6oo 



NA TURE 



[Al'KH, 24, 1902 



of igneous matter and other phenomena due to this cause are 

 considered in the present paper. — An expedition to the 

 Maldives, by A. Agassiz. The most important result of the 

 expedition was the contribution to our knowledge of atoll 

 formation. The present definition of atolls appears to be un- 

 justifiable, as there is every possible gradation between a 

 curved open crescent-shaped bank of greater or less size and an 

 absolutely closed ring of land surrounding a lagoon without 

 direct communication with the sea. — The flower-like distortion 

 of the coronas due to graded cloudy condensation, by C. Barus. 

 — Varying degrees of actinism of the X-rays, by J. O. Heinze, 

 jun. It was found that the rays which are the most active in 

 producing fluorescence are not those which act most vigorously 

 in the photographic plate, and hence that the maximum eftect 

 on a platinocyanide screen does not coincide with the greatest 

 photographic effect. 



Bulletin of the Aiiietiian Matlie/iialical Society, March. 

 — The application of the fundamental laws of algebra to the 

 multiplication of infinite series, by Prof. F. Cajori. Following 

 up his previous work (see Transactions of the Society, vol. ii. 

 pp. 25-36, and Science, vol. xiv. , September 13, 1901) and also 

 Pringsheim's (also in vol. ii. of the Transactions, pp. 404-412), 

 Prof. Cajori here establishes a class of series with real terms 

 which possesses the property of his former paper, but which 

 seems to be distinct from the class given by Pringsheim. He 

 then considers the validily of the fundamental laws in the 

 multiplication of these infinite series, and next he points out 

 another method for obtaining divergent series whose product 

 is absolutely convergent. Lastly he generalises a theorem of 

 Abel on the multiplication of series. — Dr. Fite gives a notelet 

 concernmg the class of a group of order /"' that contains 

 an operator of order p"'^'-ox f"'~^, /being a prime. — Dr. Epsteen 

 contributes a proof that the group of an irreducible linear 

 differential equation is transitive. — Another short note follows by 

 Dr. Eisenhart,on lines of length zero on surfaces. — Dr. Kasner, 

 writing on some properties of potential surfaces, extends some 

 of the results of a previous paper (Bulletin, vol. vii. pp. 392-9) 

 to the .surfaces expressed in rectangular coordinates by an 

 equation ^(jt, y, :) = o, where ^ is a rational integral solution of 



the potential equation A<p zz 



S'-(t> 5-0 

 ■x;+x-^=o. The last 



four notes were read before the Society and have numerous 

 useful references. — Prof; Osgood gives an extended review of 

 Prof. G. A. Gibson's " Elementary Treatise on the Calculus," in 

 which he remarks that though many teachers may not .=ee their 

 way to use it as a textbook during the early part of the course, 

 yet the book can be commended for collateral reading from the 

 very beginning, and that teachers will have to consider whether 

 it may not be taken asthechief text-book in the second course. — 

 Further short notices follow of Cahen's " Elements de la Thcorie 

 des Nombres" and of R. Dedekind's "Essays on the Theory 

 of Numbers" (Beman's translation) by Prof. L. E. Dickson, 

 and of the " Annuaire pour I'An 1902" by Prof. E. W. 

 Brown. 



Memoirs of the St. Petersburg Society of Naturaliils, Botany, 

 vol. XXX. — On parasite fungi found in the neighbourhoods of St. 

 Petersburg, by K. S. IvanolT. List of 153 species, with a few 

 remarks. — Critical review of the flora of Moscow, by A. N. 

 Petunnikoff. Second part, continued from Botanichesiiya 

 Zafiski, part xiii., 1896 ; full summary in German. — Botanical 

 researches in the province of Orel, by M. D. Zalessky ; 

 summary in German. A portion of this paper is given to a 

 detailed description of a Scotch-fir forest on a Loess soil, which 

 is a rare case in Russia, and which the author explains in accord- 

 ance with the views of Litwinow (Bull. Soc. Nat. Moscou, 

 1890, No. 3) on the survival of fir forests during the great 

 Pleistocene glaciation. — On dormant buds, by \V. Lubimenko, 

 with twenty nine figures; summary in German. — Exploration 

 of the flora of Pskov in 1899-1900, by N. Puring.— The flora 

 of ihe Polyesie, by Joseph Paczosski, continued. The Mono- 

 cotyledones, Nos. 951 to i29i,arenow given, and this most 

 valuable work is thus concluded. 



Vol. xxxi. — The whole of this volume is given to the first and 

 the second fascicules of " Flora Caucasica Critica," by N. Kuz- 

 netsoft, N. Buschand A. Fomin. The intention of the authors is 

 to give, in a series of monographs disposed in the same system 

 as in A. Engler's " Pflan/enfamilien," the necessary materials 

 for an abridged " Flora of the Caucasus."' This latter would be 



NO. 1695, VOL. 65] 



for general use, while the present work must be a sort of 

 preparatory work for specialists only. The successful accom- 

 plishment of this grand undertaking seems to be guaranteed — 

 the editor, Prof. Kuznelsofl, having reasons to believe that the 

 work will find the support of specialists. We may remark that 

 under the heading of habitus we find for certain species ex- 

 tremely valuable and most interesting descriptions, which will 

 be welcome to both the systematist and the geographer. The 

 present volume includes the Pirolacea>, Ericace;e and Primu- 

 lacea', by Kuznetsofl!^, and the Nymphacea;, Ceratophyllacea and 

 Ranunculacea;, by Busch. 



SOCIETIES AND ACADEMIES. 

 London. 



Royal Society, November 28, 1901. — "A Comparative 

 Study of the Spectra, Densities and Melting Points of some 

 Groups of Elements, and of the Relation of Properties to 

 Atomic Mass." By Hugh Ramage, B.A., A.R.C.Sc.L, St. 

 John's College, Cambridge. Communicated by Prof. G. D. 

 Liveing, F. R. S. 



The properties of nineteen elements were studied, namely : — 

 (i) Lithium, sodium, potassium, rubidium, c.xsium ; (2) copper, 

 silver, gold ; (3) magnesium, zinc, cadmium, mercury ; (4) 

 calcium, strontium, barium : {5) aluminium, gallium, indium 

 and thallium. The flame spectra of the metals are much 

 simpler than the arc or spark spectra : they may be regarded as 

 the fundamental spectra of the metals. They furnish purely 

 experimental data with which to begin an investigation of the 

 laws which govern the distribution of lines in spectra and by 

 which to study the relations of the physical and chemical 

 properties of the metals to their spectra. Diagrams were 

 drawn with the oscillation frequencies of the lines in the funda- 

 mental spectra, or the densities, or the melting points, of the 

 metals as abscissa*, and the atomic masses, or a function of 

 these, as ordinates. Two diagrams of spectra are reproduced 

 in the paper. The corresponding lines in homologous spectra 

 were joined by lines some of which are straight, but most are 

 curved. The densities and melting points were connected in a 

 similar way. 



The following facts have been observed in the study of the 

 diagrams : — 



(i) The metals considered may be classified into groups 

 according to the characters of their spectra. The elements in 

 each group appear to have a similar atomic constitution. 



(2) The connecting lines between ihe members of the chemical 

 groups are not continuous ; there are certain breaks in them. 

 These occur between the metals sodium, magnesium and 

 aluminium, and the metals of their respective groups with higher 

 atomic masses. The break between the sharp series in the 

 spectra of the aluminium group is very slight ; that between the 

 diffuse series is very marked and corresponds to marked changes 

 in the densities and melting points of these elements. 



(3) The cause of the displacement of corresponding lines in 

 some strictly homologous spectra is intimately connected with 

 the atomic masses. The shift of the subordinate series of 

 potassium, rubidium and casmm is approximately proportional 

 to the atomic mass, whilst the shift of the principal series is 

 very nearly proportional to the square of the atomic mass. 



(4) The second diagram, drawn from the spectra and the 

 squares of the atomic masses, shows that the lines which connect 

 the corresponding members of homologous doublets and triplets 

 approach one another as the atomic mass decreases and intersect 

 on the line of zero atomic mass. 



The spectra of potassium, rubidium and cesium change 

 regularly with the atomic mass, and it should be possible to 

 express the series in these spectra by a formula in which the 

 atomic mass is the only variable. There are obvious difficulties 

 in modifying Kayser and Runge's formula in this way, but Ryd- 

 berg's formula is more general and the constants are more easily 

 calculated. Rydberg's formula and method give better results 

 for the subordinate series than for the principal series ; also for 

 the series in the spectra of elements of low atomic mass than 

 for those of high. The best results were obtained for the 

 principal series of the three metals when in Rydberg's general 

 formula 



» = «„ '^» . 



("' + W 



