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Dec 1966

Volume 34, Issue 12, pp. 1079-1212

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Plastic Drive Belts

Arthur M. Vash, Editor

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. xv

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Dry Ice on Demand

Arthur M. Vash, Editor

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. xv

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Epoxy Dispenser

Arthur M. Vash, Editor

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. xvi

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Microspheres

Arthur M. Vash, Editor

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. xvi

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Useful Battery

Arthur M. Vash, Editor

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. xvi

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Resource Letter SAP-1 on Subatomic Particles

Clifford E. Swartz

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1079

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Prepared at the request of the AAPT Committee on Resource Letters; supported by a grant from the National Science Foundation.
This is one of a series of Resource Letters on different topics, intended to guide college physicists to some of the literature and other teaching aids that may help them improve course contents in specified fields of physics. No Resource Letter is meant to be exhaustive and complete; in time there may be more than one letter on some of the main subjects of interest. Comments and suggestions concerning the content and arrangement of letters as well as suggestions for future topics will be welcomed. Please send such communications to Professor Joel E. Gordon, Chairman Resource Letter Committee, Department of Physics, Amherst College, Amherst, Massachusetts 01002.
Notation: The letter E after an item number indicates elementary level, useful principally for freshman liberal arts through sophomore physics courses; the letter I indicates intermediate (junior, senior) level; and the letter A indicates advanced material principally suited for senior, graduate study. An asterisk (∗) indicates items particularly recommended for introductory study.
Additional copies: Available from American Institute of Physics, 335 East 45 Street, New York, New York, 10017. When ordering, request Resource Letter SAP-1 and enclose a return envelope.
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The Robert A. Millikan Lecture Award 1966

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1086

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Electrons, Photons, and Students

Alan M. Portis

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1087 | Cited 1 time

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The Robert A. Millikan Lecture Award is made annually to a physicist chosen by a special committee of the American Association of Physics Teachers because of his creative and imaginative contributions to the teaching of physics. The lecturer selected is one whom the Association wishes to honor at the Summer Meeting in the same way that it honors the Oersted Medalist at the time of the Annual Meeting. The award is made possible through the annual support of of Prentice-Hall, Inc.; the first award was made in 1964.
The recipient of this award for 1966 is Alan M. Portis, Professor of Physics at the University of California at Berkeley.
The four-year development of the Berkeley Physics Laboratory is described starting from its inception in the Summer of 1962. Reasons for the special attention given to electrons and photons are presented. The use of student groups in the laboratory trials is discussed. The wide response to the laboratory is analyzed. Finally, modifications currently being made in the Laboratory by the Berkeley Physics faculty are presented and discussed.
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Joseph Henry and the Relations between Teaching and Research

Charles Weiner

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1093

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America's leading physicist of the midnineteenth century made his major research contributions while employed full time as a science teacher. A study of Joseph Henry's unpublished correspondence and laboratory journals and the lecture notes of his students reveals the background of his career as a physics professor at Princeton in the 1830's and 1840's. These documents display a reciprocal and mutually advantageous structuring of Henry's lectures and research, which expanded the scope and increased the effectiveness of each. This close interconnection between teaching and research was established by Henry at a time when the research function of the college professor had not yet been accepted.

Accidental Degeneracy

David F. Greenberg

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1101 | Cited 6 times

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A detailed discussion of nongeometric, or “accidental,” degeneracy is presented in the context of Newtonian, relativistic, and quantum mechanics. An analogy with broken symmetries in elementary-particle physics is used to present an elementary discussion of certain recent developments in theoretical high-energy physics.

A Gravitational Paradox

Jean-Marc Lévy-Leblond and Peter Thurnauer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1110 | Cited 1 time

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Adapting an argument by Dyson in quantum electrodynamics, we point out that the attractive and long-range character of the gravitational interaction may seem to prevent the universe from being stable against decay into successively lower energy states. A straightforward solution to this paradox is given, based on the essentially nonlinear nature of gravitational theory. This nonlinearity, whose importance is thus clearly demonstrated, is shown to have a a very elementary origin. A simple approximation, incorporating the nonlinear effects in a physically transparent way, quantitatively substantiates our intuitive argument.

Compton Effect and Electron Binding

William J. Veigele, Philip T. Tracy, and E. Michael Henry

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1116 | Cited 2 times

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The usual expressions for the Compton effect are based on the assumptions that the scattering electron is free and stationary. These assumptions are reasonable when the photon energy is large compared to the electron binding energy; however, in many situations this is not the case, and the binding energy and momentum of the electron alter Compton scattering by causing (1) line broadening, (2) a discrete spectrum, (3) a line-shift defect, (4) a decrease in incoherent scattering at low angles, (5) an increase in coherent scattering at low angles, and (6) a change in recoil electron distribution. These effects are described, and differential and average cross sections for carbon are calculated on the Thomas-Fermi model to illustrate them quantitatively.

Electric Analog Network for Quantum Mechanics

E. W. Cowan

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1122

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An electric network is presented in which the energy density is distributed in three-dimensional space in the same fashion as the probability density waves for a spinless particle in any given potential field. The network is of interest in that it can be easily realized physically.

The Water Flask with Unequal Holes

Eric Weissman

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1126

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This article discusses the problem of the water flask with several unequal holes in the bottom by considering it as a nonlinear work problem which can, nevertheless, be solved by elementary considerations. It is described as a suitable fluid-mechanics experiment for elementary courses, and it is then solved analytically—first without the calculus and then with the help of the calculus. It is the solution without the calculus which is of particular interest for non physics majors, because of its comparative simplicity and lack of cumbersome equations.

Graphical Aids in the Teaching of Special Relativity

Robert H. Kohler

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1128

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The kinematics of special relativity is depicted through space-time diagrams, whereby the Lorentz transformation as well as the Galilean can be presented in graphical form rather than analytic. The space-time diagrams are then used to formulate and explain several of the paradoxes of special relativity. The method is a variation of the Minkowski diagram. The reference axes are kept fixed, and the space-time point undergoes an apparent displacement in the plot as the observation frame is changed. The graphical analysis is semiquantitative for some problems and is quantitative for others.

Interaction Energy of a Dielectric in an Electrostatic Field

Victor Gilinsky and Dennis Holliday

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1134

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A straightforward computation of the interaction field energy of a dielectric in a uniform external electrostatic field appears to yield a result different from that given by a general theorem. It is shown here that the discrepancy can be resolved by considering the uniform field of infinite extent to be the limit of a field of finite extent. A recent paper by Plesset and Venezian is discussed.

Mathematical Education for Scientists and Engineers

Hyman Serbin

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1138

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Mathematical education for scientists and engineers is defined as including not only the education required to understand currently accepted theories, but also the mathematical background which may become useful in future research. This broader requirement is confronted with the dilemma that the professional academic mathematicians emphasize the axiomatic and rigorously deductive aspects of their work. On the other hand, it is a serious error to teach mathematics from the standpoint of the applications; to do so is to forsake mathematical abstraction as an end in itself. The pure mathematicians are separated into two groups, the “creative” and the “critical,” depending on the degree of rigor. Modern mathematicians in the overwhelming majority fall within the critical school. Creative mathematicians postulate properties (sometimes implicitly) which have not been proved and arrive at new results without establishing the complete logical sequence from fundamental axioms. Mathematical education for applications should be taught by creatively oriented mathematicians. According to this point of view, the essential mathematical features of abstraction and rigor are still maintained.

Visualizing Statistical Thermodynamics: The Boltzmann Distribution Model

M. V. Sussman

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1143

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Entropy change, work and heat effects, temperature, distribution functions, Brownian movement, and other elementary concepts of statistical thermodynamics can be visually demonstrated with a mechanical device that simulates some of the microscopic thermodynamic behavior of a nonatomic ideal gas.

On Linear Friction in Lagrange's Equation

Harry H. Denman

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1147 | Cited 2 times

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A linear frictional force in the equation of motion of a particle is obtained if one modifies the Lagrange equation of motion by the addition of the frictional term, which may be expressed in terms of the Rayleigh dissipative function. It is shown that one can construct Lagrangians in several simple cases so that the Lagrange equation of motion contains such a frictional force without the addition of any terms. This method is also useful in analyzing some aspects of the motion.

Second Quantization as a Graded Hilbert Space Representation

Donald H. Kobe

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1150 | Cited 8 times

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A review of the second quantization formulation of quantum mechanics is given based on the idea of a graded Hilbert space whose elements are represented by column matrices containing zero, one, two, ⋅⋅⋅, particle functions. The creation and annihilation operators are defined in terms of intuitive ideas about adding a particle to or removing a particle from the system. The (anti)commutation relations are shown to follow from the (anti)symmetry of the wavefunctions. The field operators which describe the creation or annihilation of a particle at a point are then obtained and their properties discussed. These operators are then used to express general operators in second quantization. Finally, a basis is introduced and the equations of occupation-number space are obtained.

Quantum Fact and Fiction. II

Alfred Landé

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1160 | Cited 1 time

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Electron diffraction was shown in Part I to be due to the quantum-mechanical activity of the diffractor rather than to a fictional wave-picture manifestation of the diffracted particles. Part II aims at eliminating further fictional elements, most of them based on inconsistency of interpretation. The controversy between the extremist views of Schrödinger and Born, either frequency resonance or quantum jumps, is removed by showing that consistency compels one to admit both to occur simultaneously. Attempts at saving duality and other fictions are criticized, such as the contention that (1) “duality is a fact” seen in the contrast of obvious particle effects and not so obvious particle effects, (2) that particles are material and waves are expectations by observing subjects, (3) that statistical law means the end of the sharp separation between subject and object, (4) that Heisenberg's empirical rule for the uncertainty of prediction means indeterminacy of existence. It is pointed out that quantum mechanics can be derived as a necessary consequence of general nonquantal postulates, known from deterministic mechanics, but applied now to the construction of a probabilistic schema of connection between events.

Simple Derivation of the Bloch Equation

D. ter Haar

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1164

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It is shown how one can derive Bloch's induction equation from the equation of motion of the density matrix by coarse-graining in time. The relaxation of the magnetization is assumed to be due to a fluctuating magnetic field acting upon the spins. The derivation does not provide any new information but is sufficiently simple that it may be used as a lecture application of the density matrix.

Quantum-Mechanical Tunneling

J. H. Fermor

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1168

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An elementary method is given for the exact determination of the quantum mechanical transmission and reflection coefficients for a rectangular one-dimensional potential barrier. The method also finds application in approximate solutions for multistep barriers.

The Microscopic Interpretation of Entropy

David H. Frisch

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1171

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The Boltzmann expression S = k ln Weq is developed from the macroscopic definition S ≡ ∫dQT and the quantum-mechanical interpretations of heat and work.

Kruskal Space and the Uniformly Accelerated Frame

W. Rindler

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1174 | Cited 28 times

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The striking formal similarities between the diagram of Kruskal space in general relativity and that of the uniformly accelerated rigid rod in special relativity are shown to be the result of certain physical similarities.

Dynamic Elastic Constants

M. A. Omar

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1179

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A simple derivation of the dynamic elastic constant in a monatomic and a diatomic chain is given. The oscillation frequency for these lattices is then simply derived from the equations of the harmonic oscillator. The propagation velocity is given directly.

A Versatile, Inexpensive Neutron Howitzer

W. S. Rawls and H. G. Voss

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1182 | Cited 1 time

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A neutron howitzer has been constructed in the physics department shop, using readily available materials and commonly used tools. The neutron howitzer is versatile, of quality construction, safe for student use, and low in cost.

A Radiation Torque Experiment

P. J. Allen

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1185 | Cited 2 times

Online Publication Date: Jul 2005

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The torque exerted by circularly polarized radiation can be demonstrated and measured in a simple microwave motor experiment. A small electric dipole, delicately suspended in a circular waveguide, continuously rotates under the torque influence of an incident circularly polarized wave of low power. A component of the wave energy scattered from the dipole experiences a natural downshift in frequency equal to twice the dipole rotation frequency. This intrinsic change in wave energy completely accounts for the power extracted from the wave in turning the dipole against damping forces. The experiment is a macroscopic model of a rotational mechanism through which spectral shifts can arise in nature, and appears to be analogous to the rotational Raman effect with linear molecules. Since the interaction between wave and dipole is reversible, the energy (frequency) of an interacting circularly polarized wave is increased whenever the direction of rotation of the scattering dipole opposes the torque of the wave. Through this mechanism, energy can be transferred from one circularly polarized wave to a second of higher frequency but of less intensity. This corresponds to the generation of an anti-Stokes line.
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Estimate of Molecular Sizes and Avogadro's Number from Surface Tension

E. A. Mason

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1193

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Radiation Protection in Teaching Institutions

C. B. Braestrup

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1193

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Ground State of the One-Dimensional Hydrogen Atom

M. Andrews

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1194 | Cited 8 times

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Thermodynamical Systems Involving Magnetic Fields

J. L. Mundy and V. L. Newhouse

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1195 | Cited 1 time

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Temperature in a Sector of an Annulus

Walter P. Reid

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1196

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Laws of Reflection and Refraction: Photon Flux

John F. Streib

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1197

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Refined Method for Measuring the Sound Wavelength in Gases—Discussion

A. S. El-Hakeem, R. A. Gaggioli, and I. C. Romer, Jr.

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1197

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Another Derivation of Euler's Equations of Rigid-Body Rotation

David L. Mott

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1197

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Matrix Optics Conventions

C. K. Crawford

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1198

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Determination of “g” through Circular Motion

Francis Wunderlich

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1199

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Information Requested about Use of Computers

Alfred M. Bork

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1199

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On “Maxwell's Ovals and the Refraction of Light”

James Rainwater

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1200

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On “Maxwell's Ovals and the Refraction of Light”

Milton H. Sussman

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1200

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Thought Stimulator on Angular Momentum

S. Schultz

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1201

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Erratum: An Anschaulichkeitsbeweis for Special Relativity [Am. J. Phys. 34, 780 (1966)]

George Goe

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1202 | Cited 4 times

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Erratum: Deductions from a Kinematic Principle of Relativity [Am. J. Phys. 34, 899 (1966)]

Eric Drake

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1202

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Erratum: Nonholonomic Constraints [Am. J. Phys. 34, 406 (1966)]

John R. Ray

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1202 | Cited 1 time

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New Foundations of Quantum Mechanics

Alfred Landé, Author and R. C. Whitten, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1203

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A Textbook of Magnetohydrodynamics

J. A. Shercliff, Author and F. R. Scott, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1204

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Lectures in Theoretical Physics, 1964, Vols. VII a, b, and c

W. Brittin, Editor, A. O. Barut, Editor, L. Marshall, Editor, and David Park, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1204

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The Velocity of Light

J. H. Sanders, Author and Robert A. Lufburrow, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1204

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Kinetic Theory. Vol. 1. The Nature of Gases and Heat

S. G. Brush, Author and E. A. Mason, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1205

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Differential Equations of Applied Mathematics

G. F. D. Duff, Author, D. Naylor, Author, and Donald A. McQuarrie, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1205

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Classical Charged Particles

F. Rohrlich, Author and David Park, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1206

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Concepts in Physical Science

Sidney Rosen, Author, Robert Siegfried, Author, John M. Dennison, Author, and Raymond J. Seeger, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1206

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Men of Physics: L. D. Landau. Vol. I. Low Temperature and Solid State Physics

D. ter Haar, Editor and William D. Foland, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1207

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Lectures on Matter and Equilibrium

Terrell L. Hill, Author and Roald K. Wangsness, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1207

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Symmetries in Elementary Particle Physics

A. Zichichi, Editor and L. E. Porter, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1208

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Electric and Magnetic Fields

D. H. Tomboulian, Author and W. M. Schwarz, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1208

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The Statistical Mechanics of Simple Liquids

Stuart A. Rice, Author, Peter Gray, Author, and Andrew G. De Rocco, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1209

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Dynamical Theory of Groups and Fields

Bryce S. DeWitt, Author and Albert A. Mullin, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1209

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Early Electrodynamics—The First Law of Circulation

R. A. R. Tricker, Author and William D. Foland, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1210

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Modern Physics

R. L. Sproull, Author and Laurence Rozier Holland, Reviewer

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1210

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Abstract Unavailable
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Central Pennsylvania Section

C. Burleigh Cooper

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1211

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Michigan Section

L. B. Wocholski

American Journal of Physics -- December 1966 -- Volume 34, Issue 12, pp. 1212

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