J. A. Stratton. Electromagnetic Theory. Translated by M. S. Rabinovich and V. M. Kharitonov, edited by S. M. Rytov. State Publishing House of Technical-Theoretical Literature, Moscow–Leningrad, 1948, 33.75 printer’s sheets, print run 8000 copies, price 34 rubles.

In Russian there are several good courses on the theory of the electromagnetic field, among which first place, as it seems to us, unquestionably belongs to I. E. Tamm’s Foundations of the Theory of Electricity (1946 edition).

Therefore the appearance of a new textbook on field theory would hardly be justified. “The Theory of Electromagnetism” by Stratton, however, is by no means a university textbook; rather, it has the character of a substantial monograph devoted to macroscopic electrodynamics. Among the other, very few, expositions of this type, Stratton’s book is perhaps closest of all to the chapters on electrodynamics in Frank and Mises’ Differential and Integral Equations of Mathematical Physics. But, unlike the indicated chapters of Frank and Mises, Stratton’s book is considerably more monolithic and purposeful, contains much auxiliary and supplementary material, and, finally, is more accessible to experimental physicists and engineers. It is already clear from what has been said that “The Theory of Electromagnetism” by Stratton is a significant phenomenon in the scientific literature and should attract the attention of a wide circle of persons whose work brings them into contact with electrodynamics. Incidentally, the words “should attract” could quite properly be replaced by “has attracted,” since this book, published in English in 1941, has already gained recognition among us.

Let us dwell on the contents of the book.

The first chapter is introductory in character: Maxwell’s equations are given in it, potentials are introduced, and so on. The difference from the material found in textbooks on field theory consists only in the more detailed introduction and consideration of various curvilinear coordinates. At the end of the chapter the field equations are rewritten in four-dimensional form, which is practically immaterial for everything that follows.

In the second chapter the ponderomotive forces in an electromagnetic field are considered; for convenience the elements of the theory of elasticity are also set out here. This chapter may likewise be regarded as introductory; the only essential difference between the exposition and the standard one lies in the consideration of forces acting on a continuum in general, whereas textbooks are usually restricted to the case of fluids (i.e., they do not take into account deformations associated with shear).

Chapters III and IV are devoted to static electric and magnetic fields. In addition to a detailed investigation of general questions (determination of the field from the distribution of charges and currents, expansion of the potential in spherical functions, uniqueness of the solution of boundary-value problems, etc.), solutions are given here for the most important problems (a conducting and a dielectric sphere in the field of a point charge, an ellipsoid in an external field, the field of a polarized ellipsoid, etc.).

In Chapters V, VI, and VII, plane, cylindrical, and spherical electromagnetic waves are considered, respectively. With regard to plane waves, in addition to the usual material, the general solution of the one-dimensional wave equation in an arbitrary medium is investigated and the theory of the Laplace transform is presented. A detailed exposition of the solutions of the vector wave equation, equivalent to Maxwell’s equations, in cylindrical and spherical coordinates (Chs. VI and VII) serves as preparation for the study of the radiation of point dipoles and linear antennas (Ch. VIII) and for the solution of boundary-value problems (Ch. IX). The center of gravity of Chapter VIII lies in the theory of radiation from systems of linear antennas. Of especially great interest is the final Chapter IX, devoted, as indicated, to boundary-value problems. Here the reflection and refraction of plane waves at an interface, the passage of plane waves through plane layers with arbitrary properties, the propagation of waves along a circular cylinder, in tubes and in coaxial lines, electromagnetic oscillations in a conducting sphere and in a spherical cavity, diffraction of plane waves by a sphere, and, finally, the propagation of radio waves along the earth are considered.

The value of the book is enhanced by the presence of a large number of interesting problems, some of which have been drawn from the original literature. Unfortunately,

BIBLIOGRAPHY

there are no answers to the problems, let alone solutions (although many problems are formulated in such a way that the answer is contained in the conditions and the reader is required to find the proof of the formula or assertion given).

The book, of course, is not free from shortcomings. The author’s presentation is often uneven and clearly reflects his own tastes and interests, which in works of this kind is apparently unavoidable. Many of the formulas and transformations presented never “come into play” later and can hardly “come into play” at all.

The question of units is in a completely unsatisfactory state, at least for the Soviet physicist reader. The author uses the rational system of units MKS (the meter, kilogram-mass, second, and coulomb are taken as the fundamental units). The connection of this system with the absolute Gaussian system of units adopted in our physical literature is insufficiently explained, and the MKS system itself is introduced rather indistinctly. The author, without any explanation, gives the equality: \(1\) coulomb \(= \dfrac{1}{10}\) abs. coulomb (p. 31). One may understand that by the absolute coulomb he means the absolute electromagnetic unit of charge, and by the coulomb the “ordinary coulomb” \(= 3 \cdot 10^9\) CGSE units. Meanwhile, in our country the “ordinary coulomb,” as distinct from the well-known international coulomb, which differs very little from the absolute one, is called the absolute coulomb. The situation is further complicated by the use of a rational system of units, which differs from the ordinary one by factors of the type \(4\pi\) and \(\sqrt{4\pi}\). As a result, it seems to us that, for the physicist, the question of units is the principal obstacle to using Stratton’s book. The formulas given in it cannot be used immediately “without thinking”; one must constantly worry about the units. In any case, when in the past the reviewer had to use the book for reference, he spent 95% of the entire time required to obtain the reference on becoming acquainted with the units.

One may also point to a number of other defects or inaccuracies. Following the established tradition, the author has completely forgotten about ferroelectrics. He connects the characteristic nonlinearity of induced polarization as a function of field strength and the presence of spontaneous polarization only with ferromagnetics. Meanwhile, it is now already well known that the class of ferroelectrics, no less rich in representatives than the class of ferromagnetics, behaves in an electric field in general analogously to the behavior of ferromagnetics in a magnetic field (for this reason ferroelectrics are even sometimes called ferroelectrics). In our opinion, ferroelectrics in courses on field theory should henceforth be considered on an equal footing with ferromagnetics.

On pp. 146–147, in the question of choosing an expression for the density of electromagnetic momentum in a medium, the author displays helplessness, which he shares in this respect with many others. This question is discussed in § 116 of “Foundations of the Theory of Electricity” by I. E. Tamm.

On p. 242 the author asserts that in the case of plane electromagnetic waves in a nonconducting medium the longitudinal electric field can only be static. This is incorrect—a very interesting exception is the case of a plasma, in which the longitudinal field with frequency \(\omega\) differs from zero if \(\varepsilon(\omega) = 0\).

In a number of places the author uses the Clausius–Mossotti relation and not only fails to note the inapplicability of this relation that obtains in most cases, but even asserts the opposite (p. 130).

The author’s treatment of the question of dispersion and the propagation of waves in the ionosphere (Ch. V) is extremely, obviously, insufficient. The space that the author devotes to propagation in the ionosphere is wholly disproportionate to its importance. In dealing with the question of the velocity of propagation of signals (Ch. V, §§ 5, 17–18), the author should have considered the question of the dis-

of the swimming of the main part of the pulse (this can be done quite simply), rather than confining oneself to deriving an expression for the group velocity and discussing the question of the velocity of the wave front.

Remarks of the above type could be multiplied, but since they are for the most part of secondary importance, we shall not do so.

The translation has been done well; one feels that the translators and the editor put much labor into their work. Certain minor errors and roughnesses, practically unavoidable in so large a book, are nevertheless noticeable. For example, on p. 144 we read: “The properties of each grain or of a monocrystal of the strict (?) anisotropic.” In the original there is the word “strongly,” i.e. “strongly,” not “strictly,” which makes the phrase intelligible. Further, for example, on p. 148 we read: “...as was noted above, these...” Apparently the index is in a rather unsatisfactory state. For example, quite at random we looked up the word “coulomb” and found that there was no entry for it. Yet there is the “Coulomb law,” pp. 256, 260, 164, 217—218. On pp. 256 and 260 there is no Coulomb law even to be found. The index does not contain such words as ohm, ferromagnetic, magnetic, paramagnetic, gauss, oersted, etc. (whereas in the original, for example, “ferromagnetic medium” is present).

Unfortunately, one also cannot fail to make some comments concerning the editor’s notes to the translation. The book has no notes concerning units, although, in our opinion, it was absolutely necessary to help the reader on this point (see above). There are also no notes relating to the questions touched on above and to a number of similar ones. Meanwhile, the book is not overloaded with editorial notes (which, of course, is good), and the editor considered it appropriate to make special notes indicating, for example, that a certain vector equality is called the Laplace identity (p. 48), and that the well-known coefficients $h_i$ in curvilinear coordinates are called the Lamé coefficients (p. 53). More important is the question of notes connected with references to the literature. In the English original of the book: 1) there are almost no references to Soviet works; 2) a number of references are made to literature that is already of little relevance—in particular, to works dating from the nineteenth and the very beginning of the twentieth century; 3) seven years have passed since the book appeared, and a number of new and interesting works have appeared both in the USSR and abroad. All these circumstances, together with the natural desire to make the book as useful as possible for a wide circle of readers, made it expedient in the translation to make a number of additional references to instructional, monographic, and original literature in Russian, as well as to the newest foreign works on all the questions covered in the book. Meanwhile, with a few exceptions, the editor confined himself merely to indicating important domestic investigations in the field of the theory of radio-wave propagation above the earth.

Despite all the comments made, the great value of the Russian translation that has appeared of Stratton’s Electromagnetic Theory cannot, of course, be in any doubt.

V. Ginzburg