1.1. From the Preface.

In this first Revue de Physique, I propose to present the main progress made in the study of the phenomena of movement of liquids over the past twenty years. It was the illustrious professor of the University of Berlin, M H von Helmholtz, who, in a Memoir published in 1858 and in a short Note of 1868, put forward the two capital ideas, the origin of many and important works of von Kirchhoff, Rayleigh, J Thomson, and the speculations of such an original genius as Sir W Thomson.

Despite the obvious accuracy of the equations of the Hydrodynamics of perfect or low viscosity fluids, certain phenomena of daily observation, the formation and persistence of swirling rings, that of jets, had remained without explanation. Today these phenomena are explained in their general characters, and it does not seem doubtful that the numbers furnished by the experiment are themselves in conformity with the theory when the efforts of the mathematicians make it possible to treat completely some particular cases of these singularly difficult problems.

Here is the order adopted in this exposition:

I. Whirlpools in perfect fluids. Theory. - Experiments. Applications. - Atom-vortices.

II. Flow of liquids. Jets. Discontinuous movement. Discussion.

III. General bibliography.

2.1. From the Preface.

This book is a fairly faithful reproduction of the lessons I taught at the College de France during the year 1901-1902. It is by no means a complete and methodical treatise on electricity; it is, in accordance, I believe, with the spirit of the teaching of the College of France, a course of lessons, very unequally developed, according to whether the subject with which they treat is more or less known by French texts, or that it seemed to me to include some new historical or theoretical remarks. As for the mode of exposition and sequence of ideas and facts, I do not give it as preferable to any other, but as quite different from those which are usually adopted by French authors, and in itself quite satisfactory in the field studied to provoke comparison, make the reader think and help him build for himself the edifice best suited to the nature of his mind.

I am thinking of following this volume with a second which would contain the essential parts of the lessons of 1902-1903 and 1903-1904, leading to the theory of electrons, which now rests on a solid experimental basis.

I was helped in the drafting of this book by MM Blanc and Blein, agrégés of Physics, former students of the École Normale, who wrote the lessons and reviewed the calculations with a zeal and care for which I thank them; I therefore hope that I have not let slip any serious error, and that there are few errors in signs or notation. Almost the whole volume was printed at the beginning of the year 1903, before the experiments of MM Peuder and Crémieu put beyond doubt the magnetic effect of electric convection; but publication was delayed for several months by the last chapter. In fact I had to resume the theory of oscillations of the ellipsoid, and it seemed to me necessary to carry out the numerical calculations essential to make usable the functions which define the distribution on ellipsoids, and the law of emission by ellipsoids. These calculations were made by M Kannapell; quite a number of checks and controls were carried out; I believe that one can have full confidence in the tables which end the volume. It would be great if they were more developed; but as such, they take the H and S functions out of the limbo of pure analysis and allow them to be used in most circumstances, without being stopped by preliminary calculations of an off-putting length.

2.2. Review by Samuel Jackson Barnett.
Bull. Amer. Math. Soc. 12 (3) (1905), 141-143.

This [is a] valuable work ...

The author expects to follow this volume by another, containing the essential portions of his lectures for 1902-1903 and 1903-1904 on electron theory.

The first of the four books which make up the present volume is devoted to the pioneers of the science from Cavendish to Kirchhoff and Clausius. Cavendish and Ohm receive separate chapters, which are biographical as well as scientific, and particularly interesting. In this book, as in most other portions of the work, numerous references are given.

The second book treats of steady currents, and also of changing currents without magnetic induction. The first chapter, entitled "currents in space," considers, among other matters, the decay with time of electrification in a conducting medium, electric double layers, and the methods of Gouy and Cohn and Arons for the determination of the dielectric constants of conducting liquids. In the treatment of the first mentioned subject the relaxation time, involving the dielectric constant, is given for a number of substances, including bismuth and copper; but the dielectric constants of these substances are not given, nor is any authority quoted, while the well known dielectric constant of water is given - a procedure which can hardly be justified in view of the little that is known of the dielectric constants of metals. The second and third chapters are devoted to the resistances of conductors with electrodes of relatively high conductivity and to Rayleigh's method of approximate resistance evaluation. The resistance of a circular cylinder, with various electrodes, is treated at length by Bessel's functions, to some of the properties of which a separate chapter is devoted. Electric propagation along a cable is discussed in a long chapter after Kelvin, Kirchhoff, and Vaschy; and the book ends with two chapters on the much neglected subject of the electric field of the steady current. Attention should be called to the erroneous statement at the beginning of the book to the effect that all following equations are written in electromagnetic units. As a matter of fact the author continually expresses K, the dielectric constant, in the electrostatic unit, and therefore introduces the square of Ω, the ratio of the electromagnetic unit charge to the electrostatic unit charge, to make his equations correct. Unfortunately, M Brillouin is not alone in this practice.

The third book, on electromagnetic induction, is introduced by a brief but excellent historical chapter. Joseph Henry, however, is not mentioned, and Faraday receives scarcely better treatment. Four chapters are devoted to induction in fixed circuits ; special attention being given to parallel wires, cylindrical coils, and spherical coils. On account of the simplicity of the exact formulae and the facility of construction, the author recommends the latter form of coil for inductance standards. A chapter is devoted to the diffusion of currents in conductors, and the book ends with two chapters on electric propagation along conductors devoted largely to Kirchhoff's classic memoir of 1857.

The fourth and concluding book treats of the general electromagnetic field. After a discussion of the more general equations, involving a comparison of the theory of Maxwell with the older theories of Neumann and Helmholtz, the field of the Hertzian oscillator is treated at length, first without damping, after Hertz, and then with damping, after Pearson and Lee. The two final chapters of the work are devoted to the electric oscillations of a sphere and the electric oscillations of a prolate spheroid. Extensive numerical tables for the latter are given at the end of the volume.

The treatment appears to us to be, in general, accurate, elegant, and commendably concise. Too great brevity, however, has in some places resulted in obscurity. The book contains valuable critical remarks and considerable original work by the author not hitherto published, as well as other valuable matter not readily accessible elsewhere. The errata we have noticed are not numerous and are for the most part typographical and not likely to be misleading. Confusion will doubtless be produced in the minds of some readers by the author's indiscriminate use of for both and as ordinarily employed.

The work naturally contains little to interest the student of pure mathematics, but it can be highly recommended to the physicist and forms an acceptable addition to electrical literature.

3.1. From the Preface.

The viscosity of fluids is the simplest of all irreversible phenomena; it manifests itself within a physically homogeneous medium, the temperature of which can be uniform, which distinguishes it from thermal conductivity; it only involves mechanical actions, which distinguishes it from the release of heat by an electric current. It can therefore be studied as an example of an irreversible phenomenon, from a more especially thermodynamic point of view. We can also, particularly when it comes to gases, take molecular theory as a guide.

In fact, the phenomena of friction has played a fundamental role in the development of Thermodynamics; but the converse is not so true. In slow movements, the only ones that we know how to analyse are the forces, small of the first order like the relative speeds, which are directly measurable and important, while the work converted into heat, small of the second order, does not prevent the transformations to be practically isothermal; both in theory and in practice, it is the purely dynamic data, velocities and forces, which the first approximation provides, and from which we estimate the work, and, if applicable, the variations in temperature.

In any case, we must begin with the study of viscosity such as it is, and for itself; this is what I did in my Lessons de 1898-1899 and 1899-1900, as a substitute for M Mascart at the College de France, which, revised and brought up to date, form the subject of this Book.

In this first Volume it is only about liquids.

As always, it is experiments that provides the fundamentals. After the somewhat confused analyses of the Renaissance, Newton suspected, in the resistance of fluids to movement, various influences, which were clearly discerned only by Coulomb.

After Coulomb's Memoirs, the application of the principles of Dynamics became possible; the quantities which characterise this property as distinct from the inertia of the fluid are well defined. At constant temperature, the foundations of the physical study of viscosity are established; we can write the equations of motion of a viscous fluid. It is important to perform the exact or approximate integration in the greatest possible number of cases, either for applications, or for the construction of devices which allow the study of various influences: temperature, pressure, concentration of solutions, and chemical composition of pure liquids.

This is the subject matter of the various Chapters of Book I. Book II begins with a detailed description of the memorable experiments of Poiseuille, after which it became certain that the proportionality of the viscous resistance to the rate of deformation conforms to the experiment in a very large domain. Then come the experiments on mercury which show that the adhesion to the wall is as complete for liquids which do not wet as for those which wet. After which a Chapter is devoted to experiments on pure organic liquids and to tests of the relation between molecular viscosity and chemical constitution; it ends with Warburg's fine experiments on the critical point of carbon dioxide, and a few other things.

Finally, in a last Chapter, we will find a description of the experiments of Hagen, Reynolds and Couette on the transition from the slow regime of Poiseuille, to the rapid or hydraulic regime, and of the circumstances which influence the limit of the two regimes according to O Reynolds.

The second volume will contain the study of gases and of the general characteristics of molecular theories.

BOOK III. - Gas.

Chap I. - First research on the viscosity of gases by means of the pendulum and oscillating discs.

Chap II. - Oscillating discs. - Maxwell. - Kundt and Warburg.

Chap III. - Flow through a narrow tube at room temperature.

Chap IV. - Flow through a narrow tube, (A) temperatures below 100 °, (B) high temperatures, (C) organic vapours, (D) very high temperatures.

BOOK IV. - Molecular theory. - Conclusion

Chap I. - First theoretical tests: Navier, etc.

Chap II. - Gas. - Dynamic theories.

Chap III. - Liquids. - Kinetic theory test.

Chap IV. - Conclusion. - Overview of the viscosity of fluids in general.

3.2. Review by: Anon.
Nature 77 (1908), 341.

Both the mathematical and experimental study of viscosity are admittedly of a high order of difficulty, and the author is to be congratulated on the clear and concise manner in which he has developed his subject. After summarising in the first chapter the early work on viscosity, the mathematical treatment of the subject is fully developed in the following four chapters. The second part of the first volume is devoted to a description of experimental work. Each of the principal memoirs is described and subjected to a careful criticism; this part of the book is very complete, and is absolutely free from the tendency to ignore work done outside France occasionally met with in French standard works.

In the second part the theoretical and experimental study are taken together, the relations between the viscosity and the dynamical theory of gases being fully discussed. The concluding chapters contain a general discussion of the molecular theories of liquids and gases.

The work as a whole is characterised by clear exposition, acuteness and fairness of criticism, and completeness. It will doubtless take its place as the standard work on viscosity.