LIV. The Emission-Function of a Body emitting a HATEVER the emission-function for the energy radiated from such a body may be, it must satisfy the following conditions: i. It must vanish for all values of wave-length (λ) except those which correspond to the spectral lines. ii. That part of the function which determines the position of these lines must be independent of the temperature. An attempt has been made by P. G. Nutting (Astrophysical Journal, Oct. 1900, and Phil. Mag. Oct. 1901) to supply such a function; and he gives a series-form each term of which corresponds to a spectral maximum of infinite value. It has occurred to me that in the case of Hydrogen the following form is preferable, inasmuch as the difficulty of infinite values does not enter and, moreover, a single term is sufficient to represent all the lines in the elementary linespectrum instead of a summation of 13 terins: E=F sin' [Ne]/ sin2 v, where F is a factor to be presently examined; 4po Po-p where po=27418.3; N is any large integer, for example 1000 or 10,000, and p (=oscillation-frequency) may assume any value for which v is real. The way in which this formula is based on Balmer's formula for the position of the spectral lines will be very evident; while the march of E as v varies may at once be pictured by recalling the similar formula which occurs in connexion with diffraction-gratings. E will be of quite negligible value for most values of p, but suddenly mounts to the value N2F for the wave-length of each of the lines given by Balmer's formula: it therefore represents the position of the maxima to the accuracy of the latter formula, viz. one part in 50,000. To represent the fact that the lines are not of equal intensity the factor F must depend on λ and T; and in the absence of sufficient knowledge concerning the probable form of F, I can only suggest that these enter in the same way as in the expression for the radiation from an absolutely black body. Thus adopting Wien's formula, the emission-function will be E=C[sin Nv/sin v]2p5 exp. (-cp/T). Similar formulæ may be written down for other substances *Communicated by the Author. based on Kayser and Runge's formulæ ; but now a single term will represent only one of the several SERIES of lines which accompany one another; but a summation of not more than six terms will be adequate to include all the known lines in their spectra. Thus, making use of Rydberg's formula the formula given above is capable of forming the basis of an expression representing the distribution of energy in any one series of the majority of spectra. I have no suggestion to offer as to the rationale of this formula; but suggest it as an empirical one which may possibly be useful in representing the energy distribution in a line-spectrum. Experimental data on the relative intensity of the spectral lines are at present too scanty to test its value. Physical Department, University College, London. LV. Notices respecting New Books. An Elementary Treatise on Dynamics, containing Applications to Thermodynamics, with numerous Examples. By BENJAMIN WILLIAMSON, Sc.D., F.R.S., Senior Fellow of Trinity College, Dublin; and FRANCIS A. TARLETON, Sc.D., LL.D., Fellow of Trinity College, and Professor of Natural Philosophy in the University of Dublin. Third Edition, Revised and Enlarged. London: Longmans, Green, & Co. 1900. Pp. xvi+560. WE E know of no other work on dynamics in the English language which can compare in general usefulness to the student with the work before us, now in its third edition. The science of dynamics is admittedly one of the most difficult and intricate branches of knowledge, and on account of its fundamental character indispensable to all students of nature. The number of elementary books on dynamics published within the last quarter of a century is quite appalling, but the gap between the purely elementary and the most advanced type of text-book on this subject is far from being filled, and we have some difficulty in recollecting many satisfactory text-books of the intermediate class. The late Professor Tait's article on "Mechanics" in the Encyclopedia Britannica, now obtainable in book-form as a treatise on "Dynamics," is a masterly example of clearness and elegance of treatment, but it does not meet the wants of the student in every respect, as there are no examples by means of which he would be enabled to test his knowledge, skill, and ingenuity; and attempting to learn dynamics without working out numerous examples is as hopeless as trying to learn pure mathematics by the same method. Que very important feature of the book under review is the copious supply of examples interspersed in the text and given at the end of the book. By the aid of these, a student may always check his progress and make sure of having mastered each consecutive section of the work. Another highly commendable feature is the easy gradation by which the student is led up from the comparatively simple to the highly complex parts of the subject. The early chapters deal with kinematics, the laws of motion, impact, circular motion, work and energy. Then comes a chapter on central forces and orbits, followed by one on constrained motion and motion in a resisting medium. A consideration of general dynamical principles precedes the discussion of the motion of a rigid body. Then comes what is probably the most difficult chapter in the book, that dealing with the general equations of dynamics. The problem of small oscillations forms the subject of a special chapter, and the book concludes with a useful discussion of the principles of Thermodynamics. Ausgewählte Methoden der Analytischen Chemie. Von Prof. Dr. A. CLASSEN. Erster Band. Unter Mitwirkung von H. CLOEREN. Mit 78 Abbildungen und einer Spectraltafel. Braunschweig: F. Vieweg und Sohn. 1901. Pp. xx+940. THIS important work, which is largely the outcome of the author's varied experience, is intended as a guide for the professional chemist, and the student who has already mastered the general methods of chemical analysis. Special attention has been given to the methods for detecting and accurately estimating the amounts of a number of elements generally referred to as the "rare" elements, many of which have of late years acquired technical as well as purely scientific interest. In his preface, the author states that the methods described by him have either been frequently used by himself, or else critically examined and tested by others; it is therefore no mere indiscriminate collection of methods suitable and unsuitable that we have to deal with in this book, but, as its title implies, a careful selection of the more important and practically useful methods. The arrangement of the subject-matter follows one uniform plan, and renders it very easy to find any required information. The metallic elements, which alone are considered in this volume, are arranged in their usual analytical order, silver heading the list. The qualitative tests by means of which the presence of the particular element considered may be ascertained first receive attention. Then come the various gravimetric, electrolytic, and volumetric methods of quantitative analysis applicable to the particular element in question. Next follow methods for separating the element under consideration from those preceding it, and the final section deals with the analysis of such compounds of the metal as are of commercial importance, At the end of the book is given a most useful set of tables for facilitating the numerical calculation of the results of an analysis. Copious references to original sources of information are given; and the very complete index greatly adds to the value of the book as a highly important work of reference, which should find a place in the library of every analytical chemist. Leipzig: Entstehen und Vergehen der Welt als kosmischer Kreisprozess. Auf Grund des pyknotischen Substanzbegriffes. Zweite umgearbeitete und erweiterte Auflage. Von J. G. VOGT. Ernst Wiest Nachf. Pp. viii+1005. 1901. THIS elaborate book furnishes a good example of misdirected energy. Its author has read widely, and evidently belongs to that class of thoughtful and philosophically-inclined people who are under the impression that they have hit upon an original and correct interpretation of the universe, and feel it a bounden duty to benefit humanity by publishing the results of their speculations. The book strongly reminds us of one or two similar treatises which have recently appeared in English. One characteristic of the authors of such books appears to be a strong conviction of their competence to criticise the teachings of orthodox science. They accordingly set about finding all sorts of mares' nests in modern scientific theory, and spend an inordinate amount of energy in tilting against windmills. One or two illustrations of our author's methods will be sufficient to show in how far his wide reading has really enabled him to grasp the fundamental doctrines of modern science. He severely criticises Newton's First Law of Motion, remarking that if it were true, a body once set in motion by an impulse would become a perpetuum mobile: and is not a perpetuum mobile in flagrant contradiction with the law of the conservation of energy? Again, he will have none of the theory of a vibrating atom. For is not an atom which goes on vibrating for ever another example of a perpetuum mobile, and another violation of the principle of the conservation of energy? The teachings of science having been found wanting, the author proceeds to develop a "reale Weltanschauung," and, as might have been expected, "von durchaus neuen Gesichtspunkten." The series of phenomena now going on in the physical universe form the consecutive stages in the descending branch of a cosmical cyclic process. The true explanation of most problems is to be found in endowing matter with one fundamental property-the tendency towards condensation. A nucleus of condensation in the primordial substance out of which all the elements have arisen is termed a "pyknotum," and the author's theory of the universe is founded on the "pyknotische Substanzbegriff." This is used in accounting for the genesis of the elements, gravitation, chemical affinity, heat, light, magnetism, and electricity. Having exhausted the regions of physics and chemistry, the author next tackles biological and finally ethical problems. He is not sparing of abuse in dealing with our present social system, and his remarks in this connexion, if not altogether convincing, form piquant and interesting reading. He is an avowed pessimist: all that is most sacred to us is founded on a lie, and we must ultimately acquiesce in the sad conclusion Nur im Irrtum ist das Leben The pity and pathos of it all! That one of the author's undoubted industry should devote his time to writing a volume of over 1000 pages which, apart from questions of actual error, consist of little better than a mass of fanciful and extravagant speculations. LVI. Proceedings of Learned Societies. GEOLOGICAL SOCIETY. [Continued from p. 324.] May 8th, 1901.-J. J. H. Teall, Esq., M.A., V.P.R.S., President, in the Chair. HE following communication was read: THE 'The Influence of the Winds upon Climate during the Pleistocene Epoch; a Palæo-Meteorological Explanation of some Geological Problems.' By F. W. Harmer, Esq., F.G.S. Winds are an important factor in determining the distribution of climatic zones. Deviations of the isotherms from the normal are generally connected with the direction of the prevalent winds. The influence of marine currents is indirect rather than direct. Changes of wind cause marked and sudden changes in the weather, though the general direction of ocean-currents remains the same. Permanent alterations in climate during past epochs would have equally resulted from permanent changes in the wind. Anomalous weather is due to some unusual arrangement of high and low-pressure areas. Former cases of anomalous climate can only have occurred when the meteorological conditions were favourable. Continental areas tend to be cyclonic in summer and anticyclonic in winter, while the reverse is broadly true of the oceans. During the Glacial Period ice-covered areas would have remained more or less anticyclonic throughout the year, while low-pressure areas must have prevailed in regions to the south of them and over the adjoining oceans. This would have altered the prevalent direction of the winds and the distribution of rainfall; thus the anticyclone of the European ice-sheet may have caused cyclonic storms to pass farther south than at present, bringing oceanic winds over the Sahara, which formerly enjoyed a humid climate. Dead shells are rarely found now on the eastern shores of Norfolk and Suffolk, though they are driven on to the Dutch coast by westerly gales. Shell-débris in the Upper Crag-beds of East Anglia shows that easterly gales were common at that period. This may have been due to the altered path of cyclones, caused by the glacial conditions which were becoming established in regions to the north of Great Britain. The abundance of mammoth-remains along the shores of the Polar Sea, and the alternate humidity and desiccation of the basin of Nevada may have resulted from allied causes. It is difficult, however, to restore hypothetically the meteorological conditions of the Pleistocene epoch on the theory that the maximum glaciation of the eastern and western continents was contemporaneous. In that case an enormous anticyclone would have extended from the |