P. N. LEBEDEV AND LIGHT PRESSURE

G. P. Kravets

I first saw and heard Pyotr Nikolaevich Lebedev in the old “large” auditorium of the Polytechnic Museum. This was on October 27, 1894.

We, the students of that time, recall with gratitude some of our professors. Thus, the lectures of A. G. Stoletov and N. A. Umov made a deep impression on us. N. E. Zhukovsky was charming. But there was no organized center of science as we understand it. The university charter of 1884, introduced shortly before, did not regard scientific work as the university’s main business—it merely tolerated it, as it were, among other things.

I remember very well how Pyotr Nikolaevich, in his laboratory, told us: “Once a very venerable old man came here” (and he named the former rector of Moscow University). “Alexander Grigorievich (Stoletov) tells him that I sit here for days on end, and the old man says to me: ‘Young man, why do you exert yourself so? We do not need this at all; pass your master’s examinations, write dissertations—first a master’s, then a doctoral one; we shall appoint you first as extraordinary professor, and then as ordinary professor. That is all; there is no need to torment yourself so much.’” P. N. passionately dreamed of escaping those conditions under which a person was required only to master some minimum of knowledge, obtain official approval, and then be allowed to rest on legitimate, though cheap, laurels…

Infected by the thoughts and views of our teacher, we too learned to despise the official atmosphere, learned to set ourselves different goals…

At the end of the 1880s, when P. N. began to work, studies of electromagnetic waves stood at the center of physicists’ attention in all countries. They marked a new and decisive stage on the path toward unifying our fundamental physical views. It is no surprise that precisely in the current of this theory the entire scientific life of P. N. flowed.

In Maxwell’s original creation we had a complex mathematical theory with a cumbersome and heavy mathematical apparatus. The works of Hertz and Heaviside had not yet simplified the approaches to the substance of Maxwell’s views, and “physical knowledge of his theory was thoroughly blocked by the forests erected in its construction” (Hertz). Non-theoretical scientists still had a poor grasp of the theory itself. At that time the attention of the majority was directed to several particularly simple consequences of the theory, which astonished everyone: the identity of the speed of light and the speed of propagation of electromagnetic disturbances; the equality between the refractive index and the square root of the dielectric constant; the prediction of the existence of light pressure.

The first of these conclusions of the theory was proved by the works of Hertz himself; the second (indirectly) was the subject of P. N. Lebedev’s German doctoral dissertation; the third became the work of his life.

Already in 1891 he wrote his first independent paper, and in it he brilliantly shows that, with a decrease in the dimensions of a body, the forces of light pressure—small in comparison with the forces of gravitation for bodies of ordinary size—will at a certain moment come to the fore. If a body has the form of a small sphere, then when its diameter is reduced, say, by a factor of one hundred, its mass will decrease by \(100^3\), i.e. by a million times; its surface, however, on which the forces of light pressure can act, will fall only by \(100^2\), or by 10,000 times. At some value of the diameter it is natural to expect that the particle will be repelled from the sun more strongly by the action of its rays than it will be attracted by its mass. Hence there are broad prospects for explaining a great variety of cosmic phenomena: cosmic dust, zodiacal light, comet tails, and many other phenomena in space constitute an arena on which the forces of light pressure successfully compete with Newtonian forces of gravitation.

This work was translated into almost all languages and made P. N. well known. It became the first stage of the whole subsequent direction of his activity.

The concluding sections of this work reveal a remarkable maturity in the 25-year-old author. He considers it his duty to warn researchers against attempts to extend his theory to the molecular world: a molecule is not a sphere; it has a complex internal structure, and in connection with this its physical properties, in particular its interaction with rays of light, cannot be determined by external geometrical dimensions alone. A molecule is a resonator, and its reaction to light waves is above all, and first of all, resonance.

Thanks to this profound idea the young author happily avoided the error into which, after him, many fell, and above all the famous Svante Arrhenius.

Arrhenius was an ardent enthusiast of the forces of light pressure in cosmic life, and this is his great merit, but he often interpreted the molecule as a very small black sphere....

The idea of the molecule-resonator became firmly embedded in P. N.’s consciousness. He decided to study, on a model of molar dimensions, those actions which waves incident upon a resonator produce under various circumstances. He imagined that the picture of the action as a whole is determined by the ratio of the period of the incident wave to the period of the resonator’s own oscillation; the physical nature of the forces acting in the resonator and in the wave perceived by it should, in his opinion, be quite immaterial. And so he studies hydrodynamic, acoustic, and electromagnetic resonators and, indeed, in all three cases, so physically different, he succeeds in observing similar phenomena. Three works devoted to this theme, brought together, constituted his Russian doctoral dissertation. The preface to this dissertation is remarkable. Here the author reveals his credo, his fundamental, motivating views. He writes that after the creation of the electromagnetic theory of light we have no right to ignore the ponderomotive forces of light waves; light emitted by one molecule cannot fail to act upon another. For the explanation of intermolecular forces a new possibility is thereby opened, and they must be studied from this point of view as well.

Work on resonators occupied no less than three years of P. N.’s life. It could not but lead him to his chief task—the task of proving the existence of light pressure.

The question of light pressure has a long history, full of dramatic contradictions. Reflected in it were all the numerous changes in physicists’ basic views on the nature of light. In old times—up to and including Newton—light was regarded as a stream of particles flying out from a luminous body.

It is not difficult to imagine that such a stream carries some quantity of motion. Giving it up to an obstacle it encounters—a mirror—it, of course, must exert some pressure upon it. Kepler had already explained the formation of comet tails in a similar way.

But then Huygens, Euler, Fresnel, and Young introduce into physics the conception of the wave-like nature of light. Euler draws attention to the difficulties that arise thereby for light pressure.

However, he believes (incorrectly) that, in view of the longitudinal character of light waves, it is still possible to explain the origin of such forces. But Fresnel proves the transverse character of light waves—a new difficulty for explaining light pressure.

And, finally, Maxwell’s theory appears. In it light is represented as propagating transverse waves of electromag-

... disturbances. And nevertheless Maxwell derives from it the existence of light pressure.

Arrhenius and P. N. Lebedev, in their later surveys, set forth the history of experiments undertaken at various times to detect light pressure. If we confine ourselves to the nineteenth century, then Fresnel must be named here. But he could not discover light pressure, since in his apparatus the vane, which received the light flux, was acted upon in the strongest possible way by convective currents of gas rising from the vane as a result of its heating by light.

How can these convective currents be avoided? The natural answer is: place the entire apparatus in a vacuum. It is therefore no accident that the next stage of experiments to seek light pressure was the work of William Crookes, the famous specialist in vacuum technology of his time. Crookes hoped that by his pumping the vacuum in the experimental vessel had been brought to such a degree that convection was no longer dangerous. And yet, at this vacuum (of the order of 0.01 mm of mercury), the action of light on the vane suspended from the balance arm proved to be hundreds of times greater than the forces Crookes expected to find on the basis of Maxwell’s theory. He discovered new “radiometric forces,” extremely interesting for the kinetic theory of gases, but for detecting the forces of light pressure the phenomenon discovered was disastrous: how can one detect forces that are masked by others exceeding them by hundreds, and even thousands, of times?

Such was the state of the question when P. N. took it up. This was in 1899. And in the summer of 1900 he delivered, at the International Congress of Physics in Paris, a report on the preliminary results of his work. Here are two drawings with which P. N. illustrated his Paris report.

Fig. 1.

Here (Fig. 1) there is, in plan, a round vessel and a miniature disk; light rays fall upon it, the pressure of which we wish to meas—

...to say. \(B\) is the light source—a lamp. Having passed through a glass plate, and having been reflected by a series of mirrors, the light, collected by a lens, falls on the disk on the right. But the entire mirror system is mounted on slides. Let us move it slightly to the right. The light will describe a symmetrically arranged path and will fall on the disk from the left. This is the method for eliminating convection. Indeed, from wherever the light may fall on the disk, the same heating of the latter will produce convection, which will give the disk a deflection in one and the same direction. On the contrary, the radiometric forces and the forces of light pressure, when the direction of the rays is changed, will change their sign. Thus,

\[ \begin{aligned} \text{force from the left} &= \text{light pressure} + \text{radiometric forces} + \text{convection},\\ \text{force from the right} &= \text{light pressure} + \text{radiometric forces} - \text{convection}, \end{aligned} \]

\[ \text{Force from the left} + \text{force from the right} = 2\bigl(\text{light pressure} + \text{radiometric forces}\bigr). \]

How, then, is one to get rid of the radiometric forces?

Obviously, one must evacuate the vessel to the greatest possible extent. But here I must pause somewhat longer over a comparison of present-day vacuum technique with that which prevailed at the beginning of the twentieth century.

At the present time, a physicist, in the very first stages of his laboratory work, becomes acquainted with rather complicated, but at the same time sufficiently perfected, vacuum apparatus. The quality of this apparatus is such that in 10–20 minutes the investigator obtains almost everything that he needs for an experiment. And it is difficult for us clearly to imagine the time when, in order to obtain the same, or even a far lesser, degree of rarefaction, one had to work with the pump of that day for many days. After all, Crookes discovered his cathode rays because he knew how to pump better than his predecessors. P. N. had to take a new step forward in this matter: patience alone was no longer sufficient here. I believe that the step he took was almost equivalent to a brilliant anticipation of the future paths of vacuum technique.

At the bottom of the vessel from which the air was being pumped out, and in which the disk for measuring the forces of light pressure was suspended, there lay a drop of mercury. When the pump (the tube to the pump was in the upper part of the vessel) ceased to operate, having reached the limit of rarefaction attainable for it, P. N. Lebedev slightly—by about 5 degrees—heated the mercury. It evaporated, but the small temperature difference was still unable to produce condensation of the mercury in droplets on the walls of the vessel. It was pumped out by the pump and carried the air out of the vessel with it. Here we see, in a very imperfect form, the idea of that very diffusion pump which at the present time represents the last word in vacuum technique.

By this method P. N. succeeded in considerably lowering the gas pressure in the vessel and, correspondingly, in reducing the magnitude of the radiometric forces so harmful to the experiment.

In the next photograph (Fig. 2) one can see the miniature disks that were suspended in the experimental vessel. Given the weak means of the vacuum technology of that time, physicists were especially wary of introducing greases and the like into a vacuum. All the disks, without any grease, were attached to the thinnest wires. Some disks were blackened, while others remained shiny. P. N.’s triumph manifested itself in the fact that the pressure on the shiny disks always proved to be stronger than on the black ones. This is what the theory requires for the forces of light pressure. Radiometric forces, on the contrary, should be greater for the blackened disk, which under these conditions is heated more strongly on its front surface. P. N.’s results differ from the theory by about 20 percent, and moreover his figures are in all cases greater than the calculated ones. This shows that, at the degrees of rarefaction he achieved, he had still not managed completely to rid himself of radiometric forces, but they had been reduced to comparatively small magnitudes.

In all its details, P. N.’s work will remain a vivid example of experimental artistry, perseverance, and the ability to overcome all the difficulties arising from the imperfection of technique. This work had a resounding and fully deserved success throughout the scientific world. The principal journals in all languages reprinted it in full or in excerpts. P. N., jokingly, pointed out that true popularity begins when the fame of some discovery spreads beyond the circle of specialists and is debated among laymen. In this sense, the greatest satisfaction was given him, according to his own assertion, by one boulevard French newspaper, in which the curative action of the southern sun, on the basis of P. N.’s work, was attributed to the massaging action of rays...

Fig. 2.

After this work P. N. was repeatedly called upon to speak, both orally (at various congresses) and in print, on various questions of light pressure. Sometimes this was polemic and criticism of various authors who had fallen into error; sometimes it was a new exposition

possibilities of cosmic applications of the forces of light pressure. Especially remarkable was his speech at the congress of the German Astronomical Society in Göttingen in 1902 on the subject of the causes of deviations from Newtonian gravitational forces. Here he had occasion to meet the German astronomer Schwarzschild, an excellent mathematician, who subjected to exact mathematical study the problem, once posed by Petr Nikolaevich, of the action of light on small spheres. The solution becomes difficult when the dimensions of the sphere approach in magnitude the length of the light wave and the waves begin to flow freely around such a small obstacle.

Schwarzschild found that the ponderomotive action of waves on such a sphere (moreover, one possessing perfect conductivity), for a certain ratio of the wavelength to the diameter of the sphere, passes through a maximum, and then, with further decrease of the diameter, begins to fall. From this Schwarzschild concluded that on still smaller spheres—on molecules—light would exert pressure so weakly that it would already be difficult to speak of the cosmic significance of this pressure. P. N. easily interpreted the maximum theoretically found by Schwarzschild as the resonance of the vibrating sphere at the corresponding period. He again draws attention to the fact that in reality the resonance of a molecule is determined not by its external dimensions but by its internal structure. And here he comes right up to his last work from the cycle devoted to the general problem of light pressure—to the problem of the pressure of light on individual molecules, on gases.

This problem is extremely difficult. Light presses on a molecule insofar as it is absorbed by it.) Gases in general absorb light very weakly: with a layer thickness of 1 cm*, only 0.5–2%. Hence the forces acting on them are another 50–200 times smaller than those which Petr Nikolaevich succeeded in measuring in his work

*) This proposition, given intuitively by FitzGerald, may be proved in the following way: if a light wave falls on a molecule containing an elastically bound electron, with electric vector directed along the axis \(z\), then the magnetic field \(H\), brought by the wave (let it be directed along the axis \(y\)), will give, for the second term of the Lorentz expression of the force acting on the electron,

\[ f_x=\frac{e}{c}\frac{d\zeta}{dt}\,H_y. \]

Here \(\zeta\) is the displacement of the electron. But in “free ether” \(E_z=H_y\), and \(\frac{e}{c}E_z\frac{d\zeta}{dt}\) is the work done by the force in unit time, divided by \(c\), or the power absorbed by the electron. If it is denoted by \(U\), then \(f_x=\frac{U}{c}\). Since \(U\) can be only positive (at least, on the average over time), \(f\) is always directed along the ray.

under the pressure of light on solid bodies. In addition, here one had to experiment with those gases whose very presence manifests itself in the form of convective currents and various other harmful side phenomena. By means of prolonged effort, brilliant techniques, and a subtle penetration into the mechanics of the phenomenon, he succeeded in bringing the work to a successful conclusion and in confirming the fundamental supposition. The work is an example of unsurpassed, and perhaps unattainable, experimental art. No one attempted to repeat it. Having done it, P. N. could consider that, one after another, he had posed and solved all the problems grouped around the light pressure predicted by Maxwell.

In fact, the idea of wave pressure occupied P. N. for a long time more and yielded a number of new results, especially in the works, directed by him, of his immediate pupils.

When P. N. published his first work, which sharpened physicists’ interest in wave pressure, it was shown from various sides that other theories as well, in particular the elastic one, also lead to the necessity of this pressure; it is only necessary also to take into account the forces of second order of smallness, discarded in the elementary) theory. The first to show this was N. P. Kasterin (in a report at the First Mendeleev Congress in December 1901). N. P. Kasterin’s work remained unpublished, since almost simultaneously there appeared a paper by Rayleigh on the same question, with conclusions very close to those of N. P. Kasterin. Rayleigh subsequently returned more than once to this topic. P. N. Lebedev placed the question on experimental ground. In his laboratory there was demonstrated the pressure of waves propagating over the surface of water upon an obstacle lying in their path (N. A. Kaptsov), and also “sound pressure” (V. Ya. Al’tberg). It was also shown that sound pressure is an excellent means for the quantitative study of short sound waves, no longer audible to the ear*), which was carried out by V. Ya. Al’tberg and later, for the purpose of studying the absorption of these waves by gases, was used by N. P. Neklepaev.

It may be said that with all these works the cycle of wave pressure was brilliantly completed in P. N. Lebedev’s school.

I shall now permit myself to dwell in a few words on the clarification of the scientific perspective against whose background, even in our own day, light pressure appears as one of the central points of physicists’ theoretical thought.

Even Maxwell’s contemporary, the Italian Bartoli, completely independently of any notions about the nature of light, succeeded

*) The “second term” of the Lorentz expression for the force in the electron theory takes account precisely of forces of this order.

**) Today these waves are called ultrasonic.

to prove that light must exert pressure on an obstacle lying in the path of the rays. He only could not show what the magnitude of these forces of light pressure is. Bartoli’s reasoning, subsequently improved by Boltzmann, may in its essential features be set forth as follows: one may imagine such a mirror-like (perfectly reflecting in all its parts) pump with valves and a piston, by means of which it is possible to pump radiation from a body of lower temperature into a body of higher temperature. If the motion of the piston of this pump is not accompanied by any work, then a result is obtained which contradicts the second principle of thermodynamics—the so-called “impossibility of a perpetuum mobile of the second kind.” Consequently, work is performed in the motion of the piston, and hence the radiation being pumped by the piston exerts pressure upon it.

Boltzmann derived his famous relation

\[ E + p = T \frac{dp}{dT}, \]

where \(E\) is the energy density, \(p\) the pressure exerted by the latter, and \(T\) the absolute temperature. It is clear that from this equation alone one cannot draw conclusions about the connection of each of the two functions \(E\) and \(p\) with temperature. But it is already evident from it that if \(p = 0\), then also \(E = 0\): the pressure can be equal to zero only on the condition that the energy density is equal to zero.

Next Boltzmann makes the Maxwellian substitution, assuming that completely disordered radiation, traveling in all directions, exerts on a wall a pressure equal to \(\frac{E}{3}\). Then from this and from the equation given above there is obtained a relation of enormous importance, called the Stefan–Boltzmann law:

\[ E = \sigma T^{4}, \]

or, in words: the radiation density of a black body is proportional to the fourth power of its absolute temperature. This relation opens the way to the entire thermodynamics of radiation. And we see that its first, decisive step could not have been taken without the idea of light pressure and without Maxwell’s expression for this pressure—an expression to the proof of whose correctness the scientific life of P. N. Lebedev was devoted.

The further steps of the thermodynamics of radiation are likewise impossible without taking light pressure into account. Thus, Wien’s displacement law is based on the formula for the pressure on a moving mirror. And, finally, Planck’s revolutionary formula, in which the idea of atoms of electromagnetic radiation, of quanta or photons, first found its reflection in physics, likewise historically could not have been obtained without the idea of light pressure.

But with light pressure there are associated ideas of still another order. If radiation falls on a body and exerts pressure on it, then this means that it transfers to the body not only energy, but also a certain amount of motion. It is clear that from here there is only one step to establishing a connection between mass and energy. The connection between mass and energy in the general case was established by Einstein from the principle of relativity. But it must be remembered that, historically, for the first time the concept of the mass of radiation was scientifically substantiated before the theory of relativity, from consideration of the forces of light pressure on a body moving nonuniformly.

Thus it is obvious that the conception of the enormous stores of energy concealed in any atom possessing mass is, in its roots, firmly connected with the forces of light pressure. It is obvious that those who will write about these broadest generalizations of physical thought will, in doing so, recall the name of Lebedev.

Such is history’s answer to the question of the significance of the life’s work of Petr Nikolaevich.

Let us now dwell briefly on the continuation which, after P. N., the problem of light pressure had, first in the theoretical and then in the experimental field.

Even in connection with P. N.’s preliminary (Paris) communication, light pressure was investigated by D. A. Goldhammer (in Kazan). This is an excellent work, in which both the initial formulas and the final results are given with classical clarity and simplicity. Expressions are given for the cases of both a black body and a partially reflecting body, for the case of oblique incidence of rays, for light passing through a plane-parallel plate, and so on. The author starts from the conception of Maxwell stresses. Another path was indicated (in a brief note to the second edition of Maxwell’s Treatise) by J. J. Thomson. He describes light pressure as the result of the action of the magnetic field of a light wave on the currents excited by the wave in the material of the “mirror.” This path was later used by Planck (in his Theory of Heat Radiation) and by Drude (in his textbook of optics), though not quite correctly by the latter. This same path is entirely appropriate in the electronic interpretation of light phenomena in bodies. A major step in the theory was made by M. Abraham, who calculated the pressure of light on a moving mirror. Another important work is P. Debye’s investigation of the pressure of light on spheres. He abandons the limitation which had been made in its time by Schwarzschild, and investigates the pressure on a sphere of a substance with any electromagnetic and optical properties. Along the way he also solves the problem of the pressure on an individual molecule.

A related problem concerning the rotational actions of a light wave was studied by A. I. Sadovsky and later, from the electronic point of view, by K. N. Shaposhnikov.

Finally, one should note the remaining unpublished work of V. A. Michelson on light friction. He starts from Abraham’s expression for the pressure on a moving mirror*):

\[ p=p_0\frac{c+v}{c-v} \]

(\(p_0\) is the pressure on a stationary mirror, and \(v\) and \(c\) are the velocities of the mirror and of light, respectively) and, expanding it in a series, obtains, among other things, a term dependent on the velocity:

\[ p=p_0\left(1+\frac{2v}{c}\right)=p_0+\frac{2p_0}{c}v, \]

which may be interpreted as the frictional force experienced by a body moving in the field of a light wave. One may speak of the cosmic significance of forces of this kind.

Now to the experimental continuation of Lebedev’s work. Even during his lifetime Poynting, by a very elegant experiment, proved and measured the pressure forces of obliquely incident rays on a solid body. In his apparatus the experimental disks sat at the ends of the balance beam in a plane normal to the beam. The rays fell on the disk in a horizontal plane, obliquely. The normal component of the force could not manifest itself because of the weight of the beam. For the same reason, the action of radiometric forces also fell away. The tangential component of the force of light pressure (predicted by D. A. Goldhammer) was easily measured in pure form.

A later (1923) work that should be mentioned belongs to Alice Golsen, a student of Professor W. Gerlach. She made good use of the latest vacuum technique and, in particular, of the advantage that, as Gerlach’s student, she had in her teacher’s excellent familiarity with radiometric forces. Gerlach had carried out his own investigations in this field, which showed that, as a rule, as the rarefaction increases, radiometric forces grow up to a certain maximum and then slowly fall. Lebedev’s experiments were carried out in the region where the effect decreases. In them the latter nevertheless retains a certain magnitude, distorting the final result. A. Golsen carried out the pumping continuously and made a series of observations at gradually decreasing gas pressures. At first, at high pressures, very large (larger than follows from theory) and incorrect deflections were obtained. Then the changes became smaller, and at extreme rarefactions no further change in the action was observed. A. Golsen rightly concluded that this force, independent of the gas pressure, was the force of light pressure. It proved to be very close to the value predicted by theory.

*) V. A. Michelson arrived at this expression independently and, moreover, considerably earlier than M. Abraham.

It remains to say a few words about how the doctrine of light pressure survived the modern revolution in physics—the revolution connected with ideas about the discrete-atomic properties of radiation, i.e. with the development of quantum theory. Quantum theory gave rise to two special experiments in which the pressure of photons figures. The first of them is the well-known Compton experiment. Here a photon falls upon an electron, gives it part of its momentum and of its kinetic energy, and itself, in the form of a photon of smaller magnitude, goes on farther. In the process both the electron and the new photon change the direction of their motion. All the details of this phenomenon are easily calculated. The experiment gives results fully consistent with quantum theory. But usually here the main attention is directed to the photons scattered in the collision of the primary photon with the electron. One may, however, look at the matter from the point of view of the behavior of the electron. Then we may say that in the Compton experiment we are investigating light pressure on an individual electron. True, the “photon” here is not a light photon but an X-ray photon, but this changes the matter only quantitatively.

The second experiment on which I wished to dwell is Stern’s experiment with the so-called molecular beam. Let us imagine a thin platinum wire, silvered on the outside and placed in as nearly perfect a vacuum as possible. When the platinum is heated, the silver will begin to evaporate. Owing to the rarefaction of the gas, the particles of vapor will reach, without collisions, the carefully cooled walls of the vessel and will be deposited there in the form of a mirror. If one places along the path of the particles a series of diaphragms with slits parallel to the direction of the wire, then through them there will penetrate to the far end of the tube only a fan-shaped beam of vapor particles. This is the molecular beam—“a gas of two dimensions,” as it is also called. On the glass plate set opposite it there will be obtained a sharply outlined image of the narrow slit in the last diaphragm. Now let us throw rays of light in a direction perpendicular to the plane of the fan; if a light quantum is absorbed by a particle of silver, it will impart to it momentum in the direction of its own motion, as a result of which these particles will deviate from their former direction; the image of the slit given by them will shift from its former place to the side. Stern succeeded in obtaining a slight broadening of the image to one side. He used ordinary light for his experiment. It is permissible to think that the experiment would have succeeded better with the use of lateral illumination by X-rays, although its own difficulties would have been encountered here.

Here is a certain new formulation of P. N. Lebedev’s experiment on the pressure of light on gases. It would undoubtedly be worth repeating and continuing.

Above I have tried to show, with several examples, how P. N. involved his pupils in work within the circle of his ideas. I want

tell of the ways in which he did this and what he achieved as a result of his efforts.

The situation of the university in those days, when P. N. was beginning his work there, was a difficult one. It was almost just as difficult later as well. The tsarist officials in educational posts saw the principal task of Russian professors as the training of “pedagogues.” What was the position, in such an environment, of a man who had set as his chief task scientific work and the creation of conditions under which that scientific work would become the main aim of university education? Moreover, he had at his disposal only one means—personal example; only with this weapon could he influence the university youth, already corrupted by what had been slipped to them under the name of science; only by this means could he open the eyes of the young people to its true tasks and to the true methods of solving them.

His task was incredibly difficult. But I remember how P. N. worked with each of us in order to instill in us his ideas. I remember this from my own experience. I was probably not among the bad students, but in my first two years I simply did not reflect on the fact that scientific work is the labor of searching and of creativity. It seemed to me, as to most of my comrades, that I simply had to study and read a great deal, and that in time I would thereby become considerably more intelligent. Apparently this did not escape P. N.’s notice (at that time he was senior laboratory assistant of the old physics laboratory). Once he caught me at just such reading in the student library and said to me: “Tell me, were you interested in the question of how the books are arranged here?” I thought that he wanted to ask me to put the library in order; I replied: “It seems they are in order.” “In good order?” “Yes, it seems, in good order.” “And what, can they be rearranged in one’s head in the same order?” “I think that is probably impossible.” “Nor should one do that; the real task is not whether anyone cares whether you have become cleverer and by how much; what is important is whether, by your own work, you have managed in at least one small area to advance physics by even a fraction of a centimeter.”

This does not mean that he taught us not to read. I know that at a friend of mine, who worked in the room next to me, he shouted: “You are a lazybones! You sit in the laboratory twenty-four hours a day; any fool can do that. No—you must read! No, you must calculate! Think!”

From this one can see what an individual approach he applied to each person.

And so, by his tireless, sharp, persistent propaganda, he brought it about that around him there gradually began to form a small circle of young people who thought as he did, set themselves the same tasks, and struggled for the same conditions as did their teacher.

But conditions were still very difficult. The only center for scholarly communication among Moscow physicists at that time was in the physics section of the Society of Devotees of Natural Science, Anthropology, and Ethnography. N. E. Zhukovsky presided over the section, and it met in the Polytechnic Museum. I first saw many outstanding people at these meetings, and heard many outstanding reports. One of the principal speakers was P. N., and later A. A. Eikhenvald, who returned to Moscow at the end of the nineties. But at the same time speakers of quite another sort appeared there as well. Here was one very “honored” pseudoscientist—with reports on the self-ignition of cotton. In his opinion, there is water in cotton, and for “some reason” it decomposes. Subsequently the hydrogen combines with oxygen, heat is released—and all the rest is clear. Another speaker, who played a large role in physics circles, related that electricity is a complex body consisting of one atom of positive and two atoms of negative electricity (at the same time an experiment on the electrolysis of water was shown, and “indeed,” two volumes of hydrogen and one volume of oxygen were obtained); he asserted that the results of his own experiments were connected with this, according to which supposedly the capacity of a Leyden jar for one electricity was twice as great as for the other...

P. N. would become utterly furious at such “reports.” We, his older pupils, having heard enough of his stories about Kundt’s colloquium, more than once pestered him with the request to try to start something similar among us. He looked at our still small group, smiled distrustfully, and refused. He himself did not yet know the size of the sprout that the seed of his propaganda had put forth. But he tried. The attempt succeeded, and P. N. himself caught fire, carried away by his new success. There is no stronger memory in our life than those unforgettable gatherings, at which we, from pupils, imperceptibly to ourselves grew into beginners, but already independent scholars, and at which our teacher revealed himself in a new, unprecedented brilliance. P. N.’s enormous erudition, brilliant inventiveness, precision of scientific characterizations, and wealth of memories appeared to us only here in their full stature. His colloquium—the first in Moscow and in all of Russia at that time—now numbers dozens, if not hundreds, of continuations.

In outward appearance P. N. stood out sharply among others: of enormous height, tremendous physical strength, and with a manly face of rare beauty. I saw and heard him for the first time in the old large auditorium of the Polytechnic Museum at a public meeting of the Society of Devotees of Natural Science, Anthropology, and Ethnography. He was reading a report on artificial diamonds obtained by Moissan. I remember his concluding words as if it were now: “But

“the finest diamond is not the one obtained by Moissan, but that tireless striving for knowledge which leads the scientist to overcome all difficulties and to win ever new benefits for mankind.” The listener could not fail to be struck by the tremendous temperament with which these words were spoken, by the flame of deep faith that at that moment lit up in his eyes.

Pyotr Nikolaevich died early—at only 46. He might have lived to our own day—his contemporaries are alive and working. Everything that he managed to accomplish was done by him in 20 years of scientific activity. But what he accomplished earned him undying glory. And those who worked with him and studied under him will carry in their souls the radiant image of their teacher to the end of their lives.