PYOTR NIKOLAEVICH
LEBEDEV

FROM THE HISTORY OF PHYSICS

THE WORKS OF P. N. LEBEDEV ON LIGHT PRESSURE

V. Fabrikant

...I must work at the limit of what I am able to accomplish at all...

P. N. Lebedev

I. INTRODUCTION

This year marks two notable anniversaries, both connected with the name of the great Russian physicist P. N. Lebedev. Exactly half a century ago, in 1900, P. N. Lebedev published the first communication on the results of his work on the experimental proof of the existence of light pressure on solid bodies. In 1910, forty years ago, P. N. Lebedev published his work on the investigation of the pressure of light on gases.

Lebedev’s investigations of light pressure brought him worldwide fame and are justly regarded as classical. What makes them classical is both the fundamental significance of the results and the astonishing experimental skill with which all the exceptional difficulties that stood in the investigator’s path were overcome. It is characteristic that, although P. N. Lebedev’s experiments on the pressure of light on solid bodies were later repeated by a number of investigators, the experiments on the pressure of light on gases have never been repeated by anyone. Everyone was deterred by the difficulty of these experiments.

In assessing the greatness of P. N. Lebedev’s scientific achievement, one must also take into account the conditions of scientific work in tsarist Russia, when there were no special research laboratories or institutes. P. N. Lebedev himself, in the article “The Russian Society and Russian National Laboratories,” vividly characterized these conditions (p. 352)¹: “...A Russian scientist who has both the ability and the desire to work in the field of pure science is, by the will of fate, placed in especially difficult conditions, owing to the serf-like dependence on

of educational institutions, and if we now, on the anniversary of February 19, read with a terrible feeling the recollections of how landowners pushed around their serf artists and forced them to paint fences, then perhaps with the same terrible feeling our descendants fifty years hence will read recollections of that educational servitude which the Mendeleevs, Sechenovs, Stoletovs, and the now flourishing major Russian scholars served out, merely in order to obtain the right to carry out their scholarly work, in order to pay for the possibility of glorifying Russia with their discoveries.” The entire article constituted P. N. Lebedev’s passionate appeal in favor of the creation of special scientific-research laboratories. In another article, devoted to Lomonosov, “In Memory of the First Russian Scholar,” he wrote: “... if one looks closely at the work of our outstanding scholars, one must assert that in most cases they produced major investigations not thanks to the conditions in which they worked in Russia, but in spite of them...” (p. 361)¹. The hard fate of Lebedev himself provides a vivid illustration of his words. Of great interest in this sense are the materials recently published by T. P. Kravets in the collection Scientific Heritage (p. 551)². The materials are preceded by a very substantial introduction written by T. P. Kravets; it has been extensively used by us in the present article, as has the biography of P. N. Lebedev written by P. P. Lazarev³.

In 1904 P. N. Lebedev, having been refused the allocation of a sum needed for the purchase of instruments, submitted a petition to the trustee of the Moscow Educational District, at the end of which he wrote: “I believe that four years of a helpless situation, during which I could not, through no fault of my own, obtain the possibility of teaching and working under at least somewhat tolerable conditions, as well as the scientific investigations published by me during that time (on light pressure), give me the right to count on such a position as is enjoyed and ought to be enjoyed by full professors of the university” (p. 617)².

Somewhat later, in a letter to B. B. Golitsyn (1905), P. N. wrote: “... the surrounding reality is some uninterrupted, stupefying nightmare, hopeless despair” (p. 599)². Yet flashes of despair, caused by his surroundings and by illness, were replaced by a new creative upswing. Characteristic is one of the letters of 1909, when Lebedev was working on the investigation of the pressure of light on gases: “Truly, I am again in love with my science, in love like a boy, indeed exactly as before: I am now so carried away, I work whole days, as if I had not been ill again—I am again the same as I was before: I feel my mental strength and freshness, I play with difficulties, I feel that I am Cyrano de Bergerac in physics...” (p. 602)².

Lebedev’s early death (at the age of 46) was undoubtedly connected with his departure in 1911 from Moscow University. His departure was caused by a protest against the police measures of the Minister of Education Kasso. This departure meant the destruction of the laboratory created by P. N. Lebedev, and he took it extraordinarily hard. Without any support from the state, using public funds, and with great difficulty, he had to create a new laboratory.

All the more respect is evoked by P. N. Lebedev’s resolute refusal to go abroad to work, where he was invited by a number of foreign scientific institutions. S. Arrhenius wrote to him: “Naturally, it would be a great honor for the Nobel Institute if you wished to settle and work there, and we would undoubtedly provide you with all the necessary means so that you could continue your work... You would, of course, receive a completely free position, as befits your rank in science” (p. 28)3.

S. I. Vavilov rightly notes that “P. N. Lebedev became the pioneer of a remarkable—and, for Russia, entirely new—endeavor: large-scale collective research work (p. 247)4. The number of students working under the direct supervision of P. N. Lebedev at one time reached almost thirty. One may judge P. N. Lebedev as a supervisor and teacher from his correspondence. Especially expressive in this respect is the “Instruction to the Student Altberg” (p. 572)2. In it, alongside entirely concrete technical directions concerning individual details of the experimental setup, there is an entire paragraph devoted to the subjective features of Altberg’s psychology and having a purely educational character.

2. SOME INFORMATION FROM THE HISTORY OF THE PROBLEM

The existence of light pressure follows necessarily and in a very vivid form from any corpuscular theory of light, simply as the result of the bombardment of an illuminated body by “light particles.” Conversely, from wave conceptions it is far from so simple and evident to arrive at the necessity of the existence of light pressure. This explains the peculiar history of the question of light pressure.

Before the emergence of the wave theory of light, light pressure was very widely and frequently used to explain various phenomena. In particular, as early as Kepler, in his work De Cometis (1619), advanced the hypothesis that comet tails are “blown” by light pressure in the direction opposite to the Sun. “An indication of the reason why, from the matter of the cometary body, something is continuously driven out by the solar rays, by the force of these rays, gave me the tail of the comet, about which it is known that it always moves away in the direction opposite to the Sun, and is formed by the rays of the sun.”

Ether was also convinced that comet tails are formed because of the pressure of light rays and, being an adherent of the wave theory of light, he did try—though in a not very detailed form—to justify, from wave conceptions, the necessity of the existence of this effect.

Sometimes these references to light pressure were anecdotal in character. In his review article “The Pressure of Light” (p. 381),¹ P. N. Lebedev quotes an excerpt from Gartsoeker (1696), who wrote that: “... travelers assert that the flow of the waters of the Danube is considerably slower when the rays of the sun oppose its motion (in the morning), and becomes more rapid after noon, when the rays of the sun aid its current.”

To this we may also add that Cyrano de Bergerac, in the philosophical utopia The Other World, or the States and Empires of the Moon (1659), jested: “Therefore I say that the sun’s rays, and the action proceeding from them, striking the Earth, make it rotate, just as we make a ball rotate by striking it with the hand.”²

In the eighteenth century De Mairan and Du Fay made the first unsuccessful attempts to detect light pressure experimentally. P. N. Lebedev highly valued the experimental skill (the use of a magnetic suspension), and, above all, the force of critical thought of his distant predecessors. Having obtained at first sight a positive effect, they rightly attributed this effect to the action of secondary causes having nothing in common with light pressure.

After the victory in the nineteenth century of the wave theory of light, the problem of light pressure for a long time lost its theoretical basis. In this sense it is significant that even one of the founders of the wave theory—Fresnel—refrained from expressing any theoretical considerations concerning the existence of light pressure, although he spent much effort on unsuccessful attempts to detect light pressure experimentally (1825).⁶

Later Crookes⁷, investigating in greater detail the causes of Fresnel’s failures, discovered a new phenomenon, the so-called radiometric effect, caused by the interaction of the surrounding gas with solid bodies nonuniformly heated by light. But Crookes also could not detect light pressure. The radiometric effect constitutes the principal obstacle in the investigation of light pressure.

Only in 1873 did Maxwell, while further developing the electromagnetic theory of light, theoretically substantiate (though not quite rigorously) the necessity of the existence of light pressure. In § 792 of the Treatise on Electricity and Magnetism it was said: “The quantity \(p\left(\frac{E^2}{8\pi} + \frac{M^2}{8\pi}\right)\) represents the numerical value of half the total energy in unit volume, which is contained in it, as the energy of electric polarization and as the energy of magnetic

polarization of the medium. As a consequence of the existence of magnetic energy, in the direction of the magnetic lines of force there arises a tension whose magnitude is equal to \(p\), while in directions perpendicular to them there is a pressure having the same magnitude \(p\).

The combined action of the electric and magnetic polarizations is expressed in the form of a pressure acting in the direction of propagation of the wave; its magnitude is \(2p\). In turn, \(2p\) represents the total energy of the ray per unit volume, and therefore in a medium in which waves propagate, in the direction of their propagation there arise pressure forces which “at every point of space are numerically equal to the magnitude of the energy in each unit volume.” P. N. Lebedev explains Maxwell’s line of reasoning as follows (p. 386)\(^1\): “In order to explain how light pressure arises, Maxwell makes use of the fundamental property of Faraday’s lines of force: this property consists in the fact that in the direction of action of these forces the polarized medium experiences a tension, while in the plane perpendicular to this direction the lines of force, repelling one another and tending to spread through the medium, produce a mechanical pressure on one another and on the surfaces bounding the medium.”

Maxwell’s arguments did not by any means seem convincing to all physicists. A rigorous derivation of light pressure, based on Maxwellian electrodynamics, was given much later, in 1901, by the Kazan physicist D. A. Goldhammer\(^8\). One should also note the work of A. I. Sadovsky on the ponderomotive action of light, which was undeservedly rejected at his doctoral defense\(^9\).

The development of the thermodynamics of radiation also led Bartoli, in 1876,\(^{10}\) to the necessity of postulating the existence of light pressure. The absence of light pressure would make it possible to violate the second law of thermodynamics by transferring heat from a colder body to a warmer one by means of radiation. Boltzmann, in 1884, gave particular clarity to thermodynamic reasoning, using the hypothesis of the existence of light pressure for a theoretical derivation of the well-known Stefan–Boltzmann law\(^ {11}\). In the same work Boltzmann evidently was the first to draw attention to the discrepancy between the magnitudes of light pressure calculated from corpuscular and from wave conceptions. As is known, the corpuscular point of view, using Newtonian mechanics for “light particles,” leads to a value of the light pressure twice as large as that given by the wave theory. Thermodynamic considerations did not yield the value of the pressure and, despite their generality, likewise were not convincing to everyone. The very legitimacy of applying thermodynamics to such an object as radiation aroused doubts. It should be remembered that in those years the thermodynamics of radiation was still only being created.

In 1874 Zöllner[^12] and in 1876 Bartoli undertook new, but again unsuccessful, attempts to detect light pressure experimentally. Radiometric forces interfered. Such was the situation when in 1890 the young P. N. Lebedev first became interested in the problem of light pressure.

3. REASONS THAT DREW P. N. LEBEDEV’S ATTENTION TO THE PROBLEM OF LIGHT PRESSURE

The reasons that drew P. N. Lebedev’s attention to the problem of light pressure are highly noteworthy. His approach to this problem is characteristic of P. N. Lebedev’s entire character as a scientist.

In one of the letters of that period P. N. Lebedev writes: “I believe I have made a very important discovery in the theory of the motion of luminous bodies, especially comets... The law found applies to all celestial bodies. I informed Wiener; at first he declared that I had lost my mind, and the next day, having understood what the matter was, congratulated me very warmly. At first I was in a state of great nervous tension, but now, when the law has been proved, I am not at all disturbed, partly, perhaps, because—I shall not conceal this—I am puzzled, even overwhelmed, by its generality, which at first I had not anticipated. The law I have derived is not a matter of a momentary inspiration: for about two years I have been carrying its beginnings within me. The question with which I have long been occupied I love with all my soul, as, I imagine, parents love their children” (p. 17).[^3]

This concerns the repulsive force of light-emitting bodies. Under this title, in 1891 P. N. Lebedev published in the Proceedings of the Physical Sciences Section of the Society of Lovers of Natural Science[^13] his first, as yet purely theoretical, work devoted to light pressure.

In this work P. N. Lebedev makes a very interesting comparison of the Newtonian force of attraction with the force of repulsion caused by light emission and acting between two spherical bodies. The cause of the repulsion is the pressure of the radiation emitted by one body on the surface of another body. P. N. Lebedev’s imagination was struck by the universality of this repulsive force, always competing with Newtonian attraction. Indeed, between all bodies with a temperature different from absolute zero there exists a force of radiant repulsion.

The force of radiant repulsion also depends on distance, as does Newtonian attraction. For the first time in history, while quantitatively analyzing the question of comet tails, P. N. Lebedev clearly speaks in favor of light pressure as the principal factor, and against the hypothesis of electrostatic repulsion of cometary particles by the Sun.

At the same time P. N. Lebedev indicates that the question of the pressure on individual molecules that make up comet tails,

is much more difficult than the question of the pressure of light on macroscopic bodies. For macroscopic bodies, considerably exceeding the wavelength of light in their dimensions, P. N. Lebedev derived the following simple formula for the relative magnitude of the difference between the forces of attraction and repulsion: the difference is referred to the magnitude of the Newtonian attraction (p. 65)\(^{13}\)

\[ K' = 1 - \frac{20}{r\delta RA}. \]

The formula was derived for absolutely black bodies at \(0^\circ\mathrm{C}\); \(r\) and \(R\) are the radii of the bodies, \(\delta\) and \(A\) are the densities of the bodies. As the dimensions decrease, the role of light pressure increases, which is quite natural, since Newtonian attraction is a volume effect, whereas light pressure is a surface effect.

Lebedev’s formula leads to a conclusion which even now may cause surprise. It turns out that the force of radiant repulsion between two bodies approximately the size of an apple (\(r = R \simeq 4\ \mathrm{cm};\ \delta = A \simeq 1\)) already prevails over the force of Newtonian gravitation. This agrees poorly with our usual notions of the enormous magnitude of gravitational forces and the smallness of the forces of light pressure. The whole point, of course, lies in the magnitude of the masses that produce Newtonian attraction. Below we shall see that modern astronomy regards light pressure as a very serious factor.

At the end of the article P. N. Lebedev draws attention to the fact that radiant interaction must be taken into account in the analysis of intermolecular forces. He writes: “The interaction of molecules may be considered as a more complicated case, as the action of resonators upon one another” (p. 65)\(^{13}\).

Thus a number of problems of an enormous range were posed—from celestial mechanics to the physics of intermolecular forces. We have seen that light pressure was at the center of attention of the greatest physicists of that time, as a consequence of Maxwell’s electrodynamics and as a necessary element of the thermodynamics of radiation. But for P. N. Lebedev light pressure was something greater: it was an essential factor of the entire universe, and we shall see below that P. N. Lebedev was right.

This is what determined the main direction of all the scientific activity of P. N. Lebedev. Proving the existence of light pressure became the principal work of his life.

4. EXPERIMENTAL INVESTIGATION OF THE PONDEROMOTIVE ACTION OF WAVES ON RESONATORS

In his diary on January 4, 1891, P. N. Lebedev sets forth a plan of work on the forces of wave pressure (p. 19)\(^{3}\).

In outlining this plan, he regarded light pressure as a special case of wave pressure in general and as a special case of

P. N. Lebedev’s Works on Light Pressure

interaction of resonators with one another and therefore decided to begin with an investigation of this interaction. Having organized a laboratory at Moscow University, P. N. Lebedev at once set about carrying out his plan. He performed a series of works under the general title “Experimental Study of the Ponderomotive Action of Waves on Resonators” (p. 84)³. In the first work, published in 1894, electromagnetic resonators were investigated; in the second—in 1896—hydrodynamic resonators; and, finally, in the third—in 1897—acoustic resonators. P. N. Lebedev very interestingly argues the necessity of investigating all three indicated types of resonators: “... transferring the investigations to oscillations that are different in their physical nature and finding a connection between the laws of their ponderomotive action on resonators, we thereby extend the applicability of the laws found to those cases as well in which both the mechanism of the oscillation itself and the mechanism of the resonator receiving it may remain unknown” (p. 88)³. P. N. Lebedev was not discouraged by the failure of such a well-known experimenter as Boys, who shortly before this had unsuccessfully tried to detect ponderomotive forces between two electromagnetic resonators.

The principal difficulties consisted, according to P. N. Lebedev, “in the methods of exciting correct and sufficiently strong oscillations, ... in measuring the wavelengths of the resonators, ... in working out the construction of a special type of resonator that would combine the possibility of varying its period over wide limits with the least weight of the apparatus,—all this took about three years of work” (p. 91)³. We cannot go into details here, but it should nevertheless be noted the exceptional experimental skill displayed by P. N. Lebedev in this series of works. It is enough to point to the choice of the form of the exciter of electromagnetic oscillations, eliminating electrostatic action (p. 93, Fig. 10)³; the introduction of a compensating body in experiments with oscillating balls (p. 117)³, etc.

In P. N. Lebedev’s experiments with electromagnetic and hydrodynamic resonators, the distances between the vibrators and the resonators were considerably smaller than the wavelength. For example, in the electromagnetic experiments the wavelength was equal to 350 cm, while the distance between the vibrator and the resonator was only a few centimeters. Therefore P. N. Lebedev obtained regularities characteristic of the interaction of closely situated oscillators. When the frequency of the vibrator was varied, the force acting on the resonator followed the course shown in Fig. 1 (p. 120)³.

“When the resonator is tuned higher, attraction is observed; when it is tuned lower, repulsion. The greatest magnitudes

these opposite ponderomotive forces take place in the immediate vicinity of resonance and continuously pass into one another” (p. 121)^3.

True, for electromagnetic resonators it proved impossible to observe directly the case of complete resonance—the conductors of the circuits became so heated that convection currents of air interfered with making measurements—but the entire remaining course of the curves coincided for resonators of both types.

In experiments with acoustic resonators P. N. Lebedev succeeded in increasing the distance between the source and the receiver of oscillations to a value somewhat exceeding the wavelength. At short distances the results obtained were the same as in the two preceding works. For large distances a new result was obtained, shown in Fig. 2. Between the source and the receiver there act only repulsive forces, reaching a maximum value at complete resonance.

Fig. 1.

Fig. 2.

It is interesting to note that P. N. Lebedev was at first even somewhat puzzled by this result, but then recognized in it an analogue of the repulsion of light-emitting bodies long before indicated by himself. This served as an impetus for P. N. Lebedev’s calculation of the pressure force exerted by a plane electromagnetic wave on an oscillator, which, in turn, played a major role in the preparation of experiments on the pressure of light on gases (see below).

For his work on the interaction of resonators P. N. Lebedev received the Russian degree of doctor without first passing the master’s examination and without submitting a master’s dissertation. It should be said that at that time only a few scholars held the Russian doctoral degree (this degree should not be confused with the doctoral degree, comparatively easily defended at foreign universities, which P. N. Lebedev received at the beginning of his scientific career).

5. INVESTIGATION OF LIGHT PRESSURE ON SOLID BODIES

After completing his investigation of the interaction of resonators in 1898, P. N. Lebedev set about his principal work of proving the existence of the forces of light pressure. He was armed with the experimental experience accumulated in carrying out his previous investigations, but the task was also a rather difficult one. This was attested by the failures of his predecessors.

The chief difficulty, of course, lay in the small magnitude of the expected effect. When a beam of parallel rays falls normally on a plane surface, the light pressure should be determined by the following formula:

\[ p=\frac{E}{c}(1+\rho), \tag{1} \]

where \(E\) is the energy incident in one second on \(1\ \mathrm{cm}^2\), and \(\rho\) is the coefficient of reflection of the surface. According to the calculations of Maxwell and Bartoli, the pressure of the Sun’s rays should have lain within the limits from \(4\cdot 10^{-8}\) grams per \(1\ \mathrm{cm}^2\) for a black surface to \(8\cdot 10^{-8}\) grams per \(1\ \mathrm{cm}^2\) for an ideally reflecting surface.

In his treatise (§ 793) Maxwell indicated a possible method for detecting light pressure. This method appears simple externally, but contains great difficulties: “Concentrated electric light will probably produce still greater pressure (than sunlight), and there is nothing impossible in the fact that the rays of such light, falling on a thin metallic plate, easily suspended in a vacuum, will exert a perceptible mechanical action on this plate.”

P. N. Lebedev writes: “When I set about my experiments, I believed that the arrangement indicated by Maxwell would not lead to the goal, since on this path Tsöllner had already suffered failure; he had drawn attention to the circumstance that the numerical magnitude (of the light pressure) theoretically predicted by Maxwell is approximately 100,000 times (a later and correct calculation gives 10,000, V. F.) smaller than that which Crookes observed in one particular case (the radiometric effect). If it was possible to hope to reduce these secondary radiometric forces to a very considerable degree, still, it seemed to me, decisive significance could belong only to an experiment in which it would be possible in some way to compensate the action of these forces” (p. 154)\(^3\).

P. N. Lebedev decided to make use of the circumstance that radiometric forces are internal forces of the radiometer and therefore should not cause motion of the radiometer as a whole. Having made a miniature radiometer of mica, with a wing placed inside it and rigidly fastened to it, he suspended this radiometer on a thin thread in a glass bulb, from which

air had been pumped out. When the wing was illuminated by the light of an arc lamp, deflections were observed which, in order of magnitude, coincided with those that should have been produced by light pressure. The results of these preliminary experiments were reported by P. N. Lebedev on May 17, 1899.

However, already in the preliminary experiments P. N. Lebedev became convinced that the radiometric forces could be made very small and that “the disturbance caused by them proves to be even less than the disturbance due to convection” (p. 156)3.

Therefore, after a two-year study of radiometric forces, he returned to a simpler and at the same time more convincing method for detecting light pressure. P. N. Lebedev understood that the aim of his experiments consisted first and foremost in a convincing proof of the very fact of the existence of light pressure and therefore he paid primary attention to the evidential force, in this sense, of the experimental method. He pointed out: “However simple Maxwell’s arrangement of the experiment may be, it nevertheless encounters two substantial difficulties, caused, on the one hand, by convective currents, and on the other—by radiometric forces. At the highest rarefactions these secondary forces are considerably reduced, but even so they must still be reckoned with in measurements of light pressure” (p. 156)3.

Convective currents arose as a result of the heating of the layers of gas adjacent to the wing. This heating was caused, in turn, by the heating of the wing by the absorbed radiant energy. The danger of ascending convective currents lay in the fact that, even with a slight inclination of the plane of the wing relative to the vertical, these currents exerted an additional pressure on it and caused a noticeable displacement of the wing. However, the direction and magnitude of this displacement depended only on the degree of heating of the wing and of the gas, and did not depend on the direction of the incident rays. This circumstance was very astutely used by P. N. Lebedev to eliminate the role of convection. He simply made the rays fall alternately on one side and then on the other side of the wing.

To reduce the radiometric forces, the greatest possible rarefaction was achieved in the radiometer bulb. In addition, the wings were made of thin metal so as to reduce, as far as possible, the temperature difference between the two surfaces, which is the cause of the appearance of radiometric forces. It is clear that the thinner the wing, the smaller this temperature difference. To determine the correction for radiometric forces, P. N. Lebedev applied a very simple and elegant procedure, namely: “... if we simultaneously observe two

identical vanes having a very considerable difference in thickness, then we can calculate how large the deflection caused by the light beam would have been if the thickness of the vane had been equal to zero.” P. N. Lebedev notes that, in general, corrections for radiometric forces had to be made only for platinized vanes: for vanes with mirror surfaces the radiometric forces were vanishingly small, evidently owing to the small absorption of energy by the vanes.

P. N. Lebedev also feared the influence of certain hypothetical effects connected with the sputtering of illuminated bodies, but these effects would have depended strongly on the wavelength of the incident radiation and on the material of the vanes, which made it possible to set up the corresponding control experiments.

Let us proceed to a description of the details of the experimental apparatus.

Figure 3 shows the optical scheme of the entire apparatus (p. 158)3. This scheme corresponds so well to the problem posed that even now, after 50 years, hardly any substantial changes could be introduced into it.

Fig. 3. Scheme of the apparatus.

The image of the crater \(B\) of a thirty-ampere arc, by means of the condenser \(C\), was focused on the metal diaphragm \(D\) with an aperture \(d = 4\) mm. The diverging beam emerging from the diaphragm was transformed by the lens \(K\) into a parallel one. To absorb infrared rays (“ultra-red,” as P. N. Lebedev calls them), behind the lens there was a glass vessel \(W\) filled with water. A light filter could also be placed here, or the pure water could be replaced by a blue ammoniacal solution of copper salt. Farther on, the system of plane mirrors \(S_1\), \(S_2\), \(S_3\), \(S_4\), \(S_5\), and \(S_6\) made it possible to change by \(180^\circ\) the direction of the rays falling on the vane of the radiometer \(R\). In the arrangement shown in Fig. 3, the light beam, after successive reflections from the mirrors \(S_1\), \(S_2\), and \(S_3\), was focused by the lens \(L_1\) on

the little vane \(R\), directed from right to left. When the double mirror \((S_1, S_4)\) was shifted to the right, the light beam traveled the path \(S_4, S_5, S_6\) and was focused by the lens \(L_2\), now having the direction from left to right. Let us recall that this change of direction was necessary in order to eliminate the influence of convection. The light source chosen by P. N. Lebedev was, for that time, the most rational and sufficiently powerful one, but it is evident that much trouble was caused by the instability of its mode of combustion. P. N. Le-

Fig. 4. Movable part of the radiometer.

bedev notes that only the use of coals of the best grade made it possible to carry out the observations (p. 168)\(^3\). A modern optician would probably replace the arc with an ultra-high-pressure mercury lamp, but it should be remembered that UHP mercury lamps did not yet have even 20 years from their birth. To monitor the brightness of the light beam, P. N. Lebedev introduced into the path of the light a thin glass plate \(P_1\), placed at an angle of \(45^\circ\). The light reflected by this plate fell on a thermopile of five constantan-iron junctions. The thermocurrent was measured with a galvanometer. It is characteristic that already at that time P. N. Lebedev preferred to use the method of objective photometry. To compensate for the losses in the plate \(P_1\), on the second path of the light beam, behind the lens \(L_2\), an identical plate \(P_2\) was installed.

No less carefully thought out were the three designs of the movable parts of the radiometer, shown in Fig. 4. Here the second design was especially elegant, making it possible to avoid noticeable light pressure on the parts supporting the vanes.

The experiments were carried out with the following vanes.

By “platinized platinum” is meant platinum coated with platinum black. The use of vanes of different thicknesses, as we have already indicated, made it possible to exclude the action of the radiometric force. The movable part of the radiometer was suspended on a thin glass thread, to which a small mirror was attached, serving for the measurement of the angle of rotation of the entire system. The use of mirror readout greatly increased the sensitivity of the apparatus.

The most difficult thing, given the level of experimental technique of that time, was, of course, to obtain a sufficiently high vacuum. To fasten the thread to the bulb it was necessary to use a ground joint with mercury sealing. The pump used by P. N. Lebedev (a fore-vacuum pump in modern terminology) gave, even from the present-day point of view, a good vacuum (less than \(10^{-4}\) mm Hg). Even now, obtaining such a vacuum without the aid of diffusion pumps is regarded as evidence of the fairly good quality of a fore-vacuum pump.

However, even this vacuum was insufficient for the required weakening of convective disturbances—chiefly precisely convection currents, as P. N. Lebedev himself indicates (p. 179)\(^3\), and not radiometric forces, as is usually written when describing Lebedev’s experiments.

Remarkable is the method used by P. N. Lebedev to obtain still greater rarefaction (see Fig. 5): “... a drop of mercury \(Q\) was placed at the bottom of the glass bulb \(B\), then the air was rarefied by the pump, and the mercury drop was heated in a water bath \(K_1\) to \(5^\circ\) C above room temperature; evaporating, the mercury is drawn into the pump and carries with it the remaining air from the bulb. If the bulb is separated from the pump and the desiccator \(P\) by means of the barometric seal \(V\), then only mercury vapors will remain in the bulb; their pressure will decrease to a very small value if the vessels \(K_1\) and \(K_2\) are filled with a cooling mixture of ...

ice and salt” (p. 164)³. We see that, “playing with difficulties,” P. N. Lebedev discovered and applied the principle of operation of diffusion pumps—the foundation of all modern vacuum technology. This was done many years before the official invention of diffusion pumps.

The energy of the incident light beam was measured by means of a calorimeter. The measurements showed that the illumination of the vanes was from two to three times greater than the illumination of the earth’s surface by the sun’s rays.

Fig. 5. Diagram of obtaining a vacuum.

Before beginning the measurements, P. N. Lebedev carefully checked the influence of possible inaccuracies in the adjustment of all elements of the apparatus.

The experiments themselves had to be conducted with an assistant, who watched the burning of the arc and moved the mirror \(S_1S_4\). P. N. Lebedev writes: “My assistant in these experiments was the preparator’s assistant in the laboratory, Avtonom Fyodorov; his conscientious attitude and skillful handling of the instruments greatly facilitated these difficult observations for me.”

In the actual conduct of the observations, P. N. Lebedev’s experimental skill also showed itself. He did not wait for the system with the vanes to calm down, but, on the contrary, observed the displacement of the equilibrium position during rather large oscillations of the system. In this, evidently, the phenomenon of resonance was used. P. N. Lebedev points out: “By closing the illumination with periodic interruptions, one can bring the amplitude of the instrument’s oscillations up to the required magnitude” (p. 168)³. The displacements of the equilibrium position when the direction of illumination was changed amounted to from 30 to 40 divisions of the scale, which constituted the effect of light pressure. Regarding radiometric forces, P. N. Lebedev writes the following: “... I repeatedly made comparative measurements on thin and thick metallic (mirror), platinum, and aluminum vanes; however, I was unable to detect a sufficiently clearly expressed radiometric difference; that is why, within the limits of the errors of observation, the radiometric forces of thin metallic vanes may be considered equal to zero” (p. 179)³. Thus, the use of metallic

vanes with high thermal conductivity eliminated the main cause of the failures of previous investigators.

To determine the magnitude of the force of light pressure from the deflections obtained, it was necessary to determine the elasticity of the suspension thread. This was done by observing the oscillations of a body with a known moment of inertia, suspended on the same thread. For platinum-plated vane No. 2, in this way a value equal to \(3.08 \cdot 10^{-6}\) dynes was obtained. For comparison with theory, P. N. Lebedev made calorimetric measurements of the energy of the light beam and determined the reflection coefficients of the vanes needed for using the formula. P. N. Lebedev assessed the accuracy of his measurements very carefully and rigorously. The value of the total error that he gives, \(\pm 20\%\), is undoubtedly an upper limit.

The following detail is characteristic. P. N. Lebedev writes: “When I passed from observations at room temperature... to measurements under cooling with ice and salt, I did not expect to obtain such agreement between the observed quantities and those calculated according to Maxwell–Bartoli, which followed from my experiments; I therefore supposed that such a coincidence of calculations and observations should be attributed to chance, and therefore first replaced calorimeter I by calorimeter II, and then also instrument II with vanes by instrument III” (p. 177)\(^3\). Far from every experimenter who has obtained the desired agreement of theory with experiment would have acted as P. N. Lebedev did. Therefore the conclusions of P. N. Lebedev’s work sounded with special persuasiveness:

“1) An incident beam of light produces pressure both on absorbing and on reflecting surfaces; these ponderomotive forces are not connected with the already known secondary convection and radiometric forces caused by heating.

2) The forces of light pressure are directly proportional to the energy of the incident ray and do not depend on color.

3) The observed forces of light pressure, within the limits of observational errors, are quantitatively equal to the Maxwell–Bartoli forces of pressure of radiant energy” (p. 179)\(^3\).

The history of the publication of this classic work is instructive. Let us cite some testimony of P. N. Lebedev’s pupils. P. P. Lazarev, in his biography of P. N. Lebedev, writes\(^1\):

“Exhausted by the preceding pedagogical work and examinations (‘academic corvée,’ V. F.), P. N. during the summer of 1900 felt so ill that he could not himself perform those mechanical manipulations connected with the investigation, and during observations he was helped by an attendant in the physics laboratory. Once, during an experiment, because of an accidental jolt while pumping out, the thin thread with the instrument detecting pressure broke, and the instrument was spoiled; to the sick P. N.

it did not seem possible for him to rebuild his apparatus again, and he, although he did not regard his investigation as fully completed in the sense of precision, found it necessary to publish it “in the form in which it was at that moment.” He published a preliminary communication in the Journal of the Russian Physico-Chemical Society^14 and in August 1900 delivered a report at the First International Congress of Physics in Paris. This preliminary communication already contained all the principal results of the work and, as T. P. Kravets writes (p. 556)^2: “The date of this communication marks a sharp turn in P. N.’s scientific life: before it he had been a physicist who attracted attention; after it he became famous. Lebedev himself, however, was not satisfied with his work and immediately after the congress set about bringing it to its final form. He worked on it with extreme strain and by the summer of 1901 had brought himself to a state of complete exhaustion.” In 1901, the full exposition of the work was published in the Journal of the Russian Physico-Chemical Society.^15

In 1904, on the initiative of a commission that included such major scientists as A. M. Lyapunov, B. B. Golitsyn, and A. A. Belopolsky, the Academy of Sciences unanimously awarded P. N. Lebedev a prize for having succeeded “in proving brilliantly by experiment the undoubted existence of light pressure” (p. 615)^2.

The decision of the academic commission also noted the great importance of investigations of light pressure for astronomy. The size of the prize is curious—2862 rubles 60 kopecks. Later the Academy of Sciences elected P. N. Lebedev its corresponding member.

Of the numerous enthusiastic responses by foreign scientists, let us cite only the two most interesting—those of Kelvin and Paschen. Kelvin said to K. A. Timiryazev: “You may know that I fought all my life with Maxwell, not acknowledging his light pressure, and now your Lebedev has forced me to surrender before his experiments” (p. 244)^4.

F. Paschen, in a letter to P. N. Lebedev of December 10, 1900 (p. 569)^2, wrote: “I consider your result one of the most important achievements of physics in recent years. I value the difficulties of your experiments all the more because I myself, some time ago, set myself the goal of proving light pressure and carried out similar experiments, which, however, did not yield a positive result, because I was unable to exclude radiometric effects. Your skilful method, consisting in throwing light onto metallic disks, is the key to resolving the question.”

In the numerous works repeating P. N. Lebedev’s experiments on the pressure of light on solid bodies, there is little of princi-

initially new results, and we shall not dwell on them. It is necessary, however, to say a few words concerning the work of Nichols and Hull. The first communication on this work appeared in 1901, a year after P. N. Lebedev’s first communication. Nichols and Hull used a method of eliminating radiometric forces that was fundamentally different from P. N. Lebedev’s. They worked at comparatively high gas pressures (12 mm Hg) and with glass vanes, which had poor thermal conductivity. In doing so, use was made of the circumstance that the radiometric effect, at a certain pressure, changes sign, passing through zero. In the literature, sometimes even in Russian, it has been stated that Nichols and Hull, although later than P. N. Lebedev, obtained the same result as he did. This is completely incorrect, for the experiments of Nichols and Hull in no way possessed the evidential force of P. N. Lebedev’s experiments.

P. N. Lebedev himself evaluated the results of Nichols and Hull as follows: “Nichols and Hull must base themselves on the hypothesis that, even with the brief illuminations they used, the same equilibrium of radiometric effects takes place as is observed under stationary illumination.”

“It seems to me that it would be more correct to use Nichols and Hull’s work for the converse conclusion, namely, while admitting the existence of light pressure, to assert that the curious transition of radiometric phenomena through zero at certain pressures, discovered by Crookes, does not depend on the duration of illumination” (p. 394)^1. T. P. Kravets cites Gerlach’s opinion, which fully confirms P. N. Lebedev’s assessment: “He (Gerlach) believes that the only thing that can be said about Nichols’s experiments is that they do not contradict our conviction, independent of them, that light pressure exists in reality” (p. 558)^2. It must be emphasized that this was said by a major physicist who repeated P. N. Lebedev’s experiments with the full equipment of modern experimental technique. Therefore, Wood’s attempt to exaggerate the significance of the experiments of Nichols and Hull^16 is entirely at variance with the truth.

After completing his work on the pressure of light on solid bodies, P. N. Lebedev entrusted his students with the investigation of the pressure of sound waves and of waves on the surface of a liquid. It is important to note that these experimental works, which yielded very valuable results, preceded the corresponding theory. Strange as it may seem, the theory of the pressure of waves that are simpler in their mechanism lagged behind the theory of the more complex electromagnetic waves. Finally, it is quite surprising that, until the very...

until recently there has been a well-known confusion in these questions. For example, it was not always clear what pressure is measured in experiments with ultrasonic waves (“Rayleigh” or “Langevin”)^17.

P. N. Lebedev was always clear about the generality of the phenomena of wave pressure. In his letter to N. P. Kasterin of January 30, 1902, he writes (p. 592)^4: “One large question has long been teasing me... experiments with ponderomotive forces of waves of the most varied physical nature; their action on resonators and walls always reduces to energy, to the velocity of propagation of the wave, and, in the case of resonators, also to the relation of the oscillations. In the final formulae only these quantities enter; hence only they are necessary throughout the entire argument; but we derive light pressure in two ways (and Bartoli’s path seems to me much more natural in essence than the electromagnetic one, in which I am terribly at variance with N. N. Schiller), and sound pressure in a third way, and hydrodynamic pressure in a fourth, etc.” Such a more general approach is, to a certain extent, the use of the concept of the momentum of a wave and of the law of conservation of momentum. This approach enriched the physical content of the Umov–Poynting vector and, for electromagnetic waves, is connected with the fundamental problem of inertial mass. At the same time, the momentum approach brings the wave treatment closer to the corpuscular one (of course, already within the framework of photon concepts).

6. EXPERIMENTAL INVESTIGATION OF THE PRESSURE OF LIGHT ON GASES

If in experiments on pressure on solid bodies P. N. Lebedev relied on clear, although not universally accepted, predictions of theorists, then in the question of the pressure of light on gases the situation was the reverse. Schwarzschild^18, using the theory of diffraction, came to the conclusion that the effect of the pressure of light on free gas molecules should be vanishingly small.

We have already indicated above that for P. N. Lebedev from the very beginning it was clear (especially after work with acoustic resonators) that it was necessary to take the phenomenon of resonance into account when considering the pressure of light on individual molecules. Allowance for resonance leads to a colossal increase in the effective cross section of a molecule. P. N. Lebedev’s idea was, with the appropriate reference, developed in detail in Debye’s work^19, which appeared considerably later. Let us recall that the effective cross section of a quasielastic oscillator, small in comparison with the wavelength, no longer depends on the true dimensions of the oscillator and is of the order of the square of the wavelength. For a light wavelength of \(10^{-5}—10^{-4}\) cm this amounts to \(10^{-10}—10^{-8}\) cm\(^2\), which exceeds by six to eight orders of magnitude the gas-kinetic cross section of a molecule, \(10^{-16}\) cm\(^2\). As is known, for

for a rigorous quantitative calculation of the cross section, knowledge of the oscillator strength and of the form of the spectral line is necessary.

For the gas layer as a whole P. N. Lebedev proceeded from the perfectly correct relation:

\[ p=\frac{\alpha E}{c}, \tag{2} \]

where \(p\) is the light pressure, \(\alpha\) is the absorption coefficient of the gas layer, \(E\) is the radiant energy incident in one second on \(1\ \text{cm}^3\). This relation follows most simply from the law of conservation of momentum and is not connected with any hypotheses concerning the mechanism of interaction of the light wave with the molecules of the gas. For example, it is immaterial whether true absorption occurs or only scattering of light (owing to the absence of a resultant momentum in the secondary waves).

Judging from the entry in the diary for 1894, P. N. Lebedev at first intended to make use of gases and vapors possessing absorption bands in the visible part of the spectrum—NO\(_2\), I, Br, and Cl. In the final version of the work, however, he turned to gases absorbing infrared rays—methane, propane, butane, ethylene, acetylene, and carbon dioxide. Evidently the reason for this choice was the more successful, in this case, combination of the optical characteristics of the light source and the absorbing gas and, in addition, convenience in the work. A. K. Timiryazev indicates that P. N. Lebedev spent about ten years on the work on light pressure on gases. “Many times he was compelled to abandon the work, since he could not devise means for overcoming the difficulties standing in the way.”\(^ {20}\)

P. N. Lebedev himself writes that “the present work occupied more than three years of time” (p. 200)\(^3\); but by this he evidently means only the final, concluding stage of the work.

Published in 1910 in the Journal of the Russian Physico-Chemical Society, P. N. Lebedev’s article “An Experimental Investigation of the Pressure of Light on Gases”\(^ {21}\) reads like a fascinating tale of the experimenter’s utterly astonishing struggle with the immeasurable difficulties of the investigation. This is aided by the old, good manner of exposition, in which the author does not present the finished result in a “smoothed” form, but acquaints the reader in detail with all the difficulties and dangers encountered along his path. With such a manner of exposition one can always assess the reliability of the results obtained in the work. In the modern telegraphic style of presentation all this remains on the author’s conscience.

This is how P. N. Lebedev describes the basic principle of the method he chose: “… rays of light, exerting pressure on individual molecules, must set the whole mass of gas in motion in the direction of propagation of the light. Since the absorption coefficients of gases are very small, the forces with which

the light exerts on the gas are very small and even under the most favorable experimental conditions barely reach one hundredth of the pressure which the same beam of light would exert on a black surface. In order to be able to measure these small forces, the experiment was arranged in such a way that the gas could freely move in the direction of the rays penetrating it and produce pressure on a very sensitive piston apparatus (p. 197)3.

After the construction and testing of more than twenty different designs, P. N. Lebedev settled on the apparatus shown in Fig. 6. At the bottom of the figure is shown a section of the apparatus by the horizontal plane in which the light beam lay. The ingenuity of the scheme of this apparatus consists in the fact that the light beam penetrates the volume \(G\), filled with gas, without acting directly on the light piston \(B\), brought out into the neighboring unilluminated channel. The direct pressure of the light beam on the piston, according to what has been said above, would exceed by several orders of magnitude the desired pressure on the gas. The pressure of light causes motion of the gas in the direction indicated by the arrow, and a pressure difference arises between the windows \(F_1\) and \(F_2\). The resulting pressure difference of the gas tends to equalize through the unilluminated channel and sets the piston \(B\) in motion.

Fig. 6. Apparatus for investigating the pressure of light on gases.

The piston \(B\), with counterweight \(Z\), is fastened to the beam of a sensitive torsion balance, suspended on a quartz thread \(Q\). On the same thread is fastened a small mirror \(A\) for reading the angles of rotation. One division of the scale corresponded to a pressure difference equal to \(1.4 \cdot 10^{-6}\) dyn/cm\(^2\), i.e. \(10^{-9}\) g/cm\(^2\). The piston, of miniature dimensions, was made of a light magnesium alloy (weight less than \(0.03\) g), and, in order to eliminate attraction caused by the contact potential difference, the channel had to be bored in a sleeve made of the same material.

The optical layout of the apparatus is shown in Fig. 7. A Nernst pin served as the light source. The arc had to be abandoned because of its instability, although this was also associated with a roughly tenfold reduction in the observed effects. The light from the pin \(N\) was focused by a mirror (of high aperture) \(S\), silvered on the outside, onto the diaphragm \(O\). In front of the diaphragm there was placed a thin piece of fluorite \(F\), which absorbed the long infrared rays; this was essential, since it prevented absorption of these rays in the fluorite windows \(F_1\) and \(F_2\) of the apparatus itself and thereby eliminated their very dangerous heating.

After the diaphragm \(O\) there was placed a double silvered prism \(P_1P_2\) with smooth pneumatic control. At will, the light beam could be directed either onto the mirror \(S_1\) or onto the mirror \(S_2\), changing the direction in which the rays passed through the gas by \(180^\circ\). The mirrors \(S_1\) and \(S_2\) (which had a rather large aperture—\(1:4\)) focused the image of the diaphragm in the gas space of the piston apparatus.

Fig. 7. Optical layout of the apparatus.

To obtain the required sensitivity, the reading scale \(K\) had to be placed at an enormous distance—5.3 meters. The scale was observed in the tube \(B\) with the aid of the small mirror of the piston apparatus. Even at such a distance the observed displacements did not exceed two scale divisions, and in most cases amounted to only a few tenths of a division! Therefore P. N. Lebedev had to pay special attention to the quality of the entire reading system, and he succeeded in obtaining reliable readings with the required degree of accuracy. At the same time even zero drift, that scourge of experimenters, was used to eliminate systematic errors. The absorption of light in the gas layer was determined with the aid of two thermoelements. Here, too, enormous difficulties arose, associated with the very small values of the absorption coefficients, of the order of several tenths of a percent. Even today the determination of an absorption amounting to tenths of a percent is regarded by opticians as a very difficult task.

But, of course, the most difficult struggle was with convection currents in the volume of the gas. The currents were caused by the nonuniform absorption of radiation and by the associated nonuniform heating of the gas. Above all, the front layers of gas served as a kind of light filter for the more distant layers; then the beam of light penetrating the gas had to be made convergent in order to gain in intensity.

It is obvious that, with a strictly horizontal arrangement of the apparatus, all these effects could not have caused a displacement of the piston, but in practice there could almost always exist a slight inclination of the axis of the channel.

Fig. 8. Lebedev’s apparatus for measuring light pressure on gases.

Here P. N. Lebedev’s experimental sense and powers of observation came to the rescue. Even while carrying out the preliminary experiments, he noticed that ordinary illuminating gas gave more stable results than the purer acetylene and carbon dioxide. P. N. Lebedev had the idea that this was explained by the better thermal conductivity of illuminating gas, caused by an admixture of hydrogen. An increase in thermal conductivity leads to an equalization of temperatures and to a weakening of convection currents. After this P. N. Lebedev deliberately added hydrogen to all the gases under investigation. He writes (p. 207)\(^3\): “Only this procedure made it possible to measure the forces of light pressure acting on a gas with the necessary confidence.” But even when hydrogen was added

it was necessary to display virtuoso skill in the proper adjustment of the instrument, eliminating the role of convection currents. P. N. Lebedev artificially produced, by means of an inserted blackened aluminum grating, nonuniform heating of the air, which did not absorb radiation, and achieved such an adjustment of the instrument that heating of the grating by illumination caused no displacement of the piston. Subsequently he found a somewhat simpler method of adjustment, but one based on the assumption of the validity of formula (2). To obtain each experimental point, 31 readings were taken at intervals of 30 seconds and with changes in the direction of the rays. As in the first work, special measurements were made for the absolute calibration of the instrument and for determining the energy of the incident rays \(E\).

From the summary table of measurement results it is evident that, for methane, ethylene, acetylene, and carbon dioxide (mixed with hydrogen), when the direction of illumination was changed, mean displacements of the scale were observed quite steadily, lying within the limits from 0.55 to 0.85 of a division, with a scatter of \(\pm 0.05\)—0.07 of a division. The absorption coefficients were then 0.55—0.72 percent. At P. N. Lebedev’s request, N. D. Zelinskii prepared propane and butane for him. These gases possessed “strong” absorption, amounting to approximately two percent. Accordingly, the displacements of the scale increased to approximately two divisions. Such “large” displacements P. N. Lebedev could measure with high accuracy. The agreement of the pressure values theoretically calculated by formula (2) with the experimentally measured ones proved entirely satisfactory. It is curious to note here that, in general, the best agreement was observed for the weakly absorbing gases.

P. N. Lebedev, with complete justification, concludes his work with the following conclusions:

“1) The existence of the pressure of light on gases has been established experimentally.

2) The magnitudes of this pressure are directly proportional to the energy of the beam of light and to the absorption coefficient of the gas.

3) Within the limits of the errors of observations and calculations, relation (2) quantitatively satisfies the observations.

Thus, the hypothesis of the pressure of light on gases, put forward three hundred years ago by Kepler, has now received both theoretical and experimental substantiation.”

We have already said at the beginning of the article that to this day no one has ventured to repeat these experiments of P. N. Lebedev.

Looking at this problem through the eyes of a modern optician, one may say that there is now the possibility of a more advantageous combination of the optical characteristics of the source of radiation and of the absorbingך

gas. P. N. Lebedev was forced to use a source with a continuous spectrum; today it would be possible to use a resonance lamp. For example, taking a low-pressure mercury lamp, one could illuminate its mercury vapor. The absorption of the radiation could then be made close to complete, i.e. approximately two orders of magnitude greater than it was in P. N. Lebedev’s experiments. But it by no means follows from this that the solution of the problem became easy. First, resonance lamps have a low surface brightness, which makes them of little use in optical systems. Second, eliminating the role of convection currents under such conditions would probably be even more difficult than it was in P. N. Lebedev’s experiments.

Regardless of the development of the technique of physical experiment, P. N. Lebedev’s work will always remain a model of experimental art.

Schwarzschild was compelled, in a letter to P. N. Lebedev of February 9, 1910, to write: “I remember well with what doubt I heard in 1902 about your proposal to measure the pressure of light on a gas, and I was filled with all the greater astonishment when I read how you had removed all the obstacles” (p. 26)^3. V. Wien, in a letter to V. A. Michelson, wrote that Lebedev “possessed the art of experimentation to such a degree as hardly anyone else in our time.” The Royal Institution of Great Britain elected P. N. Lebedev an honorary member for his work on the pressure of light on gases. Finally, H. Lorentz, in his letter to P. N. Lebedev’s wife (of May 1, 1912) on the occasion of his death, wrote: “I considered him one of the first and best physicists of our time, and admired how, in the last year, under the most unfavorable conditions, he was able to preserve intact the Moscow school he had founded and to find the possibility of continuing the common work” (p. 606)^2.

7. THE ROLE OF LIGHT PRESSURE IN THE UNIVERSE

The problem of comet tails, which drew P. N. Lebedev’s attention to light pressure, has its own long and complex history. For a long time, Newton’s very distinctive theory enjoyed recognition. Here is how the famous Russian astronomer F. A. Bredikhin sets forth this theory in his classic work On the Tails of Comets: “Newton assumes that the ether surrounding the head of a comet forms around the Sun an atmosphere with density increasing toward it. Heated by rays refracted and reflected from the nucleus, this ether around the comet becomes lighter and is attracted to the Sun less than the rest of the ether adjacent to it. As a result, it begins to move away from the Sun and carries with it the lightest particles of the comet, like

“...as rarefied air rises in a stove flue and carries smoke with it”²².

In recent years the optical point of view (light pressure) and the electrical point of view (electrostatic repulsion) have been competing. For the electrical theory it is necessary to endow the Sun with a hypothetical electric charge. To calculate the forces of light pressure it is necessary to know the oscillator strengths for the molecules that make up cometary tails. Here, until very recently, there was fundamental confusion. It has recently been possible to show that these oscillator strengths had been greatly underestimated. It may now be regarded as established that the forces of light pressure play a very substantial role in the formation of cometary tails.

The role of the pressure of light on gases inside stars is also great. According to the ideas of some astrophysicists, even the limiting size of stars is determined by the forces of light pressure. When too large a star is formed, the radiation of its core, heated to a very high temperature, casts off the excess matter by the forces of light pressure.

There is one curious circumstance which, so far as we know, has not been noted in the literature.

The problem of the distribution function of molecules located in a light beam leads to the appearance of new terms in the kinetic equation. In fact, the force of light pressure acting on a molecule, because of the Doppler effect, depends on the velocity of motion of the molecule. This dependence will be very strong even for a continuous spectrum of the light source, since the front layers of the gas rapidly form narrow absorption lines. The dependence of the force on the velocity makes Liouville’s theorem invalid, and in the kinetic equation there will appear terms of the type \(f \dfrac{\partial X}{\partial \xi}\), where \(X\) is the component of the force and \(\xi\) is the component of the velocity.

In recent years works have appeared indicating the very great significance of light pressure on macroscopic solid bodies. Of course, Cyrano de Bergerac’s joke has remained a joke, but it has turned out that in the mechanics of cosmic dust, for particles with sizes up to centimeters, the action of light pressure must be taken into account.

V. G. Fesenkov, in the monograph Meteoric Matter in Interplanetary Space (p. 101)²³, examines in detail one important and at the same time paradoxical effect caused by light pressure. The light pressure of the Sun’s rays should cause particles of certain sizes to fall onto the Sun. The discussion concerns particles with sizes from several tens of microns to centimeters. For such particles, light pressure, directed along the radius vector away from the Sun, is negligible in comparison with Newtonian attraction. But if the rotation of the particles around

of the Sun, it is not difficult to establish that there will exist a tangential component of the light pressure directed opposite to the motion of the particle. The appearance of the tangential component is caused by the aberration of light as a result of the motion of the particle relative to the light source (the Sun). Owing to aberration,

Fig. 9. Aberration and light pressure.

the vector of light pressure will make with the radius vector an angle equal to the ratio of the velocity of motion of the particle to the velocity of light (see Fig. 9). Of course, this angle is small (for the Earth it is equal to \(20''.5\)), and the tangential component of the force of light pressure determined by it is small; but it should be remembered that this force no longer has any competitors. As a result of radiation braking, the particle describes a spiral orbit, approaching the Sun. V. G. Fesenkov derives a very simple formula for the time of a particle’s falling onto the Sun (p. 114)\(^{29}\):

\[ \tau = 6.5 \cdot 10^{6} \rho r_0^2 \text{ years}, \]

where \(\rho\) is the radius of the particle in cm, and \(r_0\) is the initial radius of the orbit, expressed in astronomical units. V. G. Fesenkov notes that the formula does not include the force of solar attraction. According to V. G. Fesenkov’s formula, for \(r_0 = 1\) and \(\rho = 10\mu\), \(\tau\) is equal to 6500 years, which from an astronomical point of view represents a very small interval of time. True, V. G. Fesenkov further points out that, even before reaching the surface of the Sun, the particle will evaporate, and the atoms that made up its composition will already be thrown out beyond the limits of the solar system by radial light pressure. In any case, the Sun’s rays, by means of light pressure, carry out a peculiar “cleansing” of the solar system from cosmic dust.

Finally, indications have appeared in the astronomical literature of the important role of light pressure in the formation of new cosmic bodies from cosmic dust. It turns out that the forces of Newtonian gravitation are insufficient to explain such stable formations. But to the forces of gravity there is added light pressure caused by the light of surrounding stars. Light

pressure seems to push toward one another two particles that have come close together. The latter is explained by the shielding of the particles of light, as a result of which the light pressure on the portions of the particles’ surfaces facing one another is reduced. It is not difficult to see that this theory recalls Lesage’s old theory of gravitation. Lorentz even considered the electromagnetic analogue of this theory and showed that the resultant force would be inversely proportional to the square of the distance between the particles[^24].

The examples given could be multiplied. They testify to the fact that P. N. Lebedev correctly assessed the enormous role of light pressure in cosmic phenomena.

*
* *

The works of P. N. Lebedev are the pride of national science. The name of P. N. Lebedev has forever entered the history of physics as the name of a great experimenter. Soviet physicists, working in the splendid laboratories of which P. N. Lebedev could only dream, must always take as their motto the proud words of P. N. Lebedev that stand as the epigraph to the present article.

CITED LITERATURE

1. P. N. Lebedev, Collected Works, Moscow (1913).
2. Scientific Heritage, vol. I, ed. by S. I. Vavilov et al., Moscow—Leningrad (1948).
3. P. N. Lebedev, Selected Works, ed. by A. K. Timiryazev, Moscow—Leningrad (1949).
4. S. I. Vavilov, Petr Nikolaevich Lebedev, People of Russian Science, vol. I, Moscow—Leningrad (1948).
5. Cyrano de Bergerac, The Other World, etc., p. 138, Moscow—Leningrad (1931).
6. A. Fresnel, Ann. de Chimie et Phys. (2) 29, 57, 107 (1825).
7. W. Crooks, Phil. Trans. Roy. Soc. 164, 501 (1874).
8. D. A. Goldhammer, Ann. d. Phys. 4, 834 (1901).
9. Uspekhi Fizicheskikh Nauk 50, 328 (1950), and also Essays on the History of Physics in Russia, Uchpedgiz, 1949, p. 286, 328.
10. A. Bartoli, Nuovo Cimento 15, 195 (1883).
11. L. Boltzman, Wied. Ann. 22, 33, 291, 616 (1884).
12. F. Zöllner, Pogg. Ann. 160, 154 (1877).
13. P. N. Lebedev, Proceedings of the Division of Physical Sciences of the Society of Lovers of Natural Science 4, issue 2, p. 1; see also ref. 3, p. 60.
14. P. N. Lebedev, ZhRFKhO (phys. part) 32 (1), 211 (1900).
15. P. N. Lebedev, ZhRFKhO (phys. part) 33 (1), 53 (1901). Ann. d. Phys., 6, 433, 1901.
16. R. Wood, Physical Optics, p. 821, Leningrad—Moscow (1936).
17. R. T. Beyer, Amer. J. Physics 18, 25 (1950).

1. K. Schwarzschild, Sitzber. d. Münch. Ak., Math, 31, 293 (1901).
2. P. Debye, Ann. d. Phys. 30, 57 (1909).
3. Essays on the History of Physics in Russia, Uchpedgiz, 1949, p. 154 (article by A. K. Timiryazev on P. N. Lebedev).
4. P. N. Lebedev, ZhRFKhO (Part Phys.) 42 (1), 149 (1900); Ann. d. Phys. 32, 411 (1910); Selected Works, p. 195.
5. F. A. Bredikhin, On the Tails of Comets, p. 128, Moscow—Leningrad, GTTI (1934).
6. V. G. Fesenkov, “Meteoric Matter in Interplanetary Space,” Moscow—Leningrad (1947), Bulletin of Moscow State University, Phys. Ser. 11, 29 (1949).
7. H. A. Lorentz, Kinetische Probleme, p. 88, Leipzig (1928).