S. E. Khaikin, Mechanics, GITTL, Moscow, 1940, price 8 rubles 50 kopecks + 1 ruble for binding.

S. E. Khaikin’s book is a major and gratifying phenomenon against the general background of our Soviet educational literature in physics. Of course, mechanics is an old and well-established science, and in the USSR we have a number of excellent textbooks of mechanics, beginning with the famous course by N. E. Zhukovsky and ending with the splendid book by L. G. Loitsyansky and A. I. Lur’e; but the chief purpose of these books is rather the application of the basic principles of mechanics than their critical establishment. Mechanics, as part of a course in physics, must be presented above all from the standpoint of establishing these principles from experience, demonstrating their power in various areas of physics, and indicating the limits of their applicability and accuracy. It is precisely such a book on mechanics as part of a physics course that we have lacked. Moreover, in some new books there is a mistaken point of view that in a physics course it is unnecessary to dwell especially on mechanics. An example is the first volume of Academician A. F. Ioffe’s physics course. It is not without interest to note that this point of view is reflected to a certain extent in the official syllabi of physics courses for higher educational institutions.

It cannot be left unmentioned that, not only in provincial but also in metropolitan institutions of higher education, mechanics in the physics course is taught rather unsatisfactorily—

tely, and the main reason for this was the absence of a book on physical mechanics. Now it exists, and this, undoubtedly, should have a very beneficial effect on the teaching of mechanics in higher educational institutions.

Let us note first of all the general spirit of the book. The author teaches the reader to “think physically”: he teaches one to see in the phenomenon under investigation its essential features, to formulate them, and to clothe them in calculation formulas. There is no need to close one’s eyes to the fact that it is precisely with “physical thinking” that students are often in an unfavorable position: they write all the “formulas” excellently, but what properties of the external world are expressed in these formulas they often do not understand. The entire exposition of S. E. Khaikin’s book is directed toward combating this: the “formulas” in this book are only the completion and exact expression of the results of physical thinking. From this point of view one should especially note the descriptions of a number of instructive and vivid demonstrations.

The exposition of the principles of mechanics is very successful. Here the author had to solve a rather difficult pedagogical problem: to observe the necessary degree of rigor in the exposition and at the same time not to overload it with mathematics. The author achieves this mostly by examining particular examples, in which the exposition can be carried out with sufficient rigor, while the general principle is postulated without proof. By this device the author gives, for example, the concept of the tensor of inertia, the stress tensor, etc.

Now a few words about the selection of material.

Here the author, unlike our other textbooks, has considerably expanded the content. He has quite correctly introduced an exposition of the foundations of the special principle of relativity and has managed to do this in a very accessible form; the question of conservation laws in moving coordinate systems is also introduced. Much space is devoted to the question of reference systems in general. Finally, the exposition of hydrostatics and aerodynamics is sufficiently complete and corresponds to the present state of this important field; here too the author makes a significant step forward in comparison with our contemporary textbooks.

In short, the book is excellent, and it should be strongly recommended for teaching.

Let us now dwell on several places in the book which seem to us not devoid of certain shortcomings or debatable points; however, we very much ask the reader of this review to remember that this “fly in the ointment,” of which we shall speak below, can in no way be considered to have spoiled the “barrel of honey.” First of all, on the theory of dimensions. At the beginning of the book the author mentioned it very successfully, and later left it unused, as a result of which the discussion of dimensionality turned out to be unnecessary for the reader, whereas it would not have been difficult to apply the theory of dimensions at least to the pendulum and to the Reynolds number.

The laws of dry friction are a successful part of the book, and the exposition here contains much that is new. But what the author says about rolling friction seems to us incorrect. Here one should indicate the connection established by Reynolds between rolling friction and sliding friction.

The question of the reaction forces of kinematic constraints and of constrained motion is not illuminated sufficiently. Therefore the formulas of constrained motion appear rather as Minerva from the head of Jupiter than as a systematic application of the foundations of mechanics. This would have been all the more important to do because many textbooks contain major errors in this respect, for example in the form of the assertion, in deriving the equation of oscillations of a pendulum, that the component of the force of gravity along the radius is destroyed by the resistance of the support. In S. E. Khaikin’s exposition the theory of the pendulum is given quite rigorously, but it bypasses the question of reaction forces.

Further, one may note that the question of the moment of a force with respect to a point and with respect to an axis remains somewhat unclear in the author’s exposition; the reader will not grasp the connection between them.

It is also a pity that the fundamentally important statement about the influence of initial conditions on subsequent motion and the independence of the latter from anything except these initial conditions and differential equations has fallen outside the scope of the author’s exposition.

Little that is new has been introduced by S. E. Khaikin into the exposition of acoustics, although its present development very much calls for this. A number of propositions and formulas from the theory of waves and oscillations should have been illustrated by examples from modern acoustic apparatus, seismographs, etc. It would also have been necessary to introduce something about hearing, reverberation of rooms, etc. One has to fear that acoustics will practically drop out of that course of physics whose first volume is S. E. Khaikin’s book. In any case, it would not have been at all difficult to introduce into the author’s system of exposition the concept of the flux of sound energy, for which a paragraph on the transmission of work has an appropriate preparation. And the question of emitters and receivers of sound energy should not have been passed over, even if at the cost of some reductions in other parts of the book.

In conclusion, we wish this book wide circulation.

N. N. Andreev, Moscow