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OTTO LAP ORTE
July 23,1902-March 28,1971
BY H. R. CRANE AND D. M. DENNISON~
OTTO LAPORTE was a member of the small group of brilliant
young theoretical physicists who received their training
during the middle 1920s under the guidance of Arnold Sommer-
feld in Munich.
Otto Laporte was born in Mainz Germany. His ancestral
lineage came from French Huguenot families who fled from
France to Switzerland during the period of intense religious
persecution in the late seventeenth century. They were later
allowed by Frederick the Great to move to Prussia, where they
and their descendants became, for the most part, civil servants in
the Prussian State. It appears that Otto was the first member of his
family to devote himself to science or any other scholarly career.
His father was a career officer in the Imperial German Army, and
his specialty was heavy artillery. During the years before World
War I, Colonel Laporte was successively stationed in the heavily
fortified cities of Mainz, Cologne, and Metz, and it was in these
cities that young Otto Laporte received his early schooling.
After the war broke out, the family was evacuated from Metz
and returned to Mainz, where Otto's mother's family lived. They
remained there for the duration. The first four years following
that move—Otto's twelfth to sixteenth were formative ones, and
# Dr. Dennison died April 3, 1976.
269
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BIOGRAPHICAL MEMOIRS
his real interest in science became apparent. During that perio<]
he experimented extensively with optics ant! spectra, within the
limitations of the meager materials that he could manage to come
by in time of war. His father was able to get for him a glass prism
from a periscope. Not satisfied with the dispersion of the glass
prism, he proceedecl to build a triangular cell of glass plates held
together with glazier's putty and filled with carbon disulfide.
When, in his words, "the carbon disulfide dissolved the putty,
escaped and stank up our house terribly" the method had to be
abandoned. For a light source he built a satisfactory electric arc.
He also built a spark coil that worked and embarked on building
a much larger one; however, as he recalled, the tedium of winding
the secondary overcame him, and the project was dropped. Hav-
ing received an electrostatic machine from the effects of a cousin
who was killed in the war, he did experiments that amazed on-
lookers for example, making his sister's hair stand on end.
It surely must have appeared from this early work that if Otto
Laporte was to have a career in physics, it would be in the experi-
mental rather than the theoretical direction. This idea would
have been strengthened by the fact that he was at the same time
having difficulties with mathematics and English in school. This,
he said later, was because the courses involved only repetitious
drill and endless numerical calculations requiring interpolation
of five-place logarithm tables. Since failure in these subjects
would have been a blot on the family honor, he was provided
with extra tutoring. Anyone knowing Laporte later in his life
would be hard put to understand these early difficulties, because
a command of these two skills, mathematics and languages, would}
stand out in a most striking way.
Perhaps one may conclude that even a bad experience in
school cannot completely suppress the abilities of a gifted stu-
dent. At any rate, Otto Laporte was soon to come under the
influence of excellent and inspiring teachers.
# From a taped interview; see
Acknowledgments.
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OTTo LAPORTE
271
The years immediately following the war were very difficult
ones for the Laporte family, as of course they were for many
others. In the early spring of 1920 the family moved to Frankfurt,
to stay for only a year, where the young Laporte attended the
University. It was here that he chose the branch of the road
leading to theory rather than experiment. In a taped interview
with Professor Thomas S. Kuhn of Princeton University, made
late in his life (see acknowleclgments), Laporte recalled how it
came about.
KUHN: You start out with this great interest in building things; you do
a lot of experiments at home, some of them very elaborate. You go,
though, to Sommerfeld, and your career is pretty much in theory. Was
there a conflict here? Were you always clear that you wanted to be a
theoretical physicist? How did these two sides of things relate?
LAPORTE: I think it is due to the fact that more formal teaching goes
on in theoretical physics. Experimental physics is not really being taught
except on a much lower level. When I went to Frankfurt, right away I was
under the influence of some very great men. The oldest one there was a
mathematician named Arthur Schoenflies, whom you know, of course, as
the man who first formalized the theory of the space groups of lattices,
but who has many, many other great achievements. He was then an old
man, but he gave beautiful courses. And then there were two younger
mathematicians; one was Ludwig Bieberbach and the other, a small
wizened man named Ernst Hellinger.
KUHN: You went to lectures by all of them from the very beginning?
LAPORTE: Yes.
KUHN: You were at Frankfurt for only one year, yes?
LAPOR=: Yes. And in physics I took the lectures of [Max] Born and
[Alfred] Lander Lande was then a young Privatdozent. From Born I took
heat, which was what he was doing in his cycle. Now it should perhaps be
said at this moment that it was a great disadvantage of the German system
that you don't get any advice from appointed advisors. I just took the
courses whose subjects interested me, and they were all much too difficult.
Now if I had been in the clutches of some sufficiently energetic advisor he
would have just told me not to take these courses, but I wasn't told that;
I was completely on my own.
In the summer of 1921 the Laporte family found it necessary
to leave Frankfurt. Their apartment was taken over by the
German Army of the French Occupation, and the housing short-
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BIOGRAPHICAL MEMOIRS
age in Frankfurt became so acute that there was little chance of
finding another place. The family moved to Munich. The choice
of that city was greatly influenced by the facts that Arnold
Sommerfeld was the professor of theoretical physics at the Uni-
versity of Munich and that he was establishing there one of the
foremost centers of physics in Europe. Max Born had sent
Sommerfeld a very enthusiastic recommendation regarding
Laporte, and the young man found himself accepted and wel-
comed by the group of theorists who had been drawn there by the
presence of Sommerfeld. He was given the initial task of talking
at their seminar on a new paper by Albert Einstein and W. J.
de Haas. The subject of the paper was new to Laporte, but he
was helped by Wolfgang Pauli, who was Sommerfeld's personal
assistant at that time. Other members of the group of young
theorists were Werner Heisenberg, Gregor Wentzel, Karl Herz-
feld, and Paul Ewald. This was a lively and very gifted company
into which Laporte was plunged. His continuing acceptance by
that group speaks well of the young Laporte's innate ability, since
in point of fact his training had not really been extensive.
Actually, when he arrived in Munich, he had never read Sommer-
feld's famous book A tombau und Spektrallinien, which was the
indispensable "bible" for most physicists of that era. This omis-
sion in Laporte's education was quickly repaired, however.
The central figure dominating and inspiring the group was,
of course, Arnold Sommerfeld, and it is clear that Otto Laporte,
who was then in his early twenties, acquired the clarity of expres-
sion and creativity which were to be his characteristics for the
remainder of his life. In addition to attending Sommerfeld's
lectures, Laporte had the opportunity for much personal contact
with Sommerfeld, either at Sommerfeld's home or in the course
of the long walks which they often took. These conversations
included the classical subjects of hydrodynamics and electro-
dynamics as well as the developing field of quantum theory.
Laporte's first independent research resulted in an article on the
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OTTO LAPORTE
273
diffraction of electromagnetic waves around a sphere, an article
which was published in the Annalen der Physik in 1923, just a
few months before his twenty-first birthday. In this paper
Laporte discussed a set of solutions that are now known as creep-
ing waves or Regge poles.
The old, prewave mechanics version of quantum theory was
at the height of its success in the early and middle 1920s. It had
served to correlate, and in that sense to explain, a great many
experimental results. It was, however, inherently illogical, and
there was a growing distrust of the old theory and a search for
what was to become the present-day quantum theory. Among the
directions that the search took were those of attempting to under-
stand the more complex atomic spectra, to classify the spectral
lines, and to find the energy levels. Typical spectra of this type
were those of iron, vanadium, and chromium.
At about this time Sommerfeld spent time in the United
States, mainly as a visiting, professor at the University of
Wisconsin. He also traveled to the important spectroscopic instal-
lations for example, the one at Mount Wilson. When he re-
turned to Munich, he brought with him new spectroscopic data-
in particular, data on the spectra of iron and vanadium. Laporte
set about the task of unraveling and understanding these. His
analysis of the vanadium spectrum was published in December of
1923, while that of the extremely complex iron spectrum ap-
peared the following year. This latter research formed the basis
of his dissertation for the doctoral degree, which was awarded in
1924. In the course of his successful investigations of these spec-
tra, he discovered the fundamental principle known among spec-
troscopists as the "Laporte rule." This rule classified the atomic
energy states into two types, which he had called odd and even
states. He found that no radiative transitions occurred between
unlike states. This was the first statement of the principle that
was later to be known as the conservation of parity. The principle
has assumed fundamental importance in elementary particle
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BIOGRAPHICAL MEMOIRS
theory, not only because of its almost universal validity, but also
because of the great interest attached in recent years to certain
exceptions.
The year 1924 was momentous for Otto Laporte in several
respects. In addition to his completion of the analysis of the iron
spectrum and the acceptance of his Ph.D. thesis, he was awarded
one of the first of the International Education Board fellowships.
These had been newly established by the Rockefeller Foundation
for the purpose of allowing young post-doctoral scientists to con-
tinue their research anywhere in the world. Professor Sommer-
feld had learned, while on his visit to the United States the year
before, that these fellowships were about to be set up, and he
highly recommended his student, Laporte, for one of them.
Laporte elected to spend the period of his fellowship, 1924-
1926, in Washington, D.C. at the National Bureau of Standards.
He was drawn there by the excellence of their spectroscopic
laboratory and in particular by the presence of the very able
experimental spectroscopist William F. Meggers. The advantages
of the association were mutual: Meggers and the other experi-
mentalists had been anxious to hear firsthand reporting of the
theoretical advances that were being made in Europe in the fields
relating to spectroscopy. In response to this need, Laporte was
instrumental in starting a regular weekly seminar. This grew
rapidly to include many of the scientists of the Washington area,
and it continued to meet throughout Laporte's stay at the Bureau.
Among persons included were Gregory Breit, Merle Tuve, Paul
D. Foote, F. L. Mohler, Arthur Ruark, and Harold Urey. Most
notable in the seminar series was Laporte's interpretation of the
first three papers of Schrodinger, which introduced the matrix
method in quantum theory. These talks, Laporte recalled later,
required a great deal of work on his part. That period was a yeasty
one in the Washington area, and it was remembered so fondly by
the seminar participants that they staged a reunion twenty-fi`Te
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OTTO LAP ORTE
275
years later. In Laporte's words, "We felt sheepish as well as remi-
niscent. We gave another colloquium." ~
The two years spent in Washington were formative ones as
well as productive ones for Laporte. He published a number of
spectroscopic researches. But perhaps a more important aspect for
his future was his close association with experimentalists for the
first time in his life. In spite of his early interest in experiments
he had been entirely under the influence of theorists since the age
of about eighteen. Here at the Bureau he became greatly im-
pressed with the power of experiment, and this must have had
much to do with-the fact that he turned to experimental research
in the last chapter of his career.
In the autumn of 1926 Laporte joined the staff of the Physics
Department of the University of Michigan as an instructor. In
the following year he became an assistant professor. By inviting
Laporte, Professor Harrison M. Randall, the department chair-
man, wished to build up the field of theoretical physics at
Michigan. He realized, however, that it would be necessary to
create a nucleus of theorists if the venture was to be successful.
Accordingly, in 1927 Laporte was joined by George E. Uhlen-
beck, Samuel A. Goudsmit, and David M. Dennison, who re-
mained his colleagues for many years.
In 1928 Laporte was invited to be a guest lecturer at the
Imperial University in Kyoto, Japan. During the year he received
an urgent request from Sommerfeld asking him to lecture in
Munich during the period in which Sommerfeld was to be absent
on a trip to America. Laporte was able to honor this request,
although it meant cutting his visit to Japan somewhat short. It
also meant that he had to make a nonstop journey of two weeks
duration via the trans-Siberian railway in order to arrive in
Munich on time, an adventure he did not soon forget.
~ From a taped interview; see Acknowledgments.
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276
B IOGRAPHICAL MEM OIRS
His initial visit to Japan made a lifelong impression on Otto
Laporte and led to his taking leaves of absence from the Univer-
sity of Michigan to lecture at the University of Tokyo in 1933 and
again in 1937. During these periods he became proficient in the
Japanese language and in the art and literature of Japan. FIe was
truly an expert in the understanding and appreciation of Japa-
nese poetry. While there, he submitted a haiku in a national
competition and won recognition. In the interval between these
visits, in 1935, Laporte became a naturalized United States
. .
cltlzen.
Otto Laporte's expertise in both the language and culture of
Japan was to be of great value to this country from 1954 to 1955
and again from 1961 to 1963, when he served as scientific advisor
to the American ambassador in Tokyo. The U.S. State Depart-
ment cited Laporte for playing a key role in securing the land-
mark atomic energy agreement between the two countries. These
were not the only occasions in which Laporte had served his
adopted country with distinction. From 1949 to 1950 he was
intelligence analyst for the U.S. Army of Occupation in Heidel-
berg, Germany.
A review of Laporte's bibliography shows that up until the
early 1940s his principal researches continued to be centered in
the field of spectroscopy, although a few of his publications re-
lated to various quantum mechanical problems, making use of
his great knowledge of mathematics. In 1944 he began, in effect,
a new career. He entered the field of fluid dynamics with a paper
in which he found an exact solution to the problem of the lift of
an airfoil of elliptical outline. Two years later he was presented
with the unexpected opportunity to do experiments in fluid
dynamics by means of a shock tube. Lincoln Smith, a member of
the Michigan faculty, had somewhat earlier initiated work in this
field and had assembled apparatus of an advanced design. Smith
left the University in 1946, and Laporte took over the director-
ship of the project. This was a really new departure from his
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OTTO LAPORTE
277
earlier work, since it meant taking responsibility for an experi-
mental project and directing the graduate students who hacT
started their theses under Smith. He did exceedingly well at it,
and many successful investigations resulted. These included the
use of reflected shocks to produce such high local temperatures
that spectroscopic phenomena which had hitherto been inaccessi-
ble could be studied. He continually had graduate students in
the shock tube project. His last doctoral student, John Yoder
(Ph.D., 1971), constructed a cryogenic tube and investigated
shocks in low-temperature hydrogen gas. The resulting measure-
ments clearly showed those quantum effects that arise from the
existence of the two forms of hydrogen, ortho and pare.
In some respects the final chapter of Laporte's scientific life,
which we have called a new career, was not really new but rather
the convergence of a number of the interests he had had for a long
time. The success with which he directed the experimental part
of the shock tube program perhaps harks back to his boyhood
project of constructing an arc and a workable spark coil. His
interest in the hydrodynamical problems associated with the
shock phenomena was surely related to the early days in Munich,
where many of the discussions were centered about hydro-
dynamics. For example, his friend Werner Heisenberg wrote his
Ph.D. thesis in that field. And Enally, of course, Laporte's long
experience with spectroscopic problems allowed him to recognize
the possibilities of using the shock tube for observing spectra
under conditions that had not been accessible before.
Otto Laporte was one of the charter members of the American
Physical Society's Division of Fluid Dynamics and served as its
chairman in 1965. He exerted strong influence in directing the
attention of physicists to an area of study that was to be, for many
of them, new and highly rewarding. Soon after his death the
Division of Fluid Dynamics established, in recognition not only
of his scholarship but also of his early guidance of the organiza-
tion, the Otto Laporte Memorial Lectureship, to be given annu-
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BIOGRAPHICAL MEMOIRS
ally. Richard G. Fowler gave the first of the lectures in 1972.
Fowler has published a papers based on his lecture that is rich in
detail on Laporte's contribution to the Division as well as on
facets from the history of his career.
Special recognition should be made of Otto Laporte's gradu-
ate teaching. His early association with European lecturers in
theoretical physics in an era when a certain elegant formality was
practiced came through in Otto's teaching in a desirable way, but
at the same time his lectures were not so structured that he could
not pursue byways when it suited him to do so. What came
through most strongly to the better students was his deep appre-
ciation for the beauty of physics and of mathematical proofs. In
the opinions of these select students the view of physics that they
gained from him was of more future influence than the physics
itself. Laporte's sense of mathematical discipline did much to
maintain the "tone" of teaching in the whole graduate program,
and his course was both a high point and a hurdle in each gradu-
ate student's career.
Almost by definition most people are amateurs in the areas of
their hobbies or side interests. Not so with Otto Laporte. He had
several hobbies, and he went into each with almost the intensity
and erudition he gave to physics. His mastery of the Japanese
language and knowledge of the culture that he gained cluring
several years on assignments to Japan have been mentioned. He
continued to cultivate these interests for the rest of his life; for
example, he became an authority on netsuke, small carved figu-
rines, of which he had a notable collection.
Otto Laporte was a horticulturist of much more than amateur
standing, specializing in plants of the cactus and the euphorbia
families and certain other succulents. His collection of these
plants was extensive, particularly in respect to the euphorbias of
the rare medusa form. He kept up correspondence with horticul-
# Phys. Today, 26, no. Il (1973):23-29.
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OTTO LAPORTE
279
turists in other parts of the world in his efforts to obtain unusual
specimens. He published on euphorbias and cacti. One of the
present writers (H.R.C.) once traveled with Laporte to New York
to attend a physics meeting, where immediately upon arrival the
two went to a botanical garden on Long Island. A botanist from
South Africa was waiting there, by Laporte's prior arrangement,
to talk about the Welwitschia plant, a plant that grows only in the
Nambi Desert and in the south of Angola and that is estimated to
live more than 2000 years. Laporte came away with some seeds as
well as the information he sought. An everyday kind of incident
was recalled by a former student: the student, while waiting for
Laporte's class to begin, was gazing out of the window at a row of
Lombardy poplars. Before he was aware of it, Laporte had come
up behind him and was saying, "You know, all the Lombardy
poplars in the world are one single tree—they propagate only by
cuttings because they are males and the female is no longer
extant."
Music was the third of Laporte's side interests. His own piano
playing was passable but venturesome, and was indulged in for
his own enjoyment. But his real expertise was in his wide knowl-
edge of the literature of music and his wide acquaintance with
professional musicians in this country and abroad. He was quite
at home discussing the fine points of milsic~1 romno.sition ~nc1
performance with the best of experts.
Laporte was married to Eleanor Anders in 1933. She died in
1957. He remarried in 1959. His second wife, the former Adele
Pond, and their three children, Claire, Irene, and Marianne,
survive him.
Otto Laporte died March 28, 1971, a victim of cancer which
progressed rather rapidly. His death came after his name had
been slated for presentation for election to the National Academy
of Sciences at the annual meeting in April of the same year.
Taking an action it had never before taken, the Academy elected
Otto Laporte to membership, posthumously.
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BIOGRAPHICAL MEMOIRS
ACKN OWLEDGMEN TS
THE AUTHORS WISH especially to thank the Center for History of
Physics of the American Institute of Physics for the use of the
transcript of a taped interview with Otto Laporte, which was con-
ducted by Professor Thomas S. Kuhn of Princeton University,
January 29-30, 1964, as part of the Sources for the History of
Quantum Physics Project. Much of the information throughout the
memoir was drawn from the transcript. The authors are also
indebted to Professor Richard G. Fowler of the University of
Oklahoma for important information received through private
correspondence and to Professor George W. Ford and Professor
Otto G. Graf of the University of Michigan for information and
valuable advice.
CHRONOLOGY
1902
1923
Born July 23, Mainz, Germany. Parents: Wilhelm
Laporte and Anna Geyl. Sisters: Luise and Marianne
(m. Roger Gillette) .
Analyzed iron and vanadium spectra. Enunciated
Laporte rule.
1924 Ph.D., University of Munich, under Arnold Sommer-
feld. Thesis: "Exact Treatment of Scattering of EM
Waves by a Sphere."
1924-1926 International Education Fellow; studied in Europe,
Japan, and finally in the United States in the spectro-
scopy section of the National Bureau of Standards.
Joined University of Michigan faculty as instructor in
physics.
Promoted to assistant professor.
On leave from University of Michigan; lectured at
Kyoto Imperial University.
Married Eleanor Anders (d. 1957) .
On leave from University of Michigan; lectured at
Tokyo University.
Became naturalized U.S. citizen.
On leave from University of Michigan; lectured at
Tokyo University.
1926
1927
1928
1933
1933
1935
1937
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OTTO LAP ORTE
944
945
946
949-1950
951
954-1955
1956
1965
1968
1971
1971
281
Changed field of activity from atomic spectroscopy to
fluid mechanics.
Promoted to full professor.
Assumed charge of shock tube laboratory at University
of Michigan.
Scientific Intelligence Analyst, U.S. Army of Occupa-
tion, Heidelberg.
Initiated researches on reflected shock waves.
Served as scientific attache at American Embassy in
Tokyo.
Cited by U.S. State Department as instrumental in se-
curing atomic energy agreement between the United
States and Japan.
1959 Marriage (second),to Adele fond.
1961-1963 Returned to Tokyo as scientific advisor to the U.S.
ambassador.
Chairman, Division of Fluid Dynamics, American
Physical Society.
Sabbatical leave in Munich.
Died March 28, Ann Arbor, Michigan.
Elected, posthumously, to the National Academy of
~ -
~clences.
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282
BIOGRAPHICAL MEMOIRS
BIBLIO GRAPHY
1923
Propagation of electromagnetic waves. Ann. Physik, 70:595-616.
The arrangement of vanadium lines in multiplets. Phys. Zeits.,
24:510-15.
1924
The structure of the iron spectrum. Part I. Zeits. Physik, 23:135-75.
The structure of the iron spectrum. Part II. Zeits. Physik, 26: 1-22.
1925
With G. Wentzel and A. Lande. Dashed and displaced terms in
spectra. Zeits. Physik, 31:335-38.
With W. F. Meggers. Rules of spectral structure. J. Optical Soc.
Amer. and Rev. Sci. Inst., 11 :459-63.
Primed terms in the spectra of the lighter elements. Washington
Academy of Sciences journal, 1 b: 409-1 3.
1926
With C. C. Keiss. Displaced series in the spectrum of chromium.
Science, 63:234-36.
Series and ionisation potentials in the iron spectrum. Proc. Nat.
Acad. Sci. U.S.A., 12:496-503.
Fundamental terms of spectra of first and second periods. Zeits.
Physik, 39: 123-29.
Absorption spectra of the palladium and platinum group. Phys.
Rev., 28:642-64.
With A. Sommerfeld. The spectroscopic significance of the mag-
neton numbers in the iron group. Zeits. Physik, 40:333-43.
1927
Neolith J. R. Lang. Second spark spectrum of zinc, Zn III. Phys. Rev.,
30: 378-86.
Screening constants from optical data. Phys. Rev., 29:650-54.
1928
Interpretation of paramagnetism in the iron group. Zeits. Physik,
47:761-69.
With T. E. Mack and R. T. Lang. Application of the x-ray laws to
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OTTO LAPORTE
283
optical spectra of higher rank and the classification of Ga IV
and Ge V. Phys. Rev., 31 :748-72.
1930
With D. R. Inglis. Resonance separations in configurations of type
p5S and d9s. Phys. Rev., 35: 1337~1.
1931
With G. E. Uhlenbeck. Application of spinor analysis to the
Maxwell and Dirac equations. Phys. Rev., 37: 1380-97.
1932
First spark spectrum of caesium (Cs II). Phys. Rev., 39:458-66.
First spark spectrum of rubidium (Rb II) . Phys. Rev., 38:843-53.
Approximation of geometric optics as applied to a Dirac electron
moving in a magnetic field. Phys. Rev., 42:340-47.
1933
Kowalewski's top in quantum mechanics. Phys. Rev., 43:548-51.
1937
Absorption coefficients for thermal neutrons. Phys. Rev., 52:72-74.
1938
Elastic scattering of Yukawa particles. Part I. Phys. Rev., 54:905-12.
1942
Term formulae for the configuration d5. Phys. Rev., 61:302-4.
Degeneracies among terms of a configuration of equivalent elec-
trons. Phys. Rev., 61:305-8.
1943
With J. E. Mack. The spectrum of neutral tungsten, W I. Phys.
Rev., 63:246-97.
1946
Rigorous solutions for the spanwise lift distribution of a certain
class of airfoils. Quart. Appl. Math., 2:232-50.
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284
BIOGRAPHICAL MEMOIRS
1948
Polyhedral harmonics. Zeits. Naturforsch., 3a:447.
1953
With R. N. Hollyer, fir., A. C. Hunting, and E. B. Turner. Lumi-
nosity generated by shock waves. Nature, 171:395.
1958
With W. R. Johnson. Interaction of cylindrical sound waves with a
stationary shock wave. Phys. Fluids, 1: 82.
With l. Meixner. The Kirchhoff-Young theory of the diffraction of
electromagnetic waves. Zeits. Physik, 153: 129.
1964
With T. S. Chang. Reflection of strong blast waves. Phys. Fluids,
7:1225.
1965
Sir William Rowan Hamilton. Michigan Quarterly Review, 4:254.
1966
With R. G. Fowler. Resistance of a plasma slab between juxtaposed
disk electrodes. Phys. Rev., 148: 170.
1967
With R. G. Fowler. Weber's mixed boundary-value problem in
electrodynamics. J. Math. Phys., 8:518.
1969
Spectroscopy by means of shock waves. In: Proceed ings of the
Arnold Sommejeld Centennial Memorial Meeting and of the
International Symposium on the Physics of One- and Two-Elec-
tron Atoms, Munich, September 1968. Amsterdam: North Hol-
land Press.
1970
On Kepler ellipses starting from a point in space. Amer. J. Phys.,
38:837.
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285
1971
With HI. l. Yoder. Low temperature shock waves in molecular hy-
drogen. In: Eighth International Shock Tube Symposium, Im-
perial College of Science and Technology, London, July 1971
(preprint).
1972
With T. S. Chang. Curved characteristics behind blast waves. Phys.
Fluids, 15:502.
Representative terms from entire chapter:
biographical memoirs
