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PAUL SOPHUS EPSTEIN
March 20, 1883-February 8, Z966
BY lESSE W. M. DuAlOND
PAUL SOPHUS EPSTEIN was one of the group of prominent and
very gifted mathematical physicists whose insight, creative
originality, and willingness to abandon accepted classical con-
cepts brought about that veritable revolution in our under-
standing of nature which may be said to have created "modern
physics," i.e., the physics which has been widely accepted during
the Twentieth Century. Paul Epstein's name is closely associ-
ated with those of that 'group, such as H. A. Lorentz, Albert
Einstein, H. Minkowski, I. I. Thomson, E. Rutherford, A.
Sommerfeld, W. C. Rontgen, Max von Lane, Niels Bohr, L.
de Broglie, Paul Ehrenfest, and Karl Schwarzschild.
Paul Epstein was born in 1883 in Warsaw, which was then
a part of Russia. His parents, Siegmund Simon Epstein, a busi-
nessman, and Sarah Sophia (Lurie) Epstein, were of a moder-
ately well-to-do Jewish family. He himself has told how, when
he was but four years old, his mother recognized his potential
mathematical gifts and predicted that he was going to be a
mathematician. After receiving his secondary education in the
Humanistic Hochschule of Minsk (Russia), he entered the
school of physics and mathematics of the Imperial University of
Moscow in 1901. In the third year of his undergraduate studies
he started research in experimental physics under Professor
Peter N. Lebedew, who in 1901 had become famous for his ex-
127
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128
perimental demonstration of the pressure exerted on bodies by
light or other electromagnetic radiation, an example of the
Einstein principle of the inertia of energy.
After graduation, in 1905, Epstein served as laboratory in-
structor in physics, first at the Moscow Institute of Agriculture
and later at the Imperial University, continuing his research at
the same time. In 1909 he obtained his master's degree in
physics and was appointed assistant professor (Privatdozent) at
the Imperial University. In 1910 he decided to specialize in
theoretical physics and obtained a leave of absence to do re-
search under the famous Arnold Sommerfeld at the University
of Munich (Germany).
Epstein's early research was in the theory of electromagnetic
waves and particularly the theory of their diffraction. Two of
his papers of this period were his doctoral thesis (1914), "Dif-
fraction from a Plane Screen," and an article in the German
Encyclopedia of Mathematical Sciences (1916), "Special Prob-
lems of Diffraction."
At the beginning of the First World War, in 1914, Epstein
was at Munich. Being a Russian, he was regarded as an "enemy
alien" and was automatically declared a civil prisoner. How-
ever, he was interned in a prisoner's camp only for a short time,
thanks to the kindly intervention of Professor Sommerfeld. For
the duration of the war he was allowed to live privately in
Munich with access to the facilities for doing theoretical work
and for publishing it, but of course was restricted from leaving
Germany.
By 1916 Epstein had become deeply interested in problems
of the quantum theory of atomic structure based on classical
mechanics, and he shared the early development of this branch
of physics with Niels Bohr and Arnold Sommerfeld. His most
important paper in this connection was "Zur Theorie des
Starkeffektes" (1916~. In this paper he computed the electron
orbits, atomic energy levels, and splitting of the spectral lines
BIOGRAPHICAL MEMOIRS
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PAUL SOPHUS EPSTEIN 129
for a hydrogen atom in the presence of a superimposed electric
field and compared his theoretical predictions with the experi-
mentally-observed results then available. The dramatic story
of the writing of the paper was told by Epstein years later. The
story, which follows, was taken from a tape recording of an
interview between the historian I. L. Heilbron and Paul S.
Epstein on May 25, 1962.
Paul Epstein had been understandably anxious to escape
from his captivity as an "enemy alien" in Munich, and to do
this he had hopes of finding a position as a theoretical physicist
somewhere outside Germany. Two places he had in mind were
Leyden and Zurich. But to obtain such a position as the one
in Zurich, he must write a habilitationsschrift, that is to say
a thesis for becoming Privatdozent. Sommerfeld had just writ-
ten his famous paper in which, by introducing the principle of
relativity into Bohr's theory of atomic orbits, he had arrived
at an explanation of the fine structure-splitting, till then unex-
plained by the simpler Bohr theory. A much more complicated
case of line-splitting was known, however, and was as yet com-
pletely unaccounted for by any theoretical treatment. This was
the effect, observed by Stark in 1913, when an atom is in the
presence of an externally-imposed electric field. So Epstein
proposed to Sommerfeld that he would tackle this difficult
problem as the subject of his habilitationsschrift for Zurich,
and Epstein's proposal was accepted at Zurich.
The Stark effect had been well known for three years and
in fact, as chance would have it, at the very time of which we
are speaking, Wagner, one of Rontgen's assistants in Munich,
put on a demonstration of the Stark effect using a so-called
"canal ray" tube. This was a vacuum electrical discharge tube
in which the negative electrode or cathode was provided with
holes. In such a tube most of the positive ions bombarded the
cathode and "splashed out" the electrons from it so as to main-
tain the discharge, but a few of the positive ions would go
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130 BIOGRAPHICAL MEMOIRS
on through the holes, and these were called "canal rays." Since
vacuum technique was in a very primitive stage, the mean free
path of an ion in such tubes was short, and the canal ray ions,
excited by collisions with other ions, would emit spectral lines
of much greater complexity than normal for that atomic species
if the electric field in the near vicinity of the cathode were
strong. The splitting up of the normally-to-be-expected spectral
lines into these complicated spectra was the Stark effect. Wag-
ner's timely demonstration of the effect in Munich was probably
done with mercury vapor in the tube, but the theoretical ex-
planation of the effect, even for the simplest atomic species,
hydrogen, was difficult enough to be as yet an unsolved problem
in terms of Bohr-Sommerfeld quantum theory.
This demonstration stimulated Epstein to start thinking
vigorously how he might construct a theory to explain quan-
titatively the splitting of the line spectra. He had studied
generalized mechanics from the French text of P. Appell, and
he knew from this a certain theorem of the famous mathema-
tician, Jacoby, furnishing a convenient method of integrating
the differential equations of motion for a case such as this.
Now at that time there was a famous mathematician, Karl
Schwarzschild, of powerful ability whom P. S. Epstein, as be-
hooved a much younger and less widely known man, in fact
only a young Privatdozent, held in great respect and consider-
able awe. Epstein only saw Sommerfeld infrequently, owing to
restrictions imposed on him because of his "enemy alien" status
in Munich, but at one of the meetings which he was permitted
to attend through Sommerfeld's intervention, the latter told
Epstein, "I wrote Schwarzschild that he should work on this
article " (meaning the Stark effect). Epstein relates that he "was
a little crestfallen, because I regarded this as a stab in the back,
since he ESommerfeld] knew that I was writing about it and,"
Epstein continued, "Schwarzschild was a mathematician of un-
believable energy; he could do everything in a twinkling; of
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PAUL SOPHUS EPSTEIN 131
course I couldn't reproach him ESommerfeld], but I decided:
'Now I have no prospects unless Schwarzschild should go to
heaven.' " Epstein goes on to tell how the next day when he was
going to bed he saw his way through what he needed for the
solution. He got up at 5 o'clock the next morning and by 10
o'clock he had the formula! And then the same morning he
showed his result to Sommerfeld. "And what do you know, the
same afternoon he ESommerfeld] got a letter from Schwarzschild,
and Schwarzschild had the wrong formula! It was the same
order of magnitude, but didn't agree on the positions of the
lines. So Sommerfeld wrote Schwarzschild, 'This morning
Epstein brought me the formula of the Stark effect, and this
afternoon we got your letter. But Epstein's formula agrees with
the observations.'"
When Schwarzschild had first obtained his result, he im-
mediately announced in the Berlin Academy that he would
speak about it. He did so, however, before having written to
Sommerfeld and Epstein, so the report he gave to the Academy
before he actually lectured contained his erroneous result. By
that time Epstein had already submitted his announcement of
his result for publication, and it came out dated just one day
before Schwarzschild delivered the above-mentioned lecture
to the Academy. So Epstein had the priority over Schwarzschild
by one day. In his lecture Schwarzschild had apparently cor-
rected his error verbally (undoubtedly giving credit to Epstein
for the correction), and when he received the galley or page
proof of the printed version he corrected the error and removed
all of the discrepancies. Thus Schwarzschild's final published
version came out correctly.
In substantially all textbooks and histories of physics the
theory of the Stark effect is attributed jointly to Epstein and
Schwarzschild It is clear, however, that they really solved the
~ See, for example, History of Physics by Max van Eagle, translated by Ralph
E. Oesper, Academic Press, Inc., New York, N.Y., 1950.
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132
BIOGRAPHICAL MEMOIRS
problem independently and that Epstein's solution came first and
did indeed correct an error in Schwarzschild's solution. This in-
cident, recounted directly from Epstein's own lips, illustrates
dramatically the competitive tensions that existed among this
group of European physicists in those early days of the develop-
ment of the quantum theory of atomic structure.
Paul Epstein's intimate knowledge of those exciting times
and gifted scientists at the turn of the century was a source
of great inspiration to us younger men who attended his classes
in theoretical or mathematical physics a little later after he had
come to Caltech (in 1921~. I shall never forget his account of
von Laue's accidental learning of the hypothesis (first clearly
formulated by Ludwig A. Sieber) that crystals are latticework
structures of atoms. It seems that van Laue first learned of this
when, in hopes of a consultation, he sought out Sommerfeld,
who happened to be sitting in a little summer pavilion in one
of the gardens of the University of Munich with his student,
P. P. Ewald, discussing Ewald's famous thesis in which the idea
of the "reciprocal lattice" had emerged as a mathematical device
of great power. Von Laue was electrified when he overheard
the conversation and grasped the idea of the crystalline atomic
lattice. Here, made by Nature herself, was the equivalent of
the artificial ruled grating (of Henry Rowland), the ideal tool,
perhaps, which might indeed have the appropriate fineness of
structure to answer the burning question with which van Laue
had been deeply occupied—whether or not the Rontgen rays,
discovered 17 years earlier, in 1895, were undulatory in nature
and, like visible light waves, capable of being diffracted by a
. .
grating or lattice.
By 1900 Haage and Wind had tried to determine, by dif-
fractions of x rays through fine slits, whether Rontgen's radia-
tions were undulatory in nature and, if so, of what order of
wavelength. These first results were inconclusive, but later,
Walter and Pohl repeated the slit-diffraction experiment with
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PAUL SOPHUS EPSTEIN
133
greater refinement. Not until 1912, however, through the good
fortune that the microphotometer of P. P. Koch ~ had just been
invented and developed, did it become possible to study quan-
titatively the slight broadening of the photographically-recorded
lines of Walter and Pohl. From this broadening they concluded
that the x rays observed had wavelengths of the order of 4 X
10-9 cm.l
Von Laue immediately set two young experimental phys-
icists, Friedrich and Knipping, at the University of Munich the
task of trying to see if a beam of x rays could be diffracted by
scattering from a crystalline solid. Their experiment was
fraught with many difficulties and tribulations. At that time
the only way of getting the high voltage electrical power to
operate a Ront<,en ray tube was with a "spark coil" or "Ruhm-
korff coil." Public electrical power (for lighting the university)
was only of the constant voltage, direct current variety. The
light sources were so-called "arc lamps" in which the light came
from a direct current arc maintained between two graphite
electrodes. Such a lamp has a nonlinear current-voltage char-
acteristic which tends strongly to amplify any small accidental
fluctuations in the supplied voltage. In order to operate the
Ruhmkorff coil, one needed an intermittent electrical supply to
it with an appropriate "interrupter" ~ and capacitor for gener-
ating high frequency oscillations. But the transient fluctuations
of the general voltage supply induced by the interrupter were
strongly amplified by all of the arc lights in the university,
~ P. P. Koch, Ann. Phys., 38, 507 (1912) .
t I am indebted for my dates and information on these early slit-diffraction
experiments to the famous text of A. Sommerfeld, Atomic Structure and Spectral
Lines, translation of H. L. Brose, E. P. Dutton and Co., New York, N.Y., 1923.
, A "Wehnelt interrupter," which interrupted the current about a thousand
times per second, was used. I owe some of these details to a delightful account
of the van Laue, Friedrich, and Knipping experiment at the University of
Munich written by Max van Laue himself, which was printed and privately dis-
tributed by North American Philips, Inc., on the 50th anniversary of Rontgen's
famous discovery.
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134 BIOGRAPHICAL MEMOIRS
which emitted deafening rattling noises every time the x-ray
tube was in action. Knipping had constructed an automatic
device which switched on the current from the university's
electrical system for about five seconds and then switched it off
again for twice that length of time. Fortunately the experiment
started during vacation, but before the two scientists got any
diffraction photographs, classes started and the nuisance of the
"talking arc lamps" drowning out all the lectures can be readily
imagined. Quoting from von Laue's account: "Due to some
psychological law this primitive music was contagious to the
students. They thought it a great joke to hum along with it.
The merriment grew greater and greater until finally the
whole lecture was ruined." Von Laue continues: "The rector
of the university naturally ordered a strict investigation into the
cause of the disturbance. All of the many committees which are
part of a university were set in motion. But in vain. We
physicists, who could have explained the whole thing, knew
nothing about it!
"At the end of the first three weeks of the new semester the
matter accidentally came to light. A mechanic, who had been
ordered to look for the source of the disturbance, came into the
cellar where the Wehnelt interrupter stood, listened, and at
once reported it to the higher authorities. Then the waves of
general indignation broke over all of our heads. All the various
committees came and certainly did not show us the most agree-
able side of their natures." They demanded an immediate
remedy or else suspension of the experiments.
"Faced with this need, we turned to Rontgen to ask whether
we might draw our current from his institute. We needed only
to carry a conducting wire across the university court from the
window of one institute to that of the other. And as soon as it
was established that the university would thus no longer be
disturbed, Rontgen gladly gave his consent.
"Just as matters had reached this point, the building com-
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PAUL SOPHUS EPSTEIN
135
mittee walked into Sommerfeld's institute. They were the most
powerful of all the university committees and apparently the
least popular with the professors. They, too, wanted to let us
feel the force of their anger, but we did not give them a chance
to speak. Instead, we at once told them of the arrangement that
we had made with Rontgen. They were nevertheless suspicious.
They went to Rontgen themselves to have this confirmed. They
returned a few minutes later in a state of indignation. We had
deceived them. Rontgen was absolutely opposed to supplying
current from his institute. We must therefore discontinue our
experiments at once.
"So the four of us sat there, Sommerfeld, Friedrich, Knip-
ping, and I [von Laue], and did not know what we should do
next. Luckily our quandary did not last long. The solution came
a few minutes later in the person of a mechanic, a fat, affable
Bavarian, from the Rontgen institute. In his deep bass and local
dialect, which considerably increased the humor of the situation,
he said, 'The Geheimrat (meaning Rontgen) told me to tell you
that you can go ahead and put up the wire. He is keeping to
his agreement. It is just that whenever the building commission
people come to him, the Geheimrat always says NO to them!' "
It was thus that the experiments of von Laue, Friedrich, and
Knipping were continued until the end. They had tried at first
to study the radiation diffracted by a crystal at very large angles,
i.e., in the backward direction to the incident beam. When at
last they tried placing the photographic plate on the far side of
the crystal (copper sulfate), they obtained on the plate a central
spot, produced by the direct beam going through the crystal,
and, forming a pattern around the central spot, a group of
symmetrically arranged spots of lesser intensity whose arrange-
ment and symmetry depended on how the crystal was oriented
relative to the beam. Rontgen, who was deeply impressed, did
not believe at first that the spots represented an interference
phenomenon through x-ray diffraction by the crystal lattice. The
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136 BIOGRAPHICAL MEMOIRS
complete explanation became evident only after further work
by the British physicists W. W. Bragg, his son Lawrence, and
H. G. l. Moseley at Cambridge as well as certain other work at
Munich by E. Wagner and J. Brentano. The five scientists
worked with two crystals which demonstrated the mor~ochrom-
atization of the rays in the first crystal.
Professor Epstein, after coming to Caltech, would recount
to his students very dramatically the occasion of the first suc-
cess of the von Laue, Friedrich, and Knipping experiment—
indisputably one of the truly great "breakthroughs" of early
Twentieth Century physics—much as I have given it here.
The group of physicists from the University of Munich had
the pleasant custom of meeting for luncheon and coffee at the
little round marble-topped tables out-of-doors in the garden of
the Cafe Lutz just across the way. The custom was so well estab-
lished and accepted that the waiters of The cafe would dutifully
see to it that the particular table for this group, at which on
previous days they may have been discussing mathematical
physics while writing the equations in pencil on the marble
top, would be saved from day to day without washing it off
so the discussions could continue. On a certain beautiful warm
spring day in the Easter holidays of 1912 van Laue arrived a
few minutes late at the accustomed table. Paul Epstein, P. P.
Koch, the mathematician Rosenthal, and the physicists E.
Wagner and W. Lenz were already there. But an unusual at-
mosphere prevailed at the physicists' table. Instead of con-
versing as usual, each one silently read a newspaper. Nlon Laue
sat down, ordered coffee, and took up a newspaper waiting for
a conversation to begin. But none did. One of the company
made a remark, shortly after another did the same, and so on
around the table, all of which struck van Laue as incompre-
hensible and mystifying. Finally what must have happened, but
which he had not yet heard about, dawned on him, and he said,
"Well, gentlemen, I assume from your remarks that the inter-
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PAUL SOPHUS EPSTEIN
143
In his research career, after his arrival at Caltech, Epstein at
first continued his work on Bohr's form of the quantum theory,
culminating it in 1922 with three papers in the Zeitschrift fur
Physik and one in the Physical Review. Later Epstein took part
in the development of quantum mechanics initiated by Heisen-
berg and Schroedinger. An important paper in the Physical
Review (1926), "The Stark Effect from the Point of View of
Schrodinger's Quantum Theory," ~ should be mentioned in
· .
to US COnneCtlOn.
In 1930, Epstein was elected to the National Academy of
Sciences.
P. S. Epstein also devoted considerable attention to border-
line problems related simultaneously to both physics and several
cognate sciences. Examples are "Zur Theorie des Radiometers"
(1929), "Reflection of Waves in an Inhomogeneous Absorbing,
Medium" [the Heaviside Layer] (1930), "On the Air Resistance
of Projectiles" (1931~. Other examples of borderline problems
which Epstein studied were the settling of gases in the atmo-
sphere, the theory of vibrations of shells and plates, and the
absorption of sound in fogs and suspensions. Two of his articles
in this category outside of physics are especially worthy of men-
tion. Both appeared in a monthly literary and scientific maga-
zine, Reflex, published in the 1930's in Los Angeles, California,
and edited by Dr. S. M. Melamed. The first of these articles,
"The Frontiers of Science," is a highly scholarly presentation
of certain central problems of both philosophy and religion set
forth in their relationship to recent concepts on the frontiers of
physics and mathematics. His discussion of the old philo-
sophical and religious problem of free will vs. the concept of
"scientific determinism" and the "law of causality" is particu-
larly noteworthy since, in one form or another, all of human-
~ See also in this connection "The New Quantum Theory and the Zeeman
Effect" (1926); "The Magnetic Dipole in Undulatory Mechanics" (1927).
OCR for page 151
144 BIOGRAPHICAL MEMOIRS
kind has struggled for centuries with these questions. Epstein
invokes the "principle of indetermination" of Werner Heisen-
berg, enunciated in 1927 and points out that, built into the
very structure of Nature herself, there is a basic principle which
precludes mankind from making with indefinitely high accuracy
the requisite physical measurements to predict the future from
a knowledge of the present with the ideal certainty postulated
by S. Laplace in the Seventeenth Century. This article is indeed
a rewarding one to the reader.
Epstein's other article in Reflex is "Uses and Abuses of Na-
tionalism." In it he reveals a deep and farsighted understanding
of certain patterns in the history of the political development of
nations. In this discussion Eppie's complete alignment on the
side of liberalism becomes self-evident. He takes the history of
France as the vehicle for his argument and perceives the Dreyfus
affair in the Nineteenth Century as an important turning point,
away from imperialism and militarism at home and toward
friendly cooperation abroad. In the opinion of the writer this
article of Epstein's revealed his deep prescience in world affairs.
It was written long before de Gaulle made the wise decision
to withdraw France from its military commitments, first in
Southeast Asia and later in Algeria. Other nations could well
"profit by this example."
It is a pity that these two articles, splendidly exemplifying
Paul Epstein's remarkable scholarship, erudition, and pre-
science in humanistic matters well outside his own fields of
specialization, should be lost from the far wider circulation they
deserve. The writer wishes to suggest that they be republished.
After Paul Epstein's retirement as Emeritus Professor at
Caltech in 1953 he served as a consultant for several large indus-
trial companies. Prominent among the many reports submitted
by him in such work was his "Theory of Wave Propagation in
a Gyromagnetic Medium" (1956~.
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PAUL SOPHUS EPSTEIN 145
Paul Epstein died at his home in Pasadena on February 8,
1966, at the age of 83, after suffering with admirable stoicism
a prolonged and painful illness (herpes roster or shingles). He
was beloved of many students and colleagues, and his long and
useful life stands as a splendid tribute to his brilliant mind and
his altruistic sharing of it with others.
OCR for page 153
146
KEY TO ABBREVIA TIONS
BIOGRAPHICAL MEMOIRS
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·—
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Methode der Storungsrechnung. Z. Physik., 8:211-28.
Die Storungsrechnung im Dienste der Quantentheorie. II. Die
numerische Durchfuhrung der Methode. Z. Physik., 8:305-20.
Die Storungsrechnung im Dienste der Quantentheorie. III. Kritische
Bemerkungen zur Dispersionstheorie. Z. Physik., 9:92-110.
Problems of quantum theory in the light of the theory of perturba-
tions. Phys. Rev., 19: 578-608.
The evaluation of quantum integrals. Proc. Nat. Acad. Sci., 8:166-
67.
1923
Zur Aberrationstheorie. Bemerkung zu einer Abhandlung von A.
Kopff. Physik. Z., 24:64-65.
Paramagnetism and the theory of quanta. Science, 57:532-33.
The Stark effect for strong magnetic fields. Philosophical Magazine
46:964.
Simultaneous action of an electric and a magnetic field on a hydro-
gen-like atom. Phys. Rev., 22:204. (A)
Ferromagnetism and quantum theory. Phys. Rev., 22:204. (A)
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PAUL SOPHUS EPSTEIN
149
1924
With P. Ehrenfest. The quantum theory of the Fraunhofer dif-
fraction. Proc. Nat. Acad. Sci., 10: 133-39.
On the resistance experienced by spheres in their motion through
gases. Phys. Rev., 23:710-33.
On the simultaneous jumping of two electrons in Bohr's model.
Proc. Nat. Acad. Sci., 10: 337-42.
1926
(centennial of the undulatory theory of light. Science, 63:387-93.
The Stark effect from the point of view of Schrodinger's quantum
theory. Phys. Rev., 28:695-710.
On the evaluation of certain integrals important in the theory of
quanta. Proc. Nat. Acad. Sci., 12:629-33.
The new quantum theory and the Zeeman effect. Proc. Nat. Acad.
Sci., 12:634-38.
Second order Stark effect in hydrogen. Science, 64:621-22.
1927
Two remarks on Schrodinger's quantum theory. Proc. Nat. Acad.
Sci., 13:94-96.
The magnetic dipole in undulatory mechanics. Proc. Nat. Acad.
Sci., 13:232-37.
With P. Ehrenfest. Remarks on the quantum theory of diffraction.
Proc. Nat. Acad. Sci., 13:400-408.
The dielectric constant of atomic hydrogen in undulatory mechanics.
Proc. Nat. Acad. Sci., 13: 432-38.
1928
On the theory of the radiometer. Phys. Rev., 31:914. (A)
Interference of reflected light. Phys. Rev., 32:328. (A)
1929
Zur Theorie des Radiometers. Z. Physik., 54:537-63.
With M. Muskat. On the continuous spectrum of the hydrogen atom.
Proc. Nat. Acad. Sci., 15:405-11.
Konferenz uber den Michelson-Morleyschen Versuch. Naturwiss.,
17:923-28.
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150
BIOGRAPHICAL MEMOIRS
1930
Geometrical optics in absorbing media. Proc. Nat. Acad. Sci.,
16:37~5.
Reflection of waves in an inhomogeneous absorbing medium. Proc.
Nat. Acad. Sci., 16:627-37.
Note on the nature of cosmic rays. Proc. Nat. Acad. Sci., 16:658-63.
1931
Answer to Prof. Stormer's remark. Proc. Nat. Acad. Sci., 17:160-61.
On the air resistance of projectiles. Proc. Nat. Acad. Sci., 17:532~7;
also in Phys. Rev., 37:233. (A)
1932
Uber Gasentmischung in der Atmosphare. Gerlands Beitrage zur
Geophysik, 35: 153-65.
On ferromagnetism and related problems of the theory of electrons.
Phys. Rev., 41:91-109.
1933
La resistance de Fair sur les projectiles. Extrait du Memorial de
L'Artillerie Franchise, Paris, pp. 635-50.
On the temperature dependence of ferromagnetic saturation. Proc.
Nat. Acad. Sci., 19:1044~9.
1934
The expansion of the universe and the intensity of cosmic rays.
Proc. Nat. Acad. Sci., 20: 67-78.
1935
On the bending of electromagnetic microwaves below the horizon.
Proc. Nat. Acad. Sci., 21:62-68.
The frontiers of science. Reflex, 6:19-24.
1936
Uses and abuses of nationalism. Reflex, 7:14-18.
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PAUL SOPHUS EPSTEIN
1937
151
Textbook of Thermodynamics. New York, John Wiley & Sons, Inc.
406 pp.
Physics and metaphysics. Scientific Monthly, 45:49-54.
On the magnetic energy of supraconductors. Proc. Nat. Acad. Sci.,
23:604-10.
1938
Influence of the solar magnetic field upon cosmic rays. Phys. Rev.,
53:862-66.
1941
Secondary school mathematics in relation to college physics. Am. J.
Phys., 9:34-37.
On the absorption of sound waves in suspensions and emulsions. In:
Theodore son Barman Anniversary Volume (Applied Mechan-
ics), by the friends of Theodore van Karman, pp. 162-88. Pasa-
dena, California Institute of Technology.
1942
The time concept in restricted relativity. Am. l.--Phys., 10:1-6.
The time concept in restricted relativity" A rejoinder. Am. T. Phys.,
10: 205-8.
On the theory of elastic vibrations in plates and shells. journal of
Mathematics and Physics, 21:198-209.
1945
The reality problem in quantum mechanics. Am. J. Phys., 13:127-
36.
1946
On the elastic properties of lattices. Phys. Rev., 70:915-22.
1947
Radio-wave propagation and electromagnetic surface waves. Proc.
Nat. Acad. Sci., 33:195-99.
1948
Robert Andrews Millikan as physicist and teacher. Rev. Mod. Phys.,
20: 10-25.
OCR for page 159
152
BIOGRAPHICAL MEMOIRS
1950
With M. S. Plesset. On the stability of gas bubbles in liquid-gas
solutions. Journal of Chemical Physics, 18: 1505-9.
1953
With R. R. Carhart. The absorption of sound in suspension and
emulsions. I. Water fog in air. journal of the Acoustical Society
of America, 25:553-65.
Dialektischer Materialismus und die modernen physikalischen
Theorien. Physik. Blatt., 9: 49-55.
Zur Situation der Naturwissenschaftler in der Sowjetunion. Physik.
Blatt., 9:221-26.
1954
On Planck's quantum of action. Am. I. Phys., 22:402-5.
On the possibility of electromagnetic surface waves. Proc. Nat.
Acad. Sci., 40: 1158-65.
1956
Theory of wave propagation in a gyromagnetic medium. Rev. Mod.
Phys., 28:3-17.
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Representative terms from entire chapter:
paul sophus
