A new table of relative abundances of nuclear species existing in nature has been prepared based upon the best available data on the compositions of the sun, stars, and meteorites. The general methods utilized in compiling the table are explained.

A critical survey was made of the upper atmosphere to an altitude of 300 km, reviewing present knowledge on such factors as composition, winds, temperature, pressuree and diffusion. On the basis of recent information a model atmosphere having a diurnal temperature cycle above 100 km was adopted.

Employing the adopted temperature-altitude function, it was possible to re-examine the rate of recombination occurring in the $F_2$ ionospheric layer. Considering a temperature-dependent recombination coefficient and including the effect of atmospheric contraction arising from the quotidian temperature variation, it was possible to reformulate the equation describing the rate of change of electron density. On this basis, the predicted value of electron density during darkness in the $F_2$ ionospheric layer agreed with the observed values very much better than did those obtained when the simple quadratic recombination law was employed.

In the course of the investigation, all possible sources of nocturnal ionization were examined. For the $F_2$ layer insufficient data are on hand to reveal the magnitude of horizontal transport phenomena, which may be of importance. Vertical transport is quantitatively treated. All other sources of ionization seem to be insufficient to maintain the observed ionization levels.

This paper discusses some aspects of Kron's tensor theories associated with the use of non-holonomic reference systems in the mathematical treatment of rotating electrical machines. The general theory is discussed in the first part, and is applied in the second part, by way of illustration, to a squirrel-cage induction motor.

It is shown that the thermodynamical equilibrium condition for a fluid at rest in a static gravitational field is, apart from the Tolman condition $T{\left(g_{44}\right)}^{\frac{1}{2}}=\mathrm{const}.\mathrm{}$, governed by the condition $\alpha {\left(g_{44}\right)}^{\frac{1}{2}}=\mathrm{const}.\mathrm{}$, where $\alpha$ is the chemical potential of the fluid (including mass energy) regarded as a function of the space coordinates. This relation constitutes the relativistic generalization of the well-known Gibbs condition for the equilibrium in a gravitational field.

One electron molecular orbitals for mobile electrons, subject to the potential energy of a molecular skeleton, are considered. If the atoms are far apart, the orbitals can be built up exactly from $2p$ atomic wave functions. The molecule in natural size is formed by adiabatic approach. It is shown that all the nodal surfaces reach into infinity, if the atoms are all alike, but that closed nodal surfaces may exist, if they are not. It is proved that the number of electrons inclosed in nodal surfaces is invariant against adiabatic change. Nodal surfaces for antisymmetrized molecular orbitals are then discussed.

The dynamic forces which a turbulent flow exerts on the individual protrusions of a rough wall have been measured. It was found that even in the case of an extremely high relative roughness, the drag force on the protrusions may be determined from the logarithmic friction laws. A very significant lift force which tends to pull the protrusions away from the wall and into the flow was measured. This lift force was divided into two parts: A constant average value and a random fluctuation superimposed over the average. A careful statistical analysis showed that the frequency of different pressures or lift forces at the wall follows very accurately the normal error law. This fact seems to indicate that in the description of turbulence near a rough wall, the pressures must be regarded as the primary influence, not the velocities.

It is shown that, for a particle to be at rest in a static, axially symmetric gravitational field, the force on the particle must vanish. This result is then generalized to the case of an arbitrary static gravitational field.