S.E. ; and 

 H. M. Elder, 50 City Road, E.G. Treasurer— Dr. E. Atkinson, 

 Portesbery Hill, Camberley, Surrey. Demonstrator — C. Vernon 

 Boys, F.R.S. Other members of Council — Walter Baily, Dr. 

 C. V. Burton; L. Fletcher, F.R.S.; R. T. Glazebrook, F.R.S. ; 

 Prof A. Gray, G. (Griffith, Prof G. M. Minchin, F.R.S. ; 

 Prof W. Ramsay, F.R.S. ; Prof. S. P. Thompson, F.R.S. ; and 

 Prof S. Young, F.R.S. — The Chairman read an obituary 

 notice of the late Right Hon. T. H. Huxley. — A vote of thanks 

 to the auditors was proposed by Prof Carey Foster, seconded 

 by Mr. Enright, and carried unanimously. A vote of thanks 

 to the officers was proposed by Prof A. Gray, seconded by 

 Mr. Rhodes, and carried unanimously. A vote of thanks to 

 the Chemical Society for the use of their rooms, was propo.sed by 

 the Chairman, and carried by acclamation. — The meeting was 

 then resolved into an ordinary science meeting, and a paper, on 

 the determination of high temperatures by the meldometer, by 

 Prof Ramsay and Mr. Eumorfopoulos, was read by the latter. 

 The meldometer — an instrument invented by Dr. Joly, of Dublin 

 — consists essentially of a thin platinum strip which can be 

 heated by the passage of an electric current. Small fragments 

 of a solid substance are placed on the platinum strip, and the 

 temperature at which they melt is deduced from the length of 

 the platinum strip, which has been previously calibrated by 

 means of solids of known melting-point. The authors have used 

 gold for the purpose of calibrating the strip, and have assumed 

 Violle's value, 1045° C, for the melting-point of gold. A num- 

 ber of measurements have been made of the melting-point of 

 .salts of sodium, lithium, strontium, barium, calcium, and lead. 

 The results obtained, however, differ considerably from those of 

 Heycock and Neville, and the authors have not been able to 

 account for these differences. Prof. Ramsay said the chief 

 advantage of the meldometer was that only a very minute frag- 

 ment of the substance was required for the measurement, so 

 that extreme purity of the sample could be secured. There was 

 the disadvantage, however, that many substances undergo some 

 change when heated in air. In reply to a question from Mr. 

 Blakesley, Prof Ramsay said that the property of the platinum 

 which was used to measure the temperature was its expansion. 

 Mr. Campbell asked whether the zero of the instrument was 

 found to be constant. In Cardew voltmeters it often took several 

 hours for the needle to come back to zero after heating. Mr. 

 Eumorfopoulos, in reply, .said that the zero was constant to 

 within a quarter of a degree. — Prof Ramsay also exhibited a 

 small direct-vision spectroscope, in which the eye-piece is moved 



