The general theory of anelastic substances is simplified for the case of an anelastic fluid. It is shown that slow steady motions and the diffusion of vorticity obey the same laws as in the Stokes-Navier theory of a viscous fluid. A criterion for the validity of these equations is derived.

The propagation and absorption of longitudinal isentropic waves exhibits new phenomena, however. There is hysteresis in the response of the density to the pressure. This hysteresis vanishes for very low and very high frequencies. The compressibility for these two limiting cases approaches different, real, values. For intermediate values the compressibility is a complex number, corresponding to the hysteresis. The velocity of propagation is also a complex number, which is a function of the frequency. The roots of this function are two in number, and determine two relaxation times. One of these is associated with the hysteresis mentioned above, the other with viscosity.

The free streamline theory has been used for evaluation of the cavity drag of symmetrical wedges of arbitrary angle. The required conformal transformation is derived explicitly. This calculation is an extension of Riabouchinsky's theory of the cavity drag of a flat plate. As an approximation, the pressure distribution for a two-dimensional wedge is used to calculate the cavity drag of the corresponding cone of revolution. A comparison of the result of this approximation with experimental measurements made by Reichardt shows good agreement.

An explicit expression, $E_x=f\left(x\right)\mathrm{}$, is given for the $x$ component of the electric field on the $y=0\mathrm{}$ plane in the gap between two infinite, oppositely charged conducting masses bounded by the $y=0\mathrm{}$, $x=b$ planes and the $y=0\mathrm{}$, $x=-b$ planes, respectively. The formula can be handled analytically and its maximum deviation from the rigorous value is one part in 5000. The coefficients of the Fourier expansion of $E_x$ and $V$ are given and used to write down a rapidly convergent series for the potential in the narrow gap between two right circular, coaxial conducting cylindrical electrodes. The resonant frequency of a re-entrant cylindrical cavity with a narrow gap is computed to about 0.03 percent. The radiation pattern from the open end of a rectangular wave guide terminating in an infinite conducting plane and transmitting only the $T{E}_{10}$ mode is calculated with four-place accuracy.

The frequency spectrum of a face-centered cubic crystal lattice is found by actually modeling the constant-frequency surfaces of the secular determinant in plaster of Paris and measuring the volume enclosed between successive surfaces. The frequency spectrum so obtained is used in the evaluation of the specific heat of a general crystal of the type treated, and numerical values are presented for the element silver. The present theory (that of Born and v. Karman) is in much better agreement with experimental values for temperatures below 100°K than is the Debye theory. Certain anomalies in the specific heat curves of silver and potassium chloride at temperatures below 10°K are not explicable in terms of the atomic model that is used.

A new method of determining the relaxation time and the electric dipole moment of polar substances has been worked out. This method uses dilute solutions of polar substances in non-polar solvents, and is based on measuring the dielectric constant and the coefficient of anomalous absorption of these solutions as a function of concentration. The measurements must be made at a constant frequency, in the vicinity of the maximum of anomalous absorption.

The method has been applied to formic, acetic, propionic, and $n$-butyric acids in the dioxane. The measurements have been made at 25.6-cm wave-length, using the Drude-Coolidge method, with Slatis' correction for induction effect in the condenser leads. The relaxation time data obtained were used to calculate the volume of the particle which becomes oriented by the impressed electric field. The volumes computed were proportional to the molecular volumes. This indicated that the anomalous absorption of ultra-high frequencies in fatty acids is due to the orientation of the entire molecule as a unit. This means that the dipole-bearing group of the fatty acid molecules (i.e., carboxyl) is not free to be oriented independently of the rest of the molecule. The experimental data used to calculate the relaxation time, were used to determine the dipole moments of fatty acids. The results obtained were in agreement with earlier determinations, thus furnishing a good support in favor of the validity of the relaxation time data obtained.

The photolysis of Ag sorbed on small particles of ZnO and Ti${\mathrm{O}}_2$ in two allotropic modifications is described, also the preparation of photosensitive surface complexes of this type. Gels of such materials are found to change their diffuse reflecting power for light (relative albedo) permanently upon exposure to radiation of wave-lengths up to approximately 5800A. It is possible to obtain with these materials photographic surface images without microscopically resolvable structure. The dependence of the maximal relative albedo variation (80 percent) upon the Ag concentration is found to be that corresponding to a monolayer of Ag atoms. The albedo change is interpreted as a culminative photolysis of the monolayer on the particles exposed to the radiation. This photolysis is reversible upon contact with traces of ${\mathrm{H}}_2$${\mathrm{O}}_2$ or ${\mathrm{O}}_3$. The reversion reestablishes the original photo-sensitive qualities so that the whole process can be repeated many times. A hypothesis of the mechanism of this effect is presented.

The differential equations for a plate column are solved for cases that arise in the concentration of isotopes, where there is a small difference in the concentration in the liquid and gas phases, or where the equilibrium constant for ion exchange is very nearly unity. A formula suitable for computation is deduced, and curves are given showing the rate of approach to equilibrium for various numbers of plates.

It is shown that the numbers of valence electrons assigned to the $\gamma$-alloys, $\beta$-manganese and alloys with similar structure, and $\alpha$-manganese by a new system of metallic valences agree closely with the electron numbers calculated for complete filling of important Brillouin polyhedra for these structures.