The classical theory of the dynamics of viscous fluids is based on the assumption that there is only one fundamental coefficient of viscosity, $\mu$, the coefficient of shear viscosity. The other quantity, ${\mu }^{\prime }$, the second coefficient of viscosity, is assumed to be equal to $-\frac{2\mu }{3}$ in order that $\kappa (=\frac{(2\mathrm{}\mu +3\mathrm{}{\mu }^{\prime })}{3})$, the coefficient of bulk viscosity, should be zero. In making this assumption classical hydrodynamics parts company from classical elasticity, in which two fundamental quantities, the Lamé constants $\lambda$ and $\mu$, are introduced.

The above assumption seems to have some basis in theory only in the case of ideal monatomic gases; it has, however, been carried over implicitly to both liquids and gases of all degrees of complexity. One might therefore expect some differences to exist between theoretical predictions and experimental results due to this oversimplification. The present review has been undertaken with a view to exploring the existence and the magnitude of any such differences.

Up to the present, discrepancies have been noticed in the field of investigation which deals with the transmission of sound energy through liquid and gases.

As far as liquids are concerned no work has been done on the absorption of energy associated with vibrations in the sonic range (20 to 20,000 vibrations per second). In the ultrasonic range experimental values of absorption differ from the theoretical ones by factors ranging from 3 to 1000. In gases, both in the sonic and supersonic ranges, the values differ by a factor whose magnitude lies in the range of 4 to 100.

Most of the work which has been done in this field has been concerned with the passage through liquids of sound energy in the ultrasonic range of frequencies. Here it is clear that the value of $\frac{{\mu }^{\prime }}{\mu }$ deduced from experiment is in good agreement with the value of the ratio deduced from information on excess absorption of energy. The viscosity ratio is never negative; its value ranges from about 1 to about 120 in the cases so far investigated.

The Boltzmann theory treatment of electrical discharges in gases has been one of the undeveloped fields in physics. The aim of this paper is to show what type of molecular model makes the mathematical treatment of the problem possible.

The fundamental processes of the molecular kinetic theory of electrical discharges concern the collisions between gas molecules and charged particles such as ions or electrons. The effective cross sections of the molecule for elastic, exciting, and ionizing collisions are the fundamental quantities regarding these phenomena. Two methods are considered, according to how these fundamental quantities are introduced, to establish the molecular kinetic theory.

One method is to adopt a proper molecular model for collision processes. The other method is to adopt the "exact" (i.e., observed or quantum-mechanically calculated) values of collision cross sections. This paper concerns itself with the first method, and the principal objective is to attain mathematical simplicity for the theory. The second method is abandoned because the statistical calculation on each step is complicated, and furthermore, the calculation must be achieved separately for each kind of gas. This second method may be adequately adopted after the treatment based on a model is accomplished.

It is shown that for aluminum absorbers, a single range-energy equation $R=412\mathrm{}$ ${E_0}^{1.265-0.0954\ln E_0}$ (mg/${\mathrm{cm}}^2$) will fit the most reliable published values of practical ranges of monoenergetic electrons and the maximum ranges of nuclear beta-rays in the energy region $0.01<~E_0<~2.5$ Mev. The average deviation of 59 monoenergetic measurements from this equation is +0.08 percent in energy, and -0.05 percent in energy for 35 beta-ray measurements. The mean deviation is 4.1 percent in each case. There are few ranges for energies above 2.5 Mev. All the higher energy values found in the literature and four new measurements on monoenergetic electrons are presented and are shown to be consistent with the range-energy equation $R=530\mathrm{}$ $E_0-106\mathrm{}$ (mg/${\mathrm{cm}}^2$) for $E_0>~2.5$ Mev. It is shown that the curve ($\frac{d{E}_0}{\mathrm{dR}}$) is nearly parallel to the theoretical curve for the rate of energy loss by ionization in the region between 0.01 and 20 Mev and is about 25 percent larger. The reason for this discrepancy is not known. All the methods commonly used to determine the ranges of beta-rays from absorption curves are discussed and a new method developed by the authors is presented.

The available experiments on the absorption spectra, photoelectric, and photolytic properties of the silver halide crystals are re-analyzed and interpreted. The conclusions drawn may be regarded in the nature of extensions of the Gurney-Mott theory of photolytic action. The principal speculative viewpoints are as follows:

1. The characteristic absorption spectra of the pure salts derive much of their structure from forbidden optical transitions associated with lattice distortion arising from dislocations. It is proposed that in materials prepared from the melt the dislocations are formed by condensation of lattice vacancies associated with about 0.1 percent of Schottky defects.

2. It is also concluded that some of the absorption structure is associated with "forbidden" $d^{10}\to d^{9}s$ transitions in the silver ions.

3. It is proposed that the electron traps which are responsible for the early deposits of photolytic silver are incipient halogen-ion vacancies which have an effective charge $+\frac{e}{2}$. These vacancies occur at jogs in dislocation lines, where such lines pass from one slip plane to a parallel plane, and may be enhanced by plastic flow. Incipient positive-ion vacancies, having an effective charge $-\frac{e}{2}$, also occur and act as nuclei for forming halogen clusters whose absorption bands are hidden behind the fundamental band.

4. At room temperature, the photoelectrons may be trapped by interstitial silver ions before ending at incipient halogen-ion vacancies; however this process represents only a temporary delay since the entire silver atom may migrate to the dislocation.

5. It is suggested that the addition of sulfur to the silver halides plays a role in enhancing darkenability in three ways: (a) By forming precipitates which produce distortion that enhances the number of incipient vacancies; (b) by extending the absorption spectrum toward the red end of the spectrum; and (c) by increasing the equilibrium density of interstitial silver ions.

6. It is proposed that the luminescent radiation observed in pure silver halides by Farnell, Burton, and Hallama arises from transitions within the silver ion. The emitting ions are at dislocations in AgCl and AgBr.

A sequence of experiments is suggested.

A systematics of the $\beta$-transitions of even $A$ nuclei is given. An interpretation of the character of the transitions in terms of nuclear shell structure is achieved on the hypothesis that the odd nucleon groups have the same structure as in odd $A$ nuclei, together with a simple coupling rule between the neutron and proton groups in odd-odd nuclei.

A systematics is given of all transitions for odd $A$ nuclei for which sufficiently reliable data are available. The allowed or forbidden characters of the transitions are correlated with the positions of the initial and final odd nucleon groups in the nuclear shell scheme. The nuclear shells show definite characteristics with respect to parity of the ground states. The latter is the same as the one obtained from known spins and magnetic moments in a one-particle interpretation.

A brief account is given of Dyson's proof of the finiteness after renormalization of the matrix elements for scattering processes ($S$-matrix elements) in electrodynamics (interaction of photons and electrons). It is shown to which meson interactions this proof can be extended and some of the difficulties which arose in this extension are discussed.

It is shown that the conductivity in the ohmic part of the cuprous oxide layer can be explained with the usual band picture of semiconductors only by assuming the presence of some donor-type impurities in addition to the usual acceptor type. The energy difference between the acceptors and the filled band is 0.3 electron volt, and the total number of impurity atoms is about ${10}^{14}$ to ${10}^{16}$ per ${\mathrm{cm}}^3$, the number of donors being less than but of the same order as the number of acceptors. Applying the Schottky theory of the space charge exhaustion layer, one finds from the dependence of capacity of the rectifier on bias voltage that the density of ion charge in the rectifying layer is of the same order of magnitude as the difference between the donors and acceptors found from the conductivity, thus furnishing a check for the theory. The field at the copper-cuprous oxide interface calculated from the space charge is about 2×${10}^4$ volts/cm; the height of the potential at the surface as compared with the oxide interior is about 0.5 volt; and the thickness of the space charge layer about 5.0×${10}^{-5\mathrm{}}$ cm. The diffusion equation for flow of current through this space charge region can be integrated to give the current in terms of the field at the interface and the applied potential across the space charge layer. Two currents are involved, one from the semiconductor to the metal ($I_s$) and one from the metal to the semiconductor ($I_m$) which is similar to a thermionic emission current into the semiconductor. The net current is, of course, $I=I_m-I_s$. One can get this "emission" current ($I_m$) by dividing the true current by the factor $1-\exp (-\frac{e{V}_a}{\mathrm{kT}})$, where $V_a$ is the applied potential. This emission current depends on the absolute temperature and on the field at the copper-cuprous oxide interface. At high fields the logarithm of the current is proportional to the square root of the field, and at low fields the current decreases more rapidly indicating a patchy surface having small areas of low potential maximum from which all the emission comes when the field is large. This effective potential maximum measured from the Fermi level in the copper is about 0.5 ev, and the fraction of the total area effective ranges from ${10}^{-2\mathrm{}}$ to ${10}^{-5\mathrm{}}$ depending on how the rectifier was made. This last factor—the fraction of the area having this low potential maximum—is by far the most important variable, resulting in low reverse currents when the fraction is small and large reverse currents when the fraction is large.

Ionization by electron impact in diatomic gases has been studied in this work with a mass spectrometer designed to measure $\frac{m}{e}$, appearance potential, and initial kinetic energy for each ion observed. Results have been obtained for the gases CO, ${\mathrm{N}}_2$, NO, and ${\mathrm{O}}_2$ with some confirmatory work in ${\mathrm{H}}_2$. Discussion is included of the nature and identification of dissociative ionization processes and of the retarding potential and appearance potential measurements. Values of important quantities such as the dissociation energies of CO, ${\mathrm{N}}_2$, and NO; the sublimation energy of C; the electron affinity of O; and the excitation energy of ${\mathrm{O}}^{-}$ are determined again by electron impact in this work.