ht. J. Heat Mass Trcm.sfkr. Vol. IO. pp. 1293-1304.

Pcrgamon Press Ltd. 1967.

IN COMMEMORATION

Printed in Great Britain

OF THE 100th BIRTHDAY

OF P. N. LEBEDEVIN MARCH

1966 the 100th birthday was celebrated of the famous Russian physicist Peter
Nikolayevich
Lebedev. He was born of amerchant’s family. He received his secondary
education at the Khainovsky technical school.
Since he graduated from a technical school hecould only enter one of the technical educational
Institutes. According to the rules existing at thattime graduates of technical Institutes were notadmitted to the Universities.
Upon entering the High Technical School hesoon found that he was not interested intechnical sciences. In fact he was strongly
attracted by the type of studies whose subject
was the investigation of the physical phenomenaof nature. For this reason, in 1887 Lebedev went
to Strasburg where he became a student of theStrasburg University. At that time the name ofthe prominent physicist-experimentalist
Professor A. Kundt was already famous there. Thisscientist made a tremendous impression on
Lebedev and virtually kindled in him the flameof love for physics. Lebedev wrote to his friends“From day to day I am falling in love withphysics more and more. It seems to me thatsoon I may lose my human appearance, as now
I can hardly understand how it is possible tolive without physics”.
In 1888 Kundt was invited to Berlin University to take over the chair of Hehnholtz who
had just been appointed President of the State
Physico-Technical Institute.
Lebedev followed Professor Kundt. The stayin Berlin was a great benefit to him. While hewas working in Kundt”s department he zealously
attended Hehnholtz’s lectures on theoreticalphysics. The spiritual influence of such celebrities as Kundt and Helmholtz further determined
Lebedev’s views not only on science and its

social significance but also gave him the possibility to work out the educational system foryoung scientists.
Lebedev’s first research work was done at
Kundt’s suggestion and was presented as his
doctor’s thesis at the Physico-Mathematical
Faculty of the Strasburg University.
It was an experimental confirmation of thewell-known theoretical Clausius-Massoti
relation between the dielectric constant of theliquid vapours to the space occupied by them.
Lebedev’s outstanding abilities as a physicistexperimentalist were revealed in this work inwhich he also demonstrated his ingenuity andextreme thoroughness in conducting experiments.
Every experiment carried out for checking
certain theoretical considerations should be
conducted in such a way that all the extraneous
factors involved in it must be rigorously controlled since it is never possible to eliminate themall. Lebedev understood this very well ; from thispoint of view his work is of interest even now. It
may serve as an example how to conduct anexperiment thoroughly and how, if necessary,to eliminate possible errors in observation.
Lebedev’s physical imagination was exceptional, and at first its flights had to be restrainedby that outstanding teacher-scientist Kundt.
The thorough attitude towards the work
proposed was not without consequence forLebedev for the whole complexity of histhoughts developed and widened further in thecourse of time.
To understand this, it is necessary to notethat not long before the beginning of Lebedev’s
scientific activity the great German scientist
Heinrich Hertz experimentally confirmed theidea proposed by the no less brilliant English-

1293
4N

1294

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S. PREDVODITELEV

man Maxwell that electromagnetic waves wereidentical with those of light. This means that
there should exist certain similarity between theeffect of light and el~tromagnetic waves upona substance. In other words, with the help ofelectromagnetic waves as well as with lightwaves it is possible to study properties of molecules of a substance. For instance, if a molecule
is an ideal conductor, whose sizes are small ascompared with the intermoleculardistance,then as Clausius showed, the dielectric constantof a medium may be easily calculated.
This unexpected good agreement of Lebedev’s
with Clausius’ calculations filled Lebedev’s
mind with a flood of new ideas, one morebrilliant than the other.
For about two years an idea was maturing inLehedev’s mind that if according to Maxwell
electromagnetic radiation affects matter, i.e. if
the ratio of the energy of a beam falling per unit
time on an absorbing body to its speed produces
a pressure force, then this force may be thecause for the existance of comet tails. Lebedev
communicated this thought to the well-known
German scientist Wiener who at first took it for
ravings of a madman. Only after thoroughmeditation Wiener understood the essence andcongratulated
Lebedev on his fundamental
discovery. On this occasion Lebedev wrote:“It seems to me that I have made a very important discovery in the theory of motion ofheavenly bodies, especially, of comets . . . thelaw discovered may be extended to all celestialbodies. I informed Wiener about this but at
first he told me I was mad, but on the next day,having understood the essence, he congratulatedme. At fast, I was terribly excited but now when
the law is proved, I am not a bit nervous, partly
because--and I shall not hide this-1 am perplexed, even stunned by its generality which I
did not foresee. The law I formulated is not amatter of a minute’s inspiration ; for about two
years I have been nursing it. This problem,
which I have been studying for a long time, I
love with my whole heart, in a way I imagine
parents love their children”.

The study of comet tails in connection withthe effect of electromagnetic radiation upon asubstance, directed Lebedev onto one more
important idea regarding the nature of intermolecular interaction. In his opinion, a molecule
is some complex electromagnetic system which
may be simulated to an electromagnetic resonator. Consequently, when one molecule is at arather close distance from the other, there may
occur electromagnetic interaction between themsince an electromagnetic field of each molecule
will, as we would say now, influence the electricshells of atoms containing molecules. Due toelectric disturbances in each molecule, theinteraction of electromagnetic nature shouldtake place between these molecules. As we cansee, these ideas are quite up to date.
In Lebedev’s time the electronic theory of astructure of a substance was only at the stage ofdevelopment and nothing was said about aplanetary
structureof atoms.
However,Lebedev’s extraordinary
physical intuition
showed him the path, along which he should
proceed and along which science later developed.
Lebedev never liked suggesting ideas which
could not be checked experimentally. He wasadverse to solving mathematical exercises which
would not lead to experiments capable ofverifying a hypothesis.
The stated views on the effect of electromagnetic waves upon a substance served as thebasis for carrying out a number of works on the
ponderomotive influence of waves upon resonators. Lebedev saw the nature of molecularforces in these interactions, as he clearly expressed in his collected works. In one of his
works he wrote: “In Hertz’ investigation, in
the interpretation of light oscillations as electromagnetic processes still one more unsolved
problem is not solved, namely the problem ofradiation sources, of those processes which
occur in a molecular vibrator while it releases
its light energy into the surrounding medium ;on one hand, such a problem leads to a spectrum
analysis and, on the other, unexpectedly to one

IN

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100th

of the most complex problems of modern
physics, to a study of molecular forces”, see [l]pp. 56-57.
In our opinion, the results obtained by
Lebedev in the experiments with magnetic andelectric resonators are also of fundamental
importancefor a modem study of intermolecular-interaction
potentials. They showthat between molecules there should exist forces
which at a definite approach of molecules may
convert from repulsive forces to attractive ones.
Lebedev himself formulated the discoveredlaws as follows :1. The laws of the ponderomotive effect of waves
on magnetic and electric resonators are
identical.
2. When the resonators are tuned to a higherfrequency, an incident wave rotates them sothat their excitation may increase; when theresonators are tuned to a lower-frequency therotation causes a decrease in excitation.
3. The greatest quantities of these opposite
forces appear quite near resonance, see [i],p. 79.
Further, Lebedev added that all the attempts
to study a phenomenon with gradual transition
through resonance did not lead to the desired
result.
If Lebedev’s magnetic and electric resonators
are electromagnetic systems not quite imitating
molecular systems, nevertheless they distinctly
show the nature of the ponderomotive interaction when molecules approach each otherdue to heat motion.
Lebedev did not study only the ponderomotive interaction between magnetic and electric resonators. To extend this problem, hebegan to investigate these effects on the hydrodynamic resonators. These works clearly reveal
his methodical approach to scientific research.
He understood the heuristic force of analogies
which very often lead to great discoveries. For
example, it is enough to recall the works by
Jacobi and Hamilton who managed to discover
the profound analogy between mechanics andgeometric optics.

BIRTHDAY

OF

P. N.

LEBEDEV

1295

C. Bjerknes and F. Bjerknes’s investigations
into mechanical interaction in incompressible
fluid of pulsating, relatively moving and oscillating spheres are well-known. The authors haveshown that the above interaction has reverse
analogies with respect to ponderomotive interactions with static electric and magnetic polarization (Coulomb’s interactions).
Contrary to C. Bjerknes and F. Bjerknes,
Lebedev managed to find out direct analogies,
i.e. to show that the dependence of ponderomotive forces upon hydrodynamic resonance is
identical to the laws for electromagnetic oscillations. Lebedev’s works on this problem proved
to be more complete than those by C. Bjerknes
and F. Bjerknes; for he succeeded in obtaining
a continuous transition from the repulsive
region to the attractive one. The results of theseinvestigations were formulated by Lebedev asfollows :1. The law of the ponderomotive effect of an
oscillating sphere on the appropriate resonator is identical both for longitudinal andtraverse oscillations.
2. If the resonator is tuned in a higher-wave
frequency, then attraction is observed; when
it is tuned in a lower-frequency repulsion
takes place.
3. The greatest quantities of these opposite
ponderomotive forces appear in the vicinityof resonance and continuously convert into
each other, see [l], p. 93.
If we take any modem monograph on molecular physics and look at a chart on a change in
the interaction potential, depending on a distance of approaching molecules, it is easy to seethat they are surprisingly like Lebedev’s curves.
The discrepancy is only at the reference points
on the abscissa axis. In one case the distance of
the approach is plotted and in the second, thenatural frequency of a resonator. It is notdifficult to understand that natural frequencies
of oscillation of atomic cells depend upon adistance of the molecular approach. Therefore,
there is no doubt that Lebedev’s works on the
ponderomotive effect of waves upon the reson-

A.

1296

S. PREDVODITELEV

atom may still serve as guides for physicalintuition even for a modern reader.
This is described in detail in the Appendix.
The persistant consistency of Lebedev’s
thinking was such that he was never satisfied
with his discoveries, always attempting to
generalize as far as possible. Having developed
electromagnetic and hydrodynamic resonators
he turned his interests to acoustic resonators,
and here with the help of some most original
devices he succeeded in discovering the samelaws he established in his previous works. The
investigations into the ponderomotive effect ofwaves upon acoustic resonators completed theseries of his works which he himself appraised
as follows: “The greatest interest in a study ofwave motion lies in the principal possibility toextend the discovered laws to the region of lightand thermal emissions of the individual molecules of a body and to predict the resulting
intermolecular forces and their magnitude”, see[l], p. 120.
The problem on molecular interactions statedby Lebedev is not yet finally solved up to now.
The scientists all over the world are trying tosolve this problem mainly in the direction
anticipated by our famous countryman.
CONCLUSIONS

It is enough to note that the works of thefamous English theorist London, effectively
repeat Lebedev’s ideas presented in terms ofmodern ideas on the structure of atoms andmolecules.
The experimental investigations mentioned
could bring glory to any physicist but Lebedev
was not interested in achieving fame. His passion
for knowledge was so great that he would not
be stopped by any difficulties as long as the aim
was clear and the advance of science would
justify time and labour spent.
The survival of the electromagnetic theory oflight proposed at that time by J. C. Maxwell
considerably depended on the fact, to what
degree its conclusions would be confirmed experimentally. One of the important conse-

quences of this theory was the mechanical actionof light waves.
If the beam of parallel rays falls normal to aflat surface, the value of the pressure of light p
will depend upon the amount of energy E per
second, the surface reflection coefficient I andthe beam propagation velocity c. Mathematically the Maxwell law may be expressed as:
p = (E/c) (1 + r).
The absolute value of the light pressure issmall. Nevertheless the fate of the Maxwell
theory depended upon the experimental confirmation of the above formula This confirmation involves great difficulties which could beforeseen by each experimentalist but not everyone could risk to sacrifice the labour and timerequired to overcome them. This work required
not only resourcefulness and inventiveness but
also great skill. Lebedev passionately liked
difficult experiments, especially if they involved
experimental confirmation of fundamentals ofscience. In this case nothing could stop him. He
spent ten years of hard work to pass numerous
obstacles and at last to wring out from nature
its secret which it was carefully hiding anddisguising To measure the light pressure, it wasnecessary to make tiny mills, to place them in ahigh vacuum which at that time was difficult toachieve because suitable pumps were not available. Incomplete vacuum led on one hand to aconvective gas flow, and on the other to radiometric forces, which were comparable in theirmagnitude to the light pressure. Lebedev
thoroughly studied these phenomena and atlast invented such a device which allowed theabove mentioned auxiliary effects to be eliminated. In the end this work was crowned withsuccess. He managed to prove the effect of lightpressure upon solids in accordance with theelectromagnetic Maxwell theory. From this very
moment the question “to be or not to be” forthis theory no longer arose. In 1901 the publication of the work by Lebedev was properly
appreciated by the scientific world. For example,
during the stay of K. A. Timiryazev in EnglandIN COMMEMORATION

OF

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1297

Lord Kelvin declared to him: “Perhaps you that there is no need at all to spend time andknow that all my life I was lighting against energy to check the laws which are clear andMaxwell, not acknowl~~g
his light pressure grounded theoreti~lly. Such is the psychology
but your Lebedev forced me to surrender to the of our contemporaries. It was quite different inevidence of his experiments”. Lebedev was Lebedev’s time. There were doubts and distrustawarded the prize for the works on light of the new concepts and representations alienpressure on solids by the Academy of Sciences.
to usual thinking. Thus, just the same occurred
After studying light pressure on solids when the energy conservation law was disLebedev at once began to make ex~riments
covered. Now everyone who will try to havewith the pressure of light on gases.
doubts in the correctness of the energy conThe method used by Lebedev consisted on the servation law will be considered mad. In Mayerfact that light passing through a gas containedand Helmholtz’ time the contrary opinion
in a closed vessel should cause the circulation
prevailed.
of the gas. If the motion caused by non-uniform
The human habit is the enemy of all that is
heating of a gas is eliminate from the circulation
new and frequently kills in people the respect tomotion, then the whole effect should be deter- the past, making them forget the fact that themined by the light pressure which may be present arises from the past.
measured by a piston placed on the path of theLebedev is an outstanding scientist because
moving gas. All the gases are bad heat con- he understood the necessity to light for theductors and in this respect only hydrogen
recognition of the Maxwell theory and he andoccupies a special place as its heat conduction
Hertz share the great historic merit of consoliis relatively great. If it is added to the gases dating the triumph of the Faraday-Maxwell
investigated, it is possible to achieve such theory in our century.
conditions when the effect of convective currents
Lebedev carried out a series of outstanding
will be very small and the gas motion will be and original investigations, the aim of whichcaused entirely by the light pressure. Lebedev was to support exper~entally
the Faradaybrilliantly carried out these experiments. About Maxwell concept.
these experiments the well-known astrophysicist
It is known that light waves refract, reflect,
Schwartzshield wrote in his letter of February 9, interferate and are subjected to diffraction from1910 to Lebedev: “I remember very well, with a sharp edge and a small hole, possess binary
what doubt I learned in 1902 of your suggestion refraction in crystal bodies, etc.
to measure the pressure of light on a gas and I
Lebedev proposed to show that in accordance
was extremely surprised at hearing that you with the Maxwell ideas electromagnetic waves
obviated all the obstacles”, see [l], p. 19.
also had all these properties. He invented theLebedev was elected as an Honorary Member
devices which generated 6-mm electromagneticof the British Royal Society for his investigations
waves and designed prisms and diffractionof the light pressure on solids and gases.
gratings to study their optical properties.
At present the scientists all over the world are
Lebedev’s experimental results completely
so accustomed to the Maxwell concept ex- confirmed his expectations and he finishes hispressed in his well-known differential equations
treatise with the following words: “If thethat nobody has doubts about them. Therefore,
number of the experiments described is notwhen looking into the past not everybody canlarge, nevertheless it is quite sufficient to illusperceive the ~portan~and necessity of Lebetrate Maxwell’s views on the propagation of
dev’s experiments to provide the experimental
electric oscillations in crystals which he pubgrounds to the Maxwell theory. Everything
lished in 1862 and also to show once more theseems very simple and quite natural, it appears
identity of the phenomena of the electric and

1298

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PREDVODITELEV

light oscillations in a more complex case”, see[ 11, PP. 44 159.
Lebedev was a physicist of wide scope. He
was interested almost in all the problems
relating in any way to physics. For example, he
was interested in the passage of light throughinterplanetary space, and towards the end of
his life he worked a great deal on the origin of
the earth magnetism.
Belopolsky’s spectroscopic investigations of
the binary star-B-Aurige and the discovery ofsome photometric peculiarities of variable stars
made by Nordmann abroad and by Tikhov in
Russia raised the problem of the possible dispersed properties of interplanetary space. Lebedev attached major importance to this problem ;however, he did not see enough evidence forthis statement in the observations of Belopolsky,
Tikhov and Nordmann. He thoroughly analyzed
the above observations and showed that theNordmann and Tikhov methods were notsufficient to separate the interplanatary spacedispersion, if such exists, from the collateralfactors which were, in his opinion, the thermal
effects, tide phenomena in atmospheres of thecentral bodies and satellites, etc. In general,
Lebedev has come to the conclusion that it isquite impossible to prove dispersion of interplanetary space; to his mind “space absolutely
lacks any light dispersion that could possibly
be measured”.
From our point of view, such a categoricjudgement of the famous Russian scientist isperhaps premature although his conclusions
based on some particular observations are quite
convincing. The problem of light dispersion ininterplanetary space is so fundamental that it
requires a much broader analysis of the accumulated data.
We have already mentioned that Lebedev
was particularly fond of solving difficult experimental problems if they were of significanceto science. Following Hel’s discovery of strong
magnetic fields accompanying vortex motionof a photosphere around the sun spots thethought occurred to Lebedev of a possible

parallelism of magnetic phenomena on the sun
and the earth. To confirm this idea he decided
to reproduce this cosmic phenomenon in thelaboratory and to determine directly magnetometrically and to measure the magnetic phenomena caused by the rotation of bodies. In his
opinion, when bodies rotate, due to centrifugal
accelerations there should occur mutual motionof charges entering into the structure of atoms
or molecules of a substance; and negative
charges of atoms should be displaced normal tothe axis of rotation. Lebedev’s hypothesis is thewell-known modified hypothesis of Sutherland
who maintained that magnetism of the terrestrial globe results from the shift of charges
under the influence of gravitational forces.
Undoubtedly, these well-planned experiments
were very important but also extremely difficult.
Probably only Lebedev could carry them out
because half a century has elapsed since andnobody has so far dared to repeat them. He
started these investigations at the beginning of
1911 but several months later he died in March
1912.
Lebedev brought fame to his homeland not
only through his personal works; but as a true
patriot he was the first of the Russian scientists
who propagated the idea of team work inscience. In one of his popular papers he wrote:“Large physical laboratories intended only for
research have already existed for a long time in
the West, England, Germany and America. By
their continuous work on scientific problems,
as practice has shown, they undoubtedly help
technology. The Royal Institution in London
established on private funds more than ahundred years ago, may be the striking example
of such a laboratory. First of all, the greaternumber of persons taking part in the development of science is useful for the science itself,
namely, for the development of its certain fields
which are being studied at the laboratory andhere I especially would like to point out suchcollective work . . .“.
“If more arguments are required for the
defence of a greater number of persons working

IN COMMEMORATION

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100th

in this field of science, then I should like topoint out the importance of communication ofeach person working in this field with those whoare interested in this very subject: such communication leads to a more interesting exchangeof opinions and very often helps to overcome
encountered difficulties following good advice
and . . . “.
Lebedev’s statement on cooperation in science
was dictated not only by his enthusiasm forscientific work but he understood perfectly wellthat the future of any state considerably depends
upon the fact, how rapidly the science isdeveloping in the country. Now this truth has
become an axiom.
Lebedev’s activity at the Moscow University
brightly underlines his above political credo asa scientist. Here he organized the laboratory
which worked fruitfully up to 1911. That year
a storm broke out over the Moscow University.
More than a 100 professors and readers sent intheir resignations as a protest against the encroachment of the Minister of Education Kasso
upon the University autonomy. Lebedev wasamong those who left the University. Unfortunately, this catastrophy influenced him sothat he became seriously ill and did not return
to his young pupils who following him also left
the University.
Lebedev’s laboratory, situated in the basement of the old building of the Physical Instituteat the Moscow University, was totally permeated by his ideas. Even now much work
proposed by him is being developed. We shallemphasize the most important moments in
Lebedev’s activity in this period of his life.
After the publication of the works by Clausius,
Maxwell and Boltzmann on the kinetic theoryof a substance a number of concrete problems
appeared. One such problem is heat and masstransfer in rarefied gases. This problem wasstudied by Smoluchowski who gave the firstdescription of this phenomena.
Lebedev inspired his two intimate pupils
Lazarev and Timiryazev to study this phenomenon experimentally.

BIRTHDAY

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1299

According to the Smoluchowski theory, atthe interface of a solid and a rarefied gas in thepresence of a temperature difference between thegas and wall, a temperature jump should be observed and in the case of a moving gas also a gas
slip should occur. The first problem was studied
by Lazarev and the second, by Timiryazev. The
experiments of both investigators completely
confirmed the predictions of the theory. However, these experiments and the theory itself
were limited to the case when the temperatureand velocity gradients of the moving gas were
sufficiently small at the distance comparablewith the free path of the molecules.
It should be noted that the problem formulated by Smoluchowski and Lebedev acquired
essential importance in our time due to thedevelopment of the rocket and space flightengineering. Modem space crafts and rockets
move under such conditions that in calculatingheat losses from their shells it is necessary toallow for the temperature jump and slip. However, in this case there appeared doubts in thevalidity of the application of Smoluchowski’s
approximate theory. Under the conditions of
motion of space bodies in a rarefied gas, thetemperature and velocity drops are such thattemperature and velocity gradients over thefree path of molecules are far beyond thelimitations assumed in this first work. It wasnecessary to repeat Lazarev and Timiryazev’s
experiments. These experiments were repeatedby Kulto in the U.S.A. and by Gribkova
at the Department of Molecular Physics of the
Moscow University in the Soviet Union. A
quite unexpected result was obtained : Lazarev’s
conclusions on a temperature jump and Timiryazev’s ones on slip were confirmed despite thefact that the conditions of the experiments weredifferent. This contradictory circumstance is tobe solved.
Lebedev continued his work of proving theidentity between electromagnetic
and light
waves, and proposed to his pupils Kolli andRomanov to study dispersion of electromagnetic waves in different liquid media. These

1300

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problems were developed after Lebedev’s death.
At present they are being investigated on a newbasis of radiotechnical measurements. These
investigations are of special interest in the studyof the nature of fluids and for studying special
states of gases which are now called plasma.
During the flourishing days of Lebedev’s
University laboratory the views on wave processes finally crystallized. Rayleigh’s works
appeared. It became clear that pressure is not
only an inherent property of light and electromagnetic waves but also of acoustic ones. Naturally Lebedev together with his pupils began
thoroughly to study the acoustic wave processes of the work carried out in this direction.
We must mention specifically that by Neklepaev
and Kasterin.
Neklepaev succeeded in discovering acoustic
dispersion in gases which gave impetus tonumerous investigations of the scientists allover the world. Later, these works were developed on a large scale at the Moscow University under the direction of L. I. Mandelshtam
who together with his pupil M. A. Leontovich
outlined the relaxation theory of acoustic dispersion. However, it should be noted that the
mistake which was repeated in many investigations almost for forty years slipped into Neklepaev’s investigations. Only the reader of the
Moscow University, P. E. Krasnushkin, managed to notice, what role unparallelism of an
acoustic beam may play in measuring the main
dispersed gas properties.
Kasterin’s work which was begun at thelaboratory
under the direction of Lebedev
aimed at determining the interaction of theacoustic waves with acoustic resonators. The
full theoretical solution of this problem waspresented in his doctor’s thesis which up to
now is cited in the world literature. After theGreat October Revolution P. N. Behkov, apupil of Lebedev and Lazarev, repeated
Kasterin’s experiments under more perfectconditions.
We have mentioned only three directions of
the works which were begun at Lebedev’s

laboratory. In reality, the range of the investigations conducted in that laboratory wasmuch broader. It is quite clear that in any goodteam the ideas of the leader of the laboratoryintermingled with the initiative of his young
pupils. Lebedev appreciated and stimulated thescientific initiative of a beginner.
The comparatively short existence of Lebedev’s laboratory nevertheless greatly influenced
the development of science in Russia. The wellknown Lebedev school of physicists was born,to which belonged such famous scientists as:
P. P. Lazarev, A. K. Timiryazev, V. I. Romanov,
A. P. Kolli, T. P. Kraverts, V. Ya. Albert, V. D.
Zernov, V. K. Arkadiev, N. A. Kaptsov, A. B.
Mlodzeevsky, P. S. Epstein, N. E. Uspensky,
N. K. Shchodro, E. V. Bogoslovsky, N. P.
Kasterin and many others. All these scientists
held distinguished positions in Russia andP. E. Epstein is still a leading physicist in world
science and is working in Pasadena in the U.S.A.
REFERENCE
1. P. N. LEBEDEV,Collected Works, MOSCOW(1913).

APPENDIX

To illustrate, how profound were Lebedev’s
foresights on the nature of intermolecularinteraction, we shall briefly describe his investigations.
In his work on the ponderomotive interactionof electromagnetic waves on resonators, Lebedev studied two types of resonators-magnetic
and electric. The magnetic resonator is a selfinduction circle with condenser plates similar
to the pointers of the square Thomson electrometer [See Fig. Al(a)]. This resonator was sosuspended in the electromagnetic lield that theelectric vector did not affect it. Only themagnetic forces acting upon the self-induction
circle could turn the resonator. The proper
length of the wave of the resonator 2, was359 cm. The experimental results are given in
Table 1. The first column of this table contains
the lengths of waves of incoming radiation andthe second column, the ponderomotive force inconventional units.

IN COMMEMORATION

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In this table the sign “+” corresponds toattraction and the sign “- “, to repulsion.
The electric resonator is the self-induction
circle connected with a cylindrical condenser.
This condenser is shown in Fig. Al(b). It was soplaced in the electromagnetic field that themagnetic vector could not produce forces thatwould rotate the winding thread. Only theelectric vector acting on charges accumulated
at the plates of a condenser could turn theresonator. The length of the resonator wave was.: T ;:

d

1
Q.
:
i
:

“9

Ii

::
..

I

d
.i:
d

h

k:
i
:
:.

6

\r,

ic,
::
i

93
j

FIG. Al.

OF

P. N.

LEBEDEV1301

346 cm. The measured results for the electricresonator are given in Table 2.
If Lebedev’s ideas are considered correct, i.e.
forces of intermolecular interaction are of theresonance origin, then there appears the problem
how to find the interaction potential according
to the experimental resonance curve obtained.
This problem turned out to be solvable. It is
possible to show the model, with the help of
which the interaction potential may be easily
calculated according to Lebedev’s resonance

4

f
:

I

BIRTHDAY

1302

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S. PREDVODITELEV

curve. We shall not dwell upon the ways which
led to the development of the above model but
consider only the main principles underlining
this model.
Let any molecule in a condensed medium bea resonator possessing the inherent frequency
Table 1

d

K

301
311
331
340
351
371
389
414

+3,4
+3s
+ 7.6
+ 14,s-I-52.0
-l&S
-8.5
-4.5

Table 2

d

K

283
323
333
359
376
4118

+7.6
+ 14.6
+ 195
-22.6
-8.1
-4~7

of radiation vo. The action of all the surrounding
molecules on this resonator may be replaced bysome electromagnetic field. In such a representation of a liquid structure the interaction of
one liquid molecule with another completely
imitates Lebedev’s experimental conditions.
The described model of ~te~ol~ul~
interaction is equivalent to the Rayleigh-Jeans box
where there is one resonator. AI1 the molecules
surrounding the resonator serve as the RayleighJeans box walls. The total energy of sucha box consists of radiation energy I,, energy ofresonator thermal motion Q and molecularpolarization energy W. Thus, we haveE=

WsQ+Z.

According to the laws of therm~yn~ics,
transition from one steady state of a system toanother is made in accordance with the relation :E/v = const = h.
Here the constant of adiabatic constant h should
not necessarily coincide with the Planck constant.
In our model polarization energy W is also
simply accounted for. Assume that the gap 6
between the resonator surface and the walls of
the Rayleigh-Jeans box is a binary electric or
magnetic layer. Designate the total charge ofthis binary layer by e and let the condenser
itself be spheric. Then the polarization energy
is expressed by the formula
W = e2S/R2.
Here R is the radius of the volume where theresonator was placed.
Now it is possible to write down such an
obvious relation
e26
QI
K+<+yh;.
0Here 6 is the gap of a fictitious condenser.
From the relation obtained it follows that

Up to now our considerations were of generalcharacter. Now we make some restrictions
based on the following hypothesis. Let aconstant h coincide with the Planck constant,and radiation energy I, be equal to hv,. In thiscase the relation obtained assumes the form :Designate the quantity (u - v,-$ by y, then weshall have :R2v,h6=--g--y---p?

QR2

The quantity 6 may be interpreted as the
distance measured from the closest approach ofmolecules when attractive forces still take place ;INCOMMEMORATION

OF

THE

100th

the quantity y may be taken on the basis ofLebedev’s experiments but the quantity (1,-,/3,1) = y should be used as the abscissa rather
than the wave length as used by Lebedev.
Thus, our model led to the formula allowing
representation of Lebedev’s resonance curve asa potential function of intermolecular interaction.
Proceeding from the aforesaid, we shall makean attempt to calculate the potential function
for helium. Lebedev’s resonance curve is given
in Fig. A2 where the ordinate is the ponderomotive force in conventional units and y is the

BIRTHDAY

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P. N.

1303

LEBEDEVTo impose the. Lebedev resonance curve(Fig. A2) upon the curve (Fig. A3) by means offormula (1) it is necessary to express the constant values in formula (1) by a number. It may
be done on the basis of the following data: the-O.‘l--l-m7
0.0

I

I

I

I

8
FIG. A3.

Y
FIG. A2.

abscissa. Figure A3 gives the potential of interaction for helium calculated by the virial coefficients.
The values of the potential U in relative units
are included in the ordinate and the values of 6,
in the abscissa, i.e. the distance from the closest
approach of molecules when the attraction
potential changes into the repulsion one. In
both figures the circles designate the dataobtained experimentally. The calculations of
the interaction potential by the virial coefficients are considered to be the experimental
data although in these calculations the known
theoretical conjectures were used.

quantity R is half the kinetic radius of helium.
Following Keesom it is equal to 2.54 . 10e8 cm.
The proper resonator frequency may be foundfrom optical data for helium. For v0 Kurbertson
gives the value equal to 5.9 . 1015. The total
charge of a binary layer is assumed to be equal
to one charge of electron. Thermal energy Q is
obviously equal to the latent heat of evaporation
calculated per one atom.
Taking into account the aforesaid formula (1)may be reduced to the following form:
6=2.74.10-*y-0*085.10-*.

(la)

The ratio of the conventional unit of theponderomotive interaction force to the unit of
the potential interaction given in Fig. A3 isequal to 2.04. Using this condition and relation(la) it is easy to impose Lebedev’s resonancecurve upon the attraction potential curve. The
values of the interaction potential calculated bythis method according to the Lebedev resonancecurve are marked with triangles in Fig. A3. Fromthe last figure it is seen that the imposition of
one curve upon the other may be carried out

1304

A. S. PREDVODITELEVwith sufficient accuracy. This means that Lebedev’s considerations of the nature of the intermolecular interaction are far from intuitive
guess. They simply give a new method forsolving a complex problem of a liquid state.
These considerations also allow to understand
why all the attempts to lind out the mathematicalform of a potential of interaction reach a deadlock. Formula (1) converts one resonance curve
into such a large set which obviously cannot be
represented only by the constants entering into
the interaction potential, since they can reflect
neither the polarization molecular effects, nor
the optical qualities of the condensed media.
It seems to us that the above analysis ofLebedev’s ideas gives new perspectives to thedevelopment of science.
Finally it should be noted that science is agreat ocean of contributions
by individual
scientists most of whom are of but averagevalue. Therefore, among the ocean of works it isvery difficult for an ordinary mortal to find out
without studying the history of science, theideas of great scientific significance. Only great
talents may do this without knowing thehistory, but nowadays there are only a few ofthem under the conditions of mass researchwork. Hence, one is drawn to the conclusionthat when organizing research Institutions weshould bear this in mind and following Lebedev’s advice appoint highly talented scientists
as leaders of the research groups and Institutions. Otherwise, science will be condemned toa slow development and may simply movebackwards.

A. S. PREDVODITELEV
Physical Faculty
Moscow State University