whose oscillations are due to a sudden release of a uniform electrostatic field. The solution of this case is complete. The actual values of both the period and the decrement are expressed in terms of the radius of the sphere. The smallness of the period and the exceedingly rapid rate of decay of the wave are striking.

This theory throws much light upon Hertz's method of calculating the period of an oscillator. Poincaré applies it also to the explanation of the Hertzian method of calculating the decrement due to electrical radiation and the force of Poynting's theorem is exhibited in a masterly manner, although, of course, the calculation for more general cases is not as complete as that for Lodge's oscillator. More experimental guidance is necessary and will not be sought in vain in subsequent chapters.

Phenomena of Electrical Resonance.- Wave Propagation along a Wire.-Having described Hertz's method of calculating the period and the decrement, Poincarè discusses next some of the more important experimental researches dealing with these two principal characteristics of an oscillating system. The earliest method employed in researches of this class is that devised by Hertz. A secondary circuit, the resonator, consisting of a turn of wire with an adjustable spark gap is brought into the inductive action of the oscillator. The length and intensity of the induced spark measures the inductive effect between the two. When the periods of the two are equal the effect is a maximum; they are then in resonance. But experiment reveals the fact that the resonance effect is not as pronounced as in the case of acoustical resonance. Sarasin and de la Rive (Arch. des sciences phys. 23, p. 113; 23, p. 557, Génève, 1890) inferred from this that the oscillator sends forth a complex wave which, if analyzed in the manner of a ray of sunlight, would give a continuous spectrum. Poincaré, guided by a

carefully worked general theory of resonance, ascribes the absence of a strong resonance effect to the large decrement of the oscillator. An appeal is then made to experiments bearing on this point and the subject of stationary waves in long wires is taken up. Such waves are produced in

the same way as in the case of sound waves. When a train of electrical waves travels along a wire and the leading wave reaches the end of the wire it is reflected there and by the interference between the direct and the reflected waves stationary waves are formed. Hertz's theory of propagation of these waves is given, showing that their velocity is the same all along the wire and equal to that of light for all wave lengths. If the view of Sarasin and de la Rive be correct then stationary electrical waves should have no pronounced nodes and ventral segments and, therefore, a resonator which, unlike the oscillator, gives a simple wave of definite periodicity will pick out of the stationary waves that component only which is in resonance with it. In other words, every resonator, within large limits, will respond to stationary waves and if moved along a wire which is the seat of such waves its spark will rise and fall in intensity every time the resonator passes by a node or a ventral segment of that component contained in the complex stationary wave with which it is in resonance. It measures, therefore, the wave length corresponding to its own period and not that corresponding to the period of the oscillator. This wave length divided by the calculated period of the vibrator will give, therefore, a wrong velocity of propagation. A mistake of this kind was suspected in Hertz's earliest experiments by which he obtained a different velocity of propagation along a wire from that in the dielectric. Sarazin and de la Rive called this phenomenon, first observed by them, the phenomenon of multiple resonance. It is undoubtedly one of the most

important discoveries in the region of Hertzian oscillations. It was probably (1) Poincaré (his modesty prevents him from mentioning this fact) who first recognized its full value and detected its true meaning. He devotes a large part of the present work to the discussion of this phenomenon and every serious student will appreciate heartily this very interesting feature of the noble work before us. Briefly stated Poincare's Briefly stated Poincare's explanation of multiple resonance is this. Ordinarily the oscillator has a large decrement; that of the resonator is very small, according to the results of Bjerkness' experiments. The train of waves excited in a long wire by the inductive action of an oscillator after each disruptive discharge consists of a big wave followed by a small number of waves of very rapidly decreasing amplitude. Such a train of waves is evidently not capable of forming interference waves after reflection. Their effect upon the resonator is practically the same as that of a single wave, giving the resonator an impulse when passing it on its way toward the end of the long wire and another impulse when it returns after reflection. Hence, if the time interval between these two impulses is a multiple of the period of the resonator the resulting oscillation in the resonator will be stronger than otherwise. If, therefore, the resonator be moved along the long wire its oscillations will vary, passing through a maximum at regular intervals; the distance between these intervals being equal to a wave length corresponding to the period of the resonator. But, obviously, the maxima will be most clearly pronounced when the resonator is in reson

(1) It is no more than just that a strong emphasis should be put upon the fact that Bjerkness independently (Wied. Ann. 44 p. 74 and p. 92, July, 1891) worked out the same theory and proved it by experiment at about the same time that Poincaré first published his theory (Arch. des sciences phys. 25 p. 608, Génève 15 Juin, 1891).

ance with the oscillator. This is especially true in the case of oscillators possessing a less strongly developed decrement, as for instance, Blondlot's oscillator. This explanation is illustrated by a mathematical discussion of rare elegance and simplicity. Blondlot's experiments (Jour. de Phys. 2 serie t. X., p. 549) are then carefully described and the close agreement between them, especially as regards the velocity of propagation along conducting wires, and the above theory pointed out.

Attenuation of Waves.-An important feature connected with wave propagation of Hertzian oscillations along wires was strongly emphasized by these experiments, namely, the diminution of the wave amplitude with the distance passed over. This has long since given Mr. Oliver Heaviside many an anxious thought. Poincaré is evidently not aware of that and he attacks the problem with just as much of his wellknown mathematical vigour as if its solution had not been given long ago by Mr. Heaviside. (Electr. Papers, Vol. II., p. 39, etc.) A few bold strokes of Poincaré's unerring pen disclose the interesting fact that the attenuation is due, principally, to distributed capacity of the wire, since the decrement, calculated by Poynting's theorem, is shown to be inversely proportional to the diameter of the wire. Experimental evidence bearing upon this point is then reviewed. In these experiments the employment of the resonator had to be discarded and the intensity of the wave at various points of the wire measured directly. Various methods were employed in these experiments. The most important among them are the following :

a. Hertz's method (Wied. Ann. 42, p. 407, 1891) of measuring the intensity of the wave at any point of a long wire by the mechanical force exerted upon another small conductor suspended in the vicinity of the wire. This method permits a study of the

b. The method of Bjerkness (Wied. Ann. 44, p. 74) in which two symmetrically situated points of a long loop are connected to the quadrants of a small electrometer and the difference of potential measured.

c. The thermoelectric method [first suggested by Klemencic (Wied. Ann. 42, p. 416)] employed by D. E. Jones (Rep. Brit. Assoc., 1891, p. 561-562). The intensity of the wave at any point of the wire is measured by the thermoelectric effect produced in a thermopile placed in the immediate vicinity of that point.

d. The bolometric method first employed by Rubens and Ritter (Wied. Ann. 40, p. 55, 1890).

e. Perot's micrometric spark gap method (C. R. t. CXIV., p. 165) by which the intensity of the wave at any point is measured by the maximum length of the spark gap when attached to the wire at that point.

The theory of each method is discussed briefly but quite completely, and it is shown very clearly that the results of the experimental investigations cited above are in good agreement with the theory and that they all lead to the conclusion that the oscillations of the oscillator produce simple waves, possessing a rapid rate of decay. This is in accordance with Poincaré's view of multiple resonance.

Bjerkness' experimental method (Wied. Ann. 40, p. 94, 1891) of determining the decrement of a resonator and Poincaré's theory of it are then given and it is shown that this decrement is a hundred times smaller than that of the oscillator.

A brief theoretical discussion of the curves plotted by Perot from the experiments cited above closes this exceedingly interesting and instructive part of the book.

It is pointed out now that the experiments so far discussed do not decide the

the older theories because it can be and has been predicted by older theories (Kirchhoff, Abhandl. p. 146) that the velocity of propagation of electromagnetic disturbances along a long straight wire suspended in air is the same as the velocity of light. A review of some of the older experiments in this direction is then given.

Direct Determination of the Velocity of Propagation along Conducting Wires.-The earliest experiments carried out according to methods against which no serious objections could be raised were those of Fizeau and Gounelle (1850) over telegraph lines between Paris and Amiens, a distance of 314 kilometers. The method was similar to that employed by Fizeau in the determinanation of the velocity of light. The mean velocity was found to be 105 kilometers per second for iron wire and 18X10 kilometers per second for copper wire. They employed signals of, comparatively speaking, long duration, and Poincaré shows by a reference to well known theoretical relations that in this case there is a strong distortion of the signals, so that a disturbance starting in form of a short wave returns, after passing over the whole line, in form of a more or less steep wave front followed by a long tail. This made the measurements very uncertain and the velocity of propagation necessarily much smaller than it ought to have been. The experiments of Siemens in 1875 avoided this objection, in a measure, by employing the disruptive discharge of a Leyden jar for the purpose of starting an electrical disturbance on lines of varying length, between about 7 and 25 kilometers. The velocity found was in several cases nearly 250,000 kilometers for iron wire. Here again the velocity came out smaller than that of light and for obvious reasons.

The last and in all respects most successful direct determination of the velocity of propagation was that recently carried out by

Model Engine Construction.-J. ALEXANDER. -New York and London, Whitaker & Co. 1894. Illustrated by 21 sheets of drawings and 59 engravings in the text. 12mo, pp. viii +324. Price, $3.00.

This little book is an excellent treatise on the construction of models of stationary locomotive and marine engines, and contains also instructions for building one form of hot-air engine. It is written by an author evidently familiar with his subject, and the text and illustrations are such as will serve the purpose of both artificer and amateur, desiring to produce model representations of real working engines of standard forms. Bright young mechanics will find here business-like statements of details of drawing, pattern-making, and finishing such models; and, if heedfully complied with, these instructions will result in the production of steam-engines which will actually 'steam,' and which will delight the heart of the mechanician. The drawings are all representative of British practice, and, in some respects, therefore, quite different from familiar practice in the United States; but British practice is 'not so bad,' after all, and many old mechanics, and probably every amateur, will be able to profit greatly by the careful study of this little work. R. H. T.

NOTES.

PERSONAL.

KARL HANSHOFER, Professor in the University of Munich, and well known through his researches in crystallography and other branches of mineralogy, has died at Munich at the age of fifty-four.

PROF. G. LEWITZKY has been appointed Director of the Observatory in Dorpat, and Dr. L. Sturve succeeds Professor Lewitzky at Charkow.

PROF. F. KOHLRAUSCH, of Strassburg, was proposed as the successor of Hertz at Berlin, but the death of Helmholtz intervening he will now succeed the latter in the Directorship of the Physico-Technical Institute.

MR. GEORGE F. KUNZ, Special Agent, Division of Mining Statistics and Technology, U.S. Geological Survey, has sent letters asking for imformation concerning the freshwater pearl fisheries, and concerning precious and ornamental stones of the United States.

PROF. S. P. LANGLEY, Secretary of the Smithsonian Institution, has addressed a letter to the competitors for the Hodgkins Fund Prizes of $10,000, of $2,000, and of $1,000, stating that in view of the very large number of competitors, of the delay which will be necessarily caused by the intended careful examination, and of the futher time which may be required to con

sult a European Advisory Committee, if one be appointed, it is announced that authors are now at liberty to publish these treatises or essays without prejudice to their interest as competitors.

CONGRESSES.

THE sixth International Geographical Congress will be held at London, on July 26, 1895, and continue until August 3. There will be an extensive exhibition in connection with the congress.

NEW AND FORTHCOMING PUBLICATIONS.

W. B. SAUNDERS, Philadelphia, has in preparation An American Text-book of Physiology, by Henry P. Bowditch, M. D., John G. Curtis, M. D., Henry H. Donaldson, Ph. D., William H. Howell, M. D., Frederic S. Lee, Ph. D., Warren P. Lombard, M. D., Graham Lusk, Ph. D., Edward T. Reichert, M. D., and Joseph W. Warren, M. D., with William H. Howell, Ph. D., M. D,. as Editor.

THE idea of holding International Mathematical Congresses is crystallizing into shape. Prof. Vassilief, of Kazan, has suggested an assembly of mathematicians in 1896, in order to definitely decide the organization of such congresses. The matter was pushed a little further at the Vienna meeting of the Deutsche Mathematiker Vereinigung, in September last, when it was unanimously resolved that the Committee of the Mathematical Union should take part in framing the necessary arrangements; and the Mathematical Section of the French Association for the Advancement of Science have also expressed their support of the scheme. A circular now informs us that the Editors of the Intermédiare will be glad to receive the names of mathematicians who are in favor of international meetings of the kind suggested. M. C. A. Laisant's address is 162 Avenue Victor-Hugo, Paris; and that of M. E. Lemoine, 5 rue Littrè.— Nature.

GINN & Co. announce for publication in February Molecules and the Molecular Theory of Matter, by A. D. Risteen.

APPLETON & Co. announce The Dawn of Civilization, by Prof. Maspero, and The Pygmies, translated from the French of A. de Quatrefages, by Prof. Frederick Starr.

WHITTAKER & Co. are publishing this year a weekly journal of science combining The Technical World and Science and Art.

W. ENGELMANN has begun the publication of an Archiv für Entwickelungsmechanik der Organismen, edited by Dr. W. Roux.

THE Rose Polytechnic Institute of Terre Haute, Ind., has begun the publication of a series of bulletins of which the first number is Physical Units, by Prof. Thomas Gray.

SOCIETIES AND ACADEMIES.

THE ANNUAL MEETING OF THE AMERICAN MATHEMATICAL SOCIETY.

THE annual meeting of the American Mathematical Society was held Friday afternoon, December 28th, at Columbia College, New York. In the absence of the president, Dr. Emory McClintock, and of the vice president, Dr. G. W. Hill, Professor R. S. Woodward, of Columbia College, presided. Among those present were Professor Simon Newcomb, Professor J. M. Van Vleck, Professor Henry Taber, Professor Mansfield Merriman, Professor H. D. Thompson, Professor Mary W. Whitney, Dr. E. L. Stabler, Mr. P. A. Lambert, Mr. R. A. Roberts, Dr. Charlton T. Lewis, Mr. Gustave Legras, Professor J. H. Van Amringe, Professor Thomas S. Fiske, Dr. E. M.