the recent determination, by the author and Mr. Morby, of the Dynamical Equivalent of Heat. To the student of physics as well as the advanced student of engineering, the volume is full of interest and suggestion. Butif we except a few of the shorter papers-the reading of it is a task demanding great mental concentration, and advanced mathematical knowledge; it is not a task to be undertaken lightheartedly. A word of praise is due to the publishers for the beautiful get-up" of the book. Electricité et Optique. La Lumière et les Théories Électrodynamiques. Leçons professées à la Sorbonne en 1888, 1890 et 1899 par H. POINCARE, Membre de l'Institut. Deuxième édition, revue et complétée par JULES BLONDIN et EUGÈNE NECULCEA. Paris: Georges Carré et C. Naud, 1901. Pp. x+641. For elegance and clearness of treatment, French writers of textbooks are probably unsurpassed, and of these admirable qualities the book now under review is not an unfavourable example. Its distinguished author has already, by his numerous publications on various branches of mathematical physics, done splendid service in removing the difficulties and clearing up the perplexities which beset the student of the various rival theories whose aim is to provide a purely dynamical explanation of all physical phenomena. A large portion of the book before us has already been previously published, but it now appears in a revised form, and with important additions necessitated by recent advances in the subject. The book is divided into four parts. Part I. commences with a sketch of the earlier electrical theories, the more important theorems and formulæ of electrostatics being established; this is followed by Maxwell's theory of electric displacement, the shortcomings and difficulties of which are subjected to a clear and searching analysis. Next comes an account of Poisson's theory of dielectrics, and of Maxwell's theory of the forces exerted between charged conductors. The four chapters which follow deal with the theory of electric currents in linear and solid conductors, magnetism, electromagnetism, and electrodynamics. Next come two chapters in which the theory of electromagnetic induction is developed, and the equations of the electromagnetic field are established. The way having been thus paved for it, the electromagnetic theory of light is fully considered in the next chapter, and this is succeeded by the concluding chapter of Part I., which deals with the magnetic rotation of the plane of polarization. In Part II. the author considers the older electrodynamical theories of Ampère and Weber, and compares them with those of Helmholtz and Maxwell. In Part III. we have a clear and critical account of the theories of Hertz and Lorenz. Zeeman's phenomenon and its connexion with Lorentz's theory are fully dealt with. We notice that on p. 422 the author uses the terms ion and electron indiscriminately. Part IV. contains a sketch of Larmor's theory, and explains very clearly its position relatively to the other theories. To those who, while interested in electromagnetic theory, yet feel incompetent to examine critically the mutual relationship and relative merits, as well as peculiar weaknesses, of the somewhat perplexing tangle of rival theories, we can strongly recommend the perusal of this most suggestive and interesting book, the keen critical insight of whose author enables him to pour a flood of light on problems which appear obscure, and to state boldly and clearly what is only implied or indirectly suggested by other writers. Leitfaden der Wetterkunde. Gemeinverständlich bearbeitet von Dr. R. BÖRNSTEIN, Professor an der Königl. Landwirthschaftlichen Hochschule zu Berlin. Mit 25 in den Text eingedruckten Abbildungen und 17 Tafeln. Braunschweig: F. Vieweg und Sohn, 1901. Pp. viii+181. THE subject of meteorology is one which may be rendered either most fascinating or exceedingly dry-so much depends on the method of treatment adopted. We congratulate the author of the little book before us on the amount of interest which he has succeeded in infusing into his subject. While strictly scientific in his manner of dealing with the complex phenomena with which the study of meteorology is concerned, the author has succeeded in producing a book which may be picked up at any moment by a person of ordinary intelligence, and read with as much interest and pleasure as if instruction were not its main object. It is a popular book in the highest and best sense of the term. The study of the weather involves the consideration of six meteorological elements: temperature, moisture, cloud-form, rainfall, barometric pressure, and wind. The author accordingly deals with these in succession, and explains their connexion with the weather in a manner which leaves little to be desired, and which practically pre-supposes no knowledge on the part of the reader. The more important instruments used in meteorological observatories are illustrated and briefly described. The beautiful coloured pictures of cloud-forms at the end of the book deserve special mention. Of considerable interest is the last section of the book, which deals with the arrangements adopted in different countries for supplying weather forecasts. Copious bibliographical references and an index enhance the value of this most useful and interesting little book. THE LONDON, EDINBURGH, AND DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE [SIXTH SERIES.] SEPTEMBER 1901. XXIII. The Cause of the Structure of Spectra. THE following inquiry into the cause of the structure of spectra brings out the result that the atoms of the different elements are all equipped with the same, or nearly the same, electrical apparatus, whereby the mechanical energy of the atom is made communicable to the æther for radiation. The atom with the kinetic energy assigned to it in the kinetic theory of matter exercises no direct mechanical effect on the æther, but is like a fly-wheel driving the dynamo to which we may liken the electrical equipment of the atom. The atoms of the various elements are vastly different in mass and size, as we know, but as they drive the same or nearly the same electrical appliance (arrangement of electrons) they have their spectra included in the comparatively limited region of vibrations to which the human eye is sensitive, comparatively limited, even when extended by bolometer and photographic film. It is a very remarkable fact that the most energetic part of the spectrum of so many diverse elements lies within the one poor octave of human vision; and it must be on account of the great distinctness of our colour sensations, that physicists have not realised that really the biggest essential fact discovered by the spectroscope is that the frequencies of the vibrations of the different atoms are so nearly equal. For example, it will be shown that the fundamental mechanical period of vibration of the cæsium atom is six times that of the lithium atom, and yet the ratio of *Communicated by the Author. Phil. Mag. S. 6. Vol. 2. No. 9. Sept. 1901. S the periods of the corresponding lines in their spectra is of the order 5: 4. Now the C's atom, in addition to its fundamental vibration, has harmonics, including one whose period, being a sixth of that of the fundamental, is the same as the fundamental of the Li atom. Thus all the elementary atoms have mechanical vibrations of the same or nearly the same frequency, and this mechanical vibration of characteristic frequency is the one which most efficiently forces the vibration of the atomic electrical apparatus. Thus it comes about that the spectra of the elements are only differently accentuated parts, or slightly modified forms, of the spectrum belonging to a certain common standard vibrator. As to the nature of the electrical vibrator common to the atoms, it will be shown to consist probably of two parts, whose relative motion produces the luminous vibration. It is on account of this dependence on relative motion that spectra do not show simple harmonic relations, but the complex harmonic relations implied by Balmer's formula. It will be shown that Balmer's formula can be generalized so as to bring out the principle of harmonics in spectra, and a striking harmonic series in the spectrum of magnesium will be demonstrated. The laws of the spectrum discovered by Rydberg will be discussed and extended. The work will be taken in the following order : 1. Balmer's law, and optical harmonics as overtones and undertones. 2. A special series in the magnesium spectrum confirming the existence of optical harmonics. 3. A kinematical analysis of Balmer's formula. 4. Rydberg's laws. 5. Two supplementary principles. 6. Demonstration that the atoms of the elements have fundamental mechanical periods of vibration which are harmonically related to one another. Consequences of this, such as vibrations of electrons forced by mechanical vibrations of atoms. 7. Free vibrations of the æther of atoms. 8. Further analysis of Balmer's formula and Rydberg's laws. 9. Summary. 1. Balmer's Law, and Optical Harmonics as Overtones and Undertones. From the labours of spectroscopists there have recently resulted discoveries as to the laws regulating the structure of spectra, the most important of which are Balmer's formula (Wied. Ann. xxv. 1885), expressing the wave-lengths of the chief lines in the hydrogen spectrum as terms of a simple mathematical series, and Rydberg's relating to the identification of similar series in the spectra of other elements, and the existence of beautifully simple relations between the series. Kayser and Runge, and Runge and Paschen, besides contributing valuable experimental work, have also taken part in the important work of identifying the series in complicated spectra. But the great heartening to theoretical spectroscopic students undoubtedly came from Balmer's discovery of his formula for hydrogen which, on giving m the integral values from 3 to 15, furnishes the wave-lengths of the thirteen chief lines in the hydrogen spectrum. Ames (Phil. Mag. [5] xxx. p. 48) subjected this formula to a strict comparison with his experimental measurements of the wave-lengths in the hydrogen spectrum, using it in the form λ=3647·20 m2/(m2-4) for the wave-length in vacuum, and found that from the longest wave 6564-96 × 10-8 cm. to the shortest 3713-2, the greatest discrepancy between experiment and formula was about 1 in 10, and the average discrepancy about in 10'. But in addition to this primary spectrum there is the secondary one proved by Hasselberg to belong to hydrogen, for which Ames gives the wave-lengths of 63 lines. An important fact concerning the relations of the two spectra is that brought out by Trowbridge and Richards (Phil. Mag. [5] xliii.) by means of their powerful electrical appliances, namely, that the two spectra appear together in the continuous discharge, but the primary alone in the oscillatory, as though in the latter the primary spectrum is enhanced by a sort of resonance which causes the quenching of the secondary. The simplest step in investigating theoretically the relation between the two spectra is to inquire:-What values of m in the formula for the primary spectrum would be required to give the wave-lengths observed in the secondary spectrum? These are found by solving Balmer's equation for m, using Ames's values of reduced to vacuum, and also of λo, and are given in the second row of the following table, where the fourth row contains the numbers of the form +1/s, or occasionally r+p/s, where r, s, and p are integers, such as give values nearly equal to those of m, the same numbers being |