Using a particular parametrization of paths, the free particle and the harmonic oscillator are treated by the Feynman method of summation over histories of the system. The propagators obtained are, apart from an arbitrary phase factor, those of conventional quantum mechanics.

The results of self-consistent field calculations with exchange for the ground-state configurations of F−, Fe+16, +14, Al+3, +1 are presented.

The methods introduced into the theory of atomic spectra by Racah are applied to the problem of the computation of the strengths of electric quadrupole lines. Detailed numerical results are given for two configurations of equivalent d-electrons.

With the neglect of collisions, a relativistic form of Boltzmann's transport equation is derived and its invariance under a Lorentz transformation is established.

When waves are propagated through a medium whose velocity of propagation varies gradually from place to place, the wave direction and intensity vary according to the laws of refraction. Although the geometry of ray-paths has been well explored, and so also the laws governing the intensity of a coherent train of waves, little attention has apparently been given to the variation in intensity of an incoherent beam having a broad spectrum. The transformation of the energy spectrum is of practical importance in branches of geophysics, for example, in the study of sea waves entering shallow water, or of microseismic waves propagated through inhomogeneous regions of the earth's crust. Accordingly, it seems worth while to state and prove the rule governing the transformation of the two-dimensional spectrum function of a wave disturbance undergoing refraction.

In a recent paper (1) expressions were found for the statistical distributions of the velocities of the zero-crossings and of the maxima and minima of a random moving wave-form. In the present note it will be shown that these distributions are to some extent arbitrary, depending on how the points of observation are selected.

The mean torque on an infinite fixed strip due to plane harmonic sound waves is calculated, employing simple acoustical theory as a basis and neglecting viscosity. In the range of wavelength λ small compared to the strip width δ, the torque per unit length is

where α denotes the angle between the incident wave normal and that of the strip and ρο the equilibrium density of the medium. This oscillatory character of the torque in its dependence on δ/λ is not to be found at long wavelengths where, as is well known, the torque acts only in the sense of aligning the strip broadside to the incident wave normal.

In recent years several authors have treated the fundamental problems of two-dimensional statical elasticity for isotropic and aeolotropic materials by the use of functions of a complex variable; references are given at the end of (7). In this paper Stevenson's notation (8,9) is adopted. Dawoud (2) has expressed the continuity conditions across a curve between two differently loaded regions in terms of the complex potentials and particular integrals for the two regions. A form of the boundary condition defining certain types of boundary constraint, including the rigidly clamped and hinged boundaries, has been introduced by the author and Dawoud (1). The introduction of this boundary condition is of practical importance, since neither rigidly clamped nor simply supported conditions can be realized fully under actual physical conditions and thus any case met in practice must lie somewhere between these two limiting cases.

A new type of product of field operators is considered and the equations that it satisfies obtained.

On page 674, equation (5) and the expression for H in the line above it are in error and should be deleted. The correct expressions are more complicated and will not be given.

On page 679, line 5 from the bottom should read

and the equation in the bottom line should read