V. I. Pavlov, Course of Physics, Volume I (Mechanics. Molecular Physics), Gostekhizdat, 1949, p. 447, 160 figures.

For many years now the pedagogical community has been expressing dissatisfaction with the state of textbooks for the physics course in higher education. The existing textbooks suffer from considerable shortcomings, and moreover they do not meet the requirements of the various categories of students. The book market needs at least three types of physics textbooks: a university textbook, one for technical higher educational institutions with an intermediate-sized syllabus, and one for higher educational institutions with a small physics syllabus. For higher educational institutions with a small syllabus, the existing textbooks are too large; for technical higher educational institutions with an intermediate-sized syllabus, most of the books published in the USSR are intended: the textbooks by Putilov and Artsybashev. The course under review also belongs to this same category. Whatever criticism the existing ...

textbooks, they nevertheless do exist. It is clear how much more important it is to create the missing textbooks than to duplicate existing ones.

This duplication would make complete sense if Pavlov’s physics course possessed fundamental features distinguishing it from the above-mentioned textbooks. The course under review does possess a number of features, on which we shall dwell below, but they do not have a fundamental character. Therefore, first of all, one must note with regret that the publication of Pavlov’s book does not substantially change the situation with textbooks of physics for the higher school.

Let us proceed to consider the individual chapters of Pavlov’s physics course. In the first five paragraphs of Chapter I—the foundations of mechanics—the concepts of velocity and acceleration are explained quite distinctly. The central point of this chapter—the laws of Newton—is presented unsatisfactorily. We shall not argue with the author about the advisability of presenting the laws of mechanics as a single law of mechanics, $F = ma$, of which the law of inertia is a consequence, although it seems to us that consequences of laws should not be called laws. The author introduces the concept of momentum before formulating the fundamental law of mechanics, without giving a definition of mass. It is a pity that pp. 44–45, where one of the fundamental laws of nature is discussed, are set out so vaguely.

Instead of clarifying the empirical essence of the law of dynamics, on pp. 46–48 the author engages in superfluous calculations, the purpose of which is to write the law of dynamics in integral form (formula 25). Incidentally, the average force obtained as a result of such calculations should not be called fictitious.

The equality of the forces of action and reaction is analyzed in detail and sufficiently clearly using the classic example of a cart and a horse (pp. 49 and 50). The following § 8, in which the author for some reason needed to apply integration of the law of dynamics, leaves a feeling of dissatisfaction. The integrals should be removed, and many examples illustrating the law of conservation of motion should be given. The meaning of this, again most important, question of dynamics will not be grasped by the reader from § 8.

The concept of an inertial coordinate system is introduced by the author in § 9 much too late. Literally two lines are devoted to the Coriolis force. The very brief presentation of questions about rotation of bodies and the law of conservation of angular momentum is likewise given in only a few lines.

As we mentioned above, the author uses calculations with integrals and derivatives where this is unnecessary. § 14 provides us with the opposite example. Here the author derives the equation of kinetic energy in the way this is done in school, with the aid of formulas for uniformly accelerated motion. It is precisely here that it would be quite appropriate to integrate the law of dynamics.

In §§ 14–15 the concept of potential energy is discussed in considerably greater detail than in other analogous courses. The curve of interaction of particles is examined over two pages. The concept of a potential well, and so on, is given. The exposition is clear and accessible—these paragraphs should be counted as successful.

In the paragraphs devoted to oscillations there is an excessive fascination with calculations (for example, p. 99), while the physical side of the phenomenon is presented hastily.

Part I, consisting in this way of a single chapter, ends with a brief exposition of the foundations of hydrodynamics and aerodynamics.

Part II—molecular physics—consists of 9 chapters. The first chapter of this part, devoted to a general survey of the molecular-kinetic theory of the structure of matter, is successful. We shall point only to certain

easily correctable errors. On p. 133 there is discussion of the disordered vibrations of molecules of a solid body. On p. 136 the thermal expansion is explained incorrectly; it should have been stated in several lines that the vibrations are anharmonic and the correct explanation of this effect should have been given (only two lines are devoted to this in Chap. IX). One cannot speak of a crystal lattice as of an immobile structure. In § 4 the following definition is set off in italics: “the quantity of heat in a body is the store of kinetic and potential energy of its molecules.” This same definition is repeated on p. 146 (and also later in several particular cases, for example, p. 235). At the same time, on p. 167 it is said: “the internal energy of a body is determined by the sum of the kinetic and potential energies of its molecules.” Why, then, is a second, obsolete term needed for a concept that has the more general name internal energy? This term is all the more superfluous in that it may be confused by the reader with the term for the quantity of heat communicated to a body. For it is in this, and only in this, sense that we use the term heat in thermodynamics.

Chapter II is devoted to the foundations of thermodynamics. That is what it should have been called. On p. 169 it is said that in thermodynamics it is proved that

\[ \frac{dQ}{T} \]

is a complete differential for an irreversible process. What, then, is the second law of thermodynamics? These pages of the book, too, were not successful for the author. The physical side of the matter has remained outside his attention. The essence of the second law will not be grasped by the reader.

Chapter III—gas laws—is superfluous; it entirely, and at the same level, repeats the material of secondary school.

In two large chapters the essence and applications of the kinetic theory of gases are considered. Here there are a number of successful passages. Among them should be included the general characterization of the theory, the description of experiments, the abundance of well-chosen numerical examples illustrating the basic concepts of the theory. The shortcomings include an enthusiasm for algebraic calculations, as a rule cumbersome, formal, and excessively “rigorous” (for example, pp. 191–192). Some “rigorous” arguments are also cumbersome (pp. 208, 224).

On p. 228 the author wishes to acquaint the reader with the foundations of quantum theory. This should have been done differently than it is done in the book. It was necessary to cite the facts that required explanation and to indicate that the only possibility for understanding these facts consists in accepting such-and-such hypotheses. Phrases like the following: “Planck showed that oscillators possess amounts of energy that are multiples of \(\varepsilon\)” do not create in the reader a correct conception of the methods of theoretical physics.

In our opinion, pp. 234–235 are superfluous; on them the author attempts to give a visual picture of isothermal and adiabatic processes. A clear understanding of the thermodynamic side of these processes is quite sufficient for a student who has obtained a correct idea of the foundations of the kinetic theory of gases. The usual material concerning these processes (Poisson’s equation, formulas for work, the Carnot cycle) has fallen into this chapter, whereas this material, of course, should have appeared in Chapter II.

The author sets forth the behavior of a real gas in great detail. Experimental facts are described in detail; graphs and tables are given. Much attention is devoted to the van der Waals equation. Perhaps the “rigorous” arguments by means of which this equation is justified are superfluous (p. 286 and following). The reader gets the impres-

...of the strict validity of this equation. Nowhere is it stated that about 80 different equations of state have been proposed for various gases and that it has not proved possible (and this is not accidental, but quite natural) to express the properties of all real gases by a single equation. It seems to us that it is not worth giving a naïve molecular-kinetic treatment—the “derivation” of the equation of state. On the contrary, it should have been emphasized that the peculiarity of molecular fields, the different form of the potential energy of interaction of the molecules of real gases, does not in principle permit the construction of a universal equation. Therefore § 4, entitled “Algebraic, graphical, and physical investigation of the Van der Waals equation,” ought to have been shortened. The concept of the critical point should be introduced more properly as an experimental concept, and not as a consequence of an algebraic consideration of the equation. In general, throughout this chapter one sees a more serious attitude of the author toward the Van der Waals equation than follows from experience (compare, for example, p. 296).

Nor is it necessary, in the following, necessary § 5 (“comparison of the equation with experiment”), to consider methods of “saving” the Van der Waals equation by introducing an arbitrary number of constants. It should have been emphasized that with a large number of arbitrary constants an “adjustment” of theory to experiment is always possible and that, consequently, such theories are of little value.

In Chapter VII—properties of liquids—experimental data are given on compressibility, thermal expansion, heat capacity, thermal conductivity, and viscosity of liquids. The paragraph on surface tension is well written. However, the derivation of the formula for the additional pressure on a curved surface suffers from excessive cumbersomeness. It is quite sufficient to give in two lines the derivation for a sphere and, without proof, to generalize it to the case of any surface. The foundations of the kinetic theory of liquids should be set out in the course of physics according to the new program; however, it would have been sufficient to confine oneself to the qualitative side of the question. § 6—adsorption, thin films, etc.—is very useful. The last paragraph, devoted to solutions, is also written concisely and clearly.

A few minor remarks. The author repeatedly says: such-and-such a quantity is “expressed by one or two significant figures,” wishing to say units or tens. On p. 329 it is said that the theoretical calculation of heat capacity is impossible because of the absence of definite information about the character of the thermal motion of molecules; it should have said because of the complexity of the mathematical formulation of the problem. Anomalies of water (p. 324) are explained by the author by the “variable composition of its molecules.” What is meant is the association of molecules, which, incidentally, is explained rather unsuccessfully on p. 320. It is also said there that the properties of liquids change almost not at all with temperature.

Chapter VIII—mutual transitions of the liquid and gaseous states—is written freshly. It is unclear only why there is no material on other phase transformations. It is set out only in the following chapter, and, moreover, on a single page.

In comparison with real gases and liquids, little space is allotted to solids (Chapter IX and the last). After a general introduction, the concept of the crystal lattice is given fairly well. The process of crystallization is considered quite fully, but somewhat one-sidedly. Questions of the structure of crystals are not set out, and the properties of solids are described too briefly and sketchily. The material on the theory of elasticity should have been transferred to mechanics—it is in no way connected with the rest of the content of Chapter IX.

Of the individual errors in this chapter we shall note the following. The term crystalline system cannot be applied to crystal classes. There are seven systems, and 32 classes. To say of E. S. Fedorov that he developed the doctrine of crystal symmetry is very little. E. S. Fedorov is the creator of modern crystallography. This circumstance should have been stated.

From the review of Pavlov’s course of physics that has been carried out, it is clear that, in its character, in the detail of its exposition, in the volume of material, and in its method of presentation, it meets the requirements that should be placed upon a textbook for higher educational institutions with an intermediate program in physics. As the author rightly notes in the preface, physicochemical questions are treated in somewhat greater detail than usual. Therefore Pavlov’s course will be very convenient for chemical-technological higher educational institutions.

With the introduction of a number of corrections and a rather substantial revision, especially of the chapter devoted to mechanics, the book under review can become a useful manual and textbook for a number of higher educational institutions. Let us emphasize once again that, unfortunately, the publication of this course by no means exhausts the varied needs in educational literature on physics.

A. Kitaigorodsky