edward mills purcell. 30 august 1912 −− 7 march...

Elected For.Mem.R.S. 1989 7 March 1997:−−Edward Mills Purcell. 30 August 1912

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EDWARDMILLS PURCELL30 August 1912 — 7 March 1997

Biog. Mems Fell. R. Soc. Lond. 45, 437–447 (1999)

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EDWARDMILLS PURCELL

30 August 1912 — 7 March 1997

Elected For.Mem.R.S. 1989

B B B, F.R.S.

Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK

Professor Edward Purcell was a physicist of great distinction. With Felix Bloch he received the

joint award of the Nobel Prize for Physics in 1952, for the developments respectively of

nuclear magnetic resonance (NMR) and nuclear induction. In 1951, H.L. Ewen and Purcell

(21)* detected radiation at the hydrogen hyperfine frequency of 1421 MHz coming from

interstellar space, which created a new branch of astronomy. The Smith–Purcell effect (28) is

now regarded as a potentially powerful source of radiation in the far infrared region of the

spectrum. These were further achievements of prize-winning quality.

Edward Mills Purcell was born in Taylorville, Illinois, USA, the son of Edward A. Purcell

and Mary Elizabeth Mills, both natives of Illinois. From public schools in Taylorville and

Mattoon, Illinois, he won a scholarship to Purdue University, Indiana. He graduated in 1933

in electrical engineering and published two papers (1, 2) on thin films with Professor

K. Lark-Horowitz.

Realizing that Purcell’s gifts and interests lay in mathematics and physics, Lark-Horowitz

invited him to take part in a research project on electron diffraction while he was still an

undergraduate, and then recommended him for an exchange studentship in Germany. Purcell

spent a year studying physics at the Technische Hochschule in Karlsruhe, with Professor W.

Wenzel. On his return he entered Harvard University to work under J.H. Van Vleck

(For.Mem.R.S. 1967; Nobel Laureate in Physics 1981). With Malcolm Hebb, who later

became Director of Research at the Laboratories of the General Electric Company in

Schenectady, New York, he made a theoretical study (3) of the properties of paramagnetic

salts below 1 K. This publication was widely used for the interpretation of magnetic cooling

experiments in low-temperature physics, including my own thesis work in 1937–39. Later,

when I mentioned it, Purcell, always a modest man, said, ‘that was all Hebb’.

* Numbers in this form refer to the bibliography at the end of the text.

439 © 1999 The Royal Society



440 Biographical Memoirs

Purcell received the degree of PhD in 1938 from Harvard University, and spent two years

there as an instructor in physics. He joined Kenneth Bainbridge in building the first cyclotron

at Harvard, and wrote a paper entitled ‘The focussing of charged particles by a spherical

condenser’ (4).

In the autumn of 1940 he followed Bainbridge to the Radiation Laboratory at

Massachusetts Institute of Technology (MIT), organized for military research during World

War II. In charge was Isaac Isidore Rabi (Nobel Laureate 1944), who had applied radio waves

to the study of NMR spectroscopy in atomic beams at Columbia University, where many

novel features of the spectrum of atomic hydrogen were discovered.

A section under Jerrold R. Zacharias (also from Columbia University) worked on the

development of radar (or radiolocation, as it was then known in England). It was at the

Radiation Laboratory in 1943 that I met Purcell for the first time. By 1943, Purcell was in

charge of the Fundamental Developments Group there, exploring higher frequencies and new

microwave techniques for radar at wavelengths from 10 cm down to 1.25 cm. This contained

Robert Pound and Robert Dicke, who played duets on their recorders for moments of light

relief. In 1945, Purcell and others were engaged on writing accounts of their work at the

Radiation Laboratory (6–9).

A sequel to this work arose in the 1950s. Purcell, together with others at MIT, the National

Bureau of Standards, the Carnegie Institution of Washington, Cornell University and the

Collins Radio Company reported the discovery (25) of a new type of radio propagation,

observable over distances of 2000 km from the transmitter. They suggested that it was caused

by irregularities in the ionosphere. At a frequency of 49.8 MHz, a signal was observable over

a distance of 1245 km, and was uninterrupted all day and all night. It was transmitted from

the Collins Radio Co. at Cedar Rapids, Iowa, to the National Bureau of Standards in

Virginia. In April 1951 it was found that the intensity varied with the time of day. The

mechanism suggested was scattering from irregularities in the E-layer of the ionosphere (34),

similar to reflections of the Sun from waves on the sea, and now known as ‘tropospheric

scatter’.

N

While still formally at the Radiation Laboratory, and moonlighting from there, Purcell began

experiments at Harvard University with R.V. Pound and H.C. Torrey. They made the first

observation of NMR on 15 December 1945.

This discovery (5) was announced simultaneously with that of Nuclear Induction by Bloch

et al. (1946) at Stanford University. As a result, Felix Bloch and Edward Purcell shared the

Nobel Prize for Physics in 1952. Nuclear magnetic moments are now known with high

precision for all stable isotopes, as well as some radioactive isotopes. Further applications of

NMR are discussed below; see also Abragam (1961a, b).

In 1945, Purcell returned to Harvard as an Associate Professor of Physics; he became

Gerhard Gade Professor in 1949 and was the Senior Fellow of the Society of Fellows at

Harvard University from 1950 to 1971.

The first measurements (10, 11) were quickly followed by NMR measurements of protons

in hydrogen gas (12) and of fluorine ions in a single crystal of calcium fluoride (13), where the

angular variation of the spectrum with respect to the crystal axes was explored. Studies were



Edward Mills Purcell 441

made of relaxation effects (14, 15) and of line shapes (16). NMR was also used for a precise

determination of the proton magnetic moment in Bohr magnetons (18), and it was extended

to structural investigations in crystal lattices (19).

N

An ingenious experiment in 1951 involved the reversal of an applied magnetic field,

sufficiently rapid that relaxation effects had no time to affect the populations of the two

magnetic substates of the proton. This produced a greater number of spins in the upper level,

a population inversion that is equivalent to the production of a ‘negative temperature’ (22).

D

A small shift in the NMR frequency in metals, produced by the conduction electrons, was

detected by Knight (1949). This was called ‘diamagnetic shielding’ and it is related to the

chemical shift; this arises from precession of the electrons in an atom or molecule, which

creates a small magnetic field at the nucleus in addition to the external field. It is proportional

to the external applied field; the effect can therefore not be detected by any change in the

latter. The shielding effect is small in light atoms and in molecules that have few electrons,

amounting only to a few parts per million in the hydrogen molecule, and in water and mineral

oil. It is most noticeable in heavy molecules, for which the values are much larger; a detailed

analysis was given in an analysis by Ramsey (1950). A full discussion can be found in Ramsey

(1956).

Such observations of a slight change in the measured nuclear frequency led to important

developments. The local field varies with the environment, so that the ‘chemical shift’ that is

produced varies slightly from substance to substance. NMR has become a major tool in

chemistry and biology, while in medicine magnetic resonance imaging (MRI) provides a

non-invasive technique for taking pictures of the inside of the human body. A recent

development is the Oxford Centre for Functional Magnetic Resonance Imaging of the Brain

(Oxford University Gazette, 28 May 1998).

Purcell foresaw that NMR techniques would be widely used. When his first NMR

experiments began to yield results, he perceived ‘the snow on his doorstep as heaps of protons

quietly precessing in the earth’s magnetic field’ (R.V. Pound in The Guardian, 26 March 1997).

A development from dynamic nuclear polarization is the production of ordered nuclear

systems with either ferromagnetic or antiferromagnetic configurations, used as targets for

experiments in nuclear and particle physics (Abragam & Goldman 1982).

Magnetic resonance in very low magnetic fields (17), with the use of free precession of the

proton spins, has become a major tool in archaeology: before digging begins, buried sites can

be detected through the local anomaly in the Earth’s magnetic field above the surface (Aitken

1978, 1990).

Electronic implants with tiny NMR transmitters inserted into freshwater fish are being

used to track their movements (The Guardian, 21 November 1996).

A recent account of the applications of NMR to food analysis has been given by

Colquhoun (1998). One example quoted by him is ‘the use of deuterium NMR to measure




deuterium/hydrogen isotope ratios … allows values to be obtained for individual sites within a

molecule … in contrast to mass spectrometry which gives an overall figure’.

M

Another type of interaction with the simple formula (the scalar product of the two

spins) was observed (24) in molecules of HD (1H2H) gas and attributed to a mechanism

involving the hyperfine interactions on each atom and the electronic exchange interaction

(the scalar product of the two spins) between them. It followed the detection of an

interaction of this type, with magnitude ca. 2.8 Hz, in a spin-echo experiment of Hahn &

Maxwell (1951).

(I ⋅ I)

(S ⋅ S)

Fine structure was discovered in the spectra of both 1H and 2H nuclei in HD gas at

frequencies of 5 and 30 MHz. For the deuterium line the measured splitting was 43.5 Hz, with

an accuracy of 1 Hz (26). Another development with Fred Reif (29) was NMR in solid

hydrogen in 1953, together with liquids under high pressure a year later, with George Benedek

(30). Measurements on the protons in liquid and solid hydrogen (29) were soon followed by

work in Oxford. This was started by Bernard Rollin (1946); more measurements were made by

Rollin & Hatton (1947) and Rollin et al. (1947).

M

Purcell was not content to rest on his laurels after NMR; he made a number of profound

contributions in other areas of physics. In 1946 he showed that the rate of spontaneous

emission from an atom is changed if it is placed inside a conducting ‘high-Q’ cavity. The

theory was given in classical terms; much later it was treated by quantum theory, and this has

generated another branch of physics, now called ‘cavity quantum dynamics’. In a recent

theoretical paper, Dutra (1997) has applied the correspondence principle to derive a master

equation for the decay mechanism. This gives a simple treatment for a simple classical

electromagnetic field and shows how the damping effect can be described in quantum

mechanical terms.

T S–P

A paper (28) published in 1953, entitled ‘Visible light from localized charges moving across a

grating’, described an experiment in which a beam of radiation was produced by the

interaction of electrons of energy 300 keV when passed parallel and close to the surface of an

aluminium diffraction grating. Light was generated by the movement of the image charge

within the corrugated surface.

This is now known as the ‘Smith–Purcell effect’, and it led to an unpublished note by

Smith and Purcell in 1993, containing a detailed explanation of the mechanism and a

calculation of the power emitted. The last sentence reads: ‘so, if one asks what “Smith–

Purcell” radiation is good for, the answer may be not much except teaching physics’. This




gloomy prediction is likely to be a great understatement, as it has received renewed attention

over the past thirty years. A private letter from George Doucas (17 June 1997) suggests

instead that ‘it may prove to be a very effective and relatively inexpensive way of producing

coherent, tuneable radiation in the infra-red, where sources are sparse’. The spectral

distribution of the power emitted, with a maximum between 0.4 and 2 mm in wavelength, is in

good agreement with the theory (Brownell et al. 1997).

A

In 1951 Purcell’s interests turned to astronomy. With Ewen, he detected radiation at the

frequency of the hydrogen hyperfine line at 1421 MHz coming from interstellar space (21).

This was followed by a paper (27) on the lifetime of an excited state of atomic hydrogen, the

metastable state of the doublet S-state with n = 2. Further publications considered the

influence of collisions on the hyperfine level populations of hydrogen atoms (31) in

interstellar space. The effects of grains of dust were discussed at length in a series of papers

(37–44, 46). The Kramers–Kronig relations were applied to the interstellar medium, regarded

as a vacuum sparsely populated by spheroidal grains. A lower limit was derived for the

equilibrium temperature of grains of a given size and shape, together with an upper bound on

the attainable emissivity in the far infrared (38).

E

In 1950, Purcell and N.F. Ramsey (20) pointed out that the usual arguments from parity

against the existence of electric dipole moments had no experimental confirmation. In 1957

this led to the derivation of an experimental upper limit to the electrical dipole moment of the

neutron (32), followed by a discussion of the role of nuclear electric dipole moments in the

relaxation of nuclear spins (33). A search for the Dirac monopole was made with 30 GeV

protons (35), and further papers on monopoles (47, 48) appeared in 1982 and 1983.

A more recent summary of the position has been given by Eugene D. Cummins (1996) in

Amazing light, the volume for the 80th birthday of C.H. Townes, For.Mem.R.S.

With H.C. Berg of Harvard University, Purcell published two joint papers, one on the

physics of chemoreception (45), the other (53) on strategies for chemotaxis, the latter with

M.J. Schnitzner and S.M. Block as other co-authors. In 1984 Berg and Purcell were jointly

awarded the Biological Physics Prize of the American Physical Society for their work on the

motion of bacteria.

T

A number of short pieces were published under this title over the years 1983 to 1988 in

American Journal of Physics (49–52). Typically they took the form of three new problems with

solutions to those set the previous month. An example from December 1983 is:

(1) Could a snowflake cooled to 10 microkelvins be lifted with an ordinary permanent magnet acting

on the induced nuclear polarization?




(2) Is it likely or unlikely that your next breath will contain an atom of nitrogen that was in your first

breath?

(3) If the moon is receding from the earth at the rate of centimeters per year, how much power is being

dissipated in tidal friction?

The overwhelming majority, but not all, of the problems were set by Purcell himself, but

occasionally he appealed for problems from others.

P

All who met Purcell found him a charming and modest man. When asked a question, a

typical reply that I have heard was ‘Gee! I just dunno!’, but this was often followed by a long

and informative discussion. If started in his office in the Lyman Physics Laboratory at

Harvard University, it generally continued out in the corridor where he had installed a row of

blackboards. Passers-by were welcome to join in.

Purcell received honorary doctorates from Purdue University and Washington University

in St Louis, and a National Medal of Science in 1979. He gave the Halley Lecture at Oxford

University in 1983, and was elected a Foreign Member of the Royal Society in 1989. The

Jubilee of Magnetic Resonance was celebrated at Harvard University on 10 December 1995

and at the 28th Colloque Ampère (Canterbury, September 1996).

Purcell died on 7 March 1997, aged 84, at his home in Wright Street, Cambridge,

Massachusetts. For some years he had suffered the after-effects of a serious back injury,

incurred by falling downstairs at his home when answering the telephone late one night. He is

survived by his wife, Beth (née Busser, whom he married in 1937), and two sons.

A lively and attractive person, Purcell enjoyed warm relations with colleagues, students

and visitors from many other countries, who deemed it a privilege to work with him.

A symposium ‘in honor of Edward M. Purcell’ was held at the Harvard University Science

Centre on 17 and 18 October 1997, at which the closing words were spoken by Denis Purcell.

It was followed by a Memorial Concert in Christ Church, Cambridge, Massachusetts.

B

Electricity and magnetism (35) appeared as volume II in the Berkeley Physics Course

(McGraw-Hill) in 1965, with a second edition and a solutions manual in 1985. In an article

entitled ‘The present status of Maxwell’s displacement current’, John Roche (1998) has

written:

E.M. Purcell in 1985, with exemplary clarity, showed that the displacement currents produced by

conservative fields are composed of spherically symmetrical current elements whose symmetry

prohibits them from generating magnetic fields … D.F. Bartlett in 1990 again proved the same result

using a transformation of an integral expression for the magnetic field generated by the displacement

current. In 1987 Zapolsky showed, on the other hand, that it is the conservative part, only, of a

displacement current which contributes to current closure in an open circuit.




A

This memoir is based mainly on the material held in Purcell’s Personal Record at the Royal

Society, together with the obituary ‘Edward Purcell 1912–97’ by Robert Pound in Physics

World, May 1997, pp. 61–62. I am particularly indebted to Robert Pound for a list of E.M.

Purcell’s publications, and to G. Doucas for the paper on the Smith–Purcell effect (Brownell et

al. 1997).

The frontispiece photograph was taken in 1952. © The Nobel Foundation.

R

Abragam, A. 1961a The principles of nuclear magnetism. Oxford: Clarendon Press.

Abragam, A. 1961b Les principes du magnétisme nucléaire. Paris: Presses Universitaires de France.

Abragam, A. & Goldman, M. 1982 Nuclear magnetism: order and disorder. Oxford: Clarendon Press.

Aitken, M.J. 1978 Archaeological involvements of physics. Phys. Rep. C 40, 277–351.

Aitken, M.J. 1990 Science-based dating in archaeology. London: Longmans.

Bartlett, D.F. 1990 Conduction current and the magnetic field in a circular capacitor. Am. J. Phys. 42, 1168–

1172.

Bloch, F., Hansen, W.W. & Packard, M. 1946 The nuclear induction experiment. Phys. Rev. 70, 474–485.

Brownell, J.H., Doucas, G., Kimmitt, M.F., Mulvey, J.H., Omori, M. & Walsh, J.E. 1997 The angular

distribution of the power produced by Smith–Purcell radiation. J. Phys.D 30, 2478–2481.

Colquhoun, I.J. 1998 High resolution NMR spectroscopy in food analysis and authentication. In Spectroscopy

Europe vol. 10, part 1, pp. 8–18. Chichester: Wiley–VCH.

Cummins, E.D. 1996 Parity nonconservation in atoms and searches for permanent electric dipole moments. In

Amazing light (ed. R.Y. Chiao), pp. 125–141. New York: Springer-Verlag.

Dutra, S.M. 1997 Correspondence principle approach to cavity losses. Eur. J. Phys. 18, 194–198.

Hahn, E. & Maxwell, D.E. 1951 Chemical shift and field independent frequency modulation of the spin echo

envelope. Phys. Rev. 84, 1246–1247.

Knight, W.D. 1949 Nuclear magnetic resonance shift in metals. Phys. Rev. 76, 1259–1260.

Müller, C.A. & Oort, J.H. 1951 The interstellar hydrogen line at 1420 Mc/sec., and an estimate of galactic

rotation. Nature 168, 357–358.

Ramsey, N.F. 1950 The internal diamagnetic field corrections in measurements of the proton magnetic

moment. Phys. Rev. 77, 567; 78, 699–703.

Ramsey, N.F. 1956Molecular beams. Oxford: Clarendon Press.

Roche, J. 1998 The present status of Maxwell’s displacement current. Eur. J. Phys. 19, 155–166.

Rollin B.V. 1946 Nuclear magnetic resonance and spin lattice equilibrium. Nature 159, 669–670.

Rollin, B.V. & Hatton, J. 1947 Nuclear magnetic resonance at low temperatures. Nature 159, 201.

Rollin, B.V., Hatton, J., Cooke, A.H. & Benzie, R.J. 1947 Nuclear magnetic resonance at low temperatures.

Nature 160, 436–437.

Zapolsky, H.S. 1987 Magnetic shielding and the discovery of the chemical shift. Am. J. Phys. 55, 1140.

B

The following publications are those referred to directly in the text. A full bibliography

appears on the accompanying microfiche, numbered as in the second column. A photocopy is

available from the Royal Society Library at cost.




(1) (1) 1934 (With K. Lark-Horowitz & H.J. Yearian) Electron diffraction from vacuum-sublimated

layers. Phys. Rev. 45, 123.

(2) (2) 1935 (With K. Lark-Horowitz & J.D. Howe) method of making extremely thin films. Rev. Sci.

Instrum. 6, 401–403.

(3) (4) 1937 (With M.H. Hebb) A theoretical study of magnetic cooling experiments. J. Chem. Phys.

5, 338–350.

(4) (5) 1938 The focusing of charged particles by a spherical condenser. Phys. Rev. 54, 818–825.

(5) (6) 1946 (With H.C. Torrey & R.V. Pound) Resonance absorption by nuclear moments in a solid.

Phys. Rev. 69, 37–38.

(6) (7) 1947 The radar equation. In Radar system engineering (ed. L.N. Ridenour), ch. 2. New York:

McGraw-Hill.

(7) (8) Limits of pulse radar. In Radar system engineering (ed. L.N. Ridenour), ch. 4. New

York: McGraw-Hill.

(8) (9) 1951 (With J.H. Van Vleck & H. Goldstein) Atmospheric attenuation. In Propagation of short

radio waves (ed. D.E. Kerr), ch. 8. New York: McGraw-Hill.

(9) (10) 1948 (With C.G. Montgomery & R.H. Dicke) Principles of microwave circuits. New York:

McGraw-Hill.

(10) (11) 1946 (With R.V. Pound & H.C. Torrey) Measurement of magnetic resonance absorption by

nuclear moments in a solid. Phys. Rev. 69, 681.

(11) (12) (With H.C. Torrey & R.V. Pound) Theory of magnetic resonance absorption by nuclear

moments in a solid. Phys. Rev. 69, 680.

(12) (14) (With R.V. Pound & N. Bloembergen) Nuclear magnetic resonance absorption in

hydrogen gas. Phys. Rev. 70, 986–987.

(13) (15) (With N. Bloembergen & R.V. Pound) Resonance absorption by nuclear moments in a

single crystal of CaF2. Phys. Rev. 70, 988.

(14) (16) 1947 (With N. Bloembergen & R.V. Pound) Nuclear magnetic relaxation. Nature 160, 475–

476.

(15) (17) 1948 (With N. Bloembergen & R.V. Pound) Relaxation effects in nuclear magnetic resonance

absorption. Phys. Rev. 73, 679–712.

(16) (19) 1949 (With G.E. Pake) Line shapes in nuclear paramagnetism. Phys. Rev. 74, 1184–1188.

(Erratum. Phys. Rev. 75, 534.)

(17) (20) (With R.M. Brown) Nuclear magnetic resonance in weak fields. Phys. Rev. 75, 1262–

1263.

(18) (21) (With J.H. Gardner) A precise determination of the proton magnetic moment in Bohr

magnetons. Phys. Rev. 76, 1262–1263.

(19) (22) (With H.S. Gutowshky, G.B. Kistiakowsky and G E. Pake) Structural investigations by

means of nuclear magnetism. 1. Rigid crystal lattices. J. Chem. Phys. 17, 972–981.

(20) (23) 1950 (With N.F. Ramsey) On the possibility of electric dipole moments for elementary

particles and nuclei. Phys. Rev. 78, 807.

(21) (24) 1951 (With H.L. Ewen) Observations of a line in the galactic radio spectrum. Nature 168,

356.

(22) (26) (With R.V. Pound) A nuclear spin system at a negative temperature. Phys. Rev. 81, 279–

280.

(23) (27) Nuclear resonance in crystals. Physica 17, 282–302.

(24) (28) 1952 (With N.F. Ramsey) Interactions between nuclear spins in molecules. Phys. Rev. 85, 143–

144.

(25) (29) (With D.K. Bailey, R. Bateman, L.V. Berkner, H.G. Booker, G.F. Mongomery, W.W.

Salisbury & J.B. Wiesner) A new kind of radio propagation at very high frequencies

observable over long distances. Phys. Rev. 86, 141–145.

(26) (30) (With H.Y. Carr) Interaction between nuclear spins in HD gas. Phys. Rev. 88, 415–436.

(27) (31) The lifetime of the 2 2S½ state of hydrogen in an ionized atmosphere. Astrophys. J. 116,

457.




(28) (34) 1953 (With S.J. Smith) Visible light from localized charges moving across a grating. Phys. Rev.

92, 1069.

(29) (35) (With F. Reif) Nuclear magnetic resonance in solid hydrogen. Phys. Rev. 91, 631–641.

(30) (37) 1954 (With G.B. Benedek) Nuclear magnetic resonance in liquids under high pressure. J.

Chem. Phys. 22, 2003–2012.

(31) (41) 1956 (With G.B. Field) Influence of collisions upon populations of hyperfine states in

hydrogen. Astrophys. J. 124, 542–549.

(32) (45) 1957 (With J.H. Smith & N.F. Ramsey) Experimental limit to the electric dipole moment of

the neutron. Phys. Rev. 108, 120–122.

(33) (46) 1960 Nuclear spin relaxation and nuclear electric dipole moments. Phys. Rev. 117, 829–831.

(34) (48) Radio astronomy and communication through space. Brookhaven Lecture Series BNL

658 (T-214). (Reprinted in Interstellar communication (ed. A.G.W. Cameron), 1963.)

(35) (53) 1963 (With G.B. Collins, J. Hornbostel, T. Fujii & F. Turkot) Search for the Dirac monopole

with 30-BeV protons. Phys. Rev. 129, 2326–2336

(36) (54) 1965 Electricity and magnetism (Berkeley Physics Course, vol. II). New York: McGraw-Hill.

(37) (56) 1969 On the alignment of interstellar dust. Physica 41, 100–127.

(38) (57) On the absorption and emission of light by interstellar grains. Astrophys. J. 158, 435–

440.

(39) (59) 1971 (With L. Spitzer, Jr) Orientation of rotating grains. Astrophys. J. 167, 31–62.

(40) (60) 1973 (With P. Aanestad) Interstellar grains. A. Rev. Astron. Astrophys. 11, 309–372.

(41) (61) (With C.R. Pennypacker) Scattering and absorption and emission of light by

non-spherical dielectric grains. Astrophys. J. 158, 443–440.

(42) (62) 1975 Interstellar grains as pinwheels. In The dusty universe, pp. 155–168. Neal Watson

Academic Publications.

(43) (63) 1976 Temperature fluctuations in very small interstellar grains. Astrophys. J. 206, 685–690.

(44) (66) 1977 (With P.R. Shapiro) A model for the optical behaviour of grains with resonant

impurities. Astrophys. J. 214, 92–105.

(45) (67) (With H.C. Berg) Physics of chemoreception. Biophys. J. 208, 193–219.

(46) (69) 1979 Suprathermal rotation of interstellar grains. Astrophys. J. 231, 404–416.

(47) (72) 1982 (With S. Diminopoulos, S.L. Glashow & F.W. Wilczek) Is there a local source of

magnetic monopoles? Nature 298, 824–825.

(48) (73) 1983 Monopoles and the galactic magnetic field. In Magnetic monopoles (ed. R.A. Carrigan

& W.P. Trower), pp. 141–149. London: Plenum Press.

(49) (74) 1983 The back of the envelope. Am. J. Phys. 51, 11, 107, 205, 299, 391, 494, 586, 874, 970,

1068.

(50) (75) 1984 The back of the envelope. Am. J. Phys. 52, 8, 107, 203, 301, 394, 490, 588, 681.

(51) (76) 1987 The back of the envelope. Am. J. Phys. 55, 680, 778, 876, 972, 1066.

(52) (77) 1988 The back of the envelope. Am. J. Phys. 56, 12, 108, 202, 298, 392, 490.

(53) (82) 1990 (With M.J. Schnitzer, S.M. Block & H.C. Berg) Strategies for chemotaxis. In General

Biology Symposium 46, pp. 15–34.



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