points the spike rarely settles, but oscillates about the surface with great rapidity. With steel points, on the other hand, the discharge frequently anchors itself to one spot, and there remains quite steady, only moving about when the field is increased almost to Qashover. It is not unusual for the stem to take up a position off, and inclined to, the axis of symmetry. When the point is subsequently examined under the microscope it is usually found that the spot favored by the root of the discharge, coincides with a small crater on the surface. These form more readily on steel than on platinum, the process no doubt being assisted by chemical action, and this may account for the effect referred to.Discourse on the mechanism of the transition from the Trichel pulse regime to the pulse-free discharge would be little more than speculation at this stage, comment is therefore reserved until a more thorough investigation of the phenomenon has been made. It is perhaps worth stating that too much importance should not be attached to the changes in shape of the induced Trichel pulses as the transition is approached, since these are largely conditioned by the circuit. PH YSICAL REVIEWSolutions of the three-dimensional Schrodinger equation are discussed for a potential which is the sum of a potential with the periodicity of the crystal lattice plus a perturbing potential. A general theory of large over-all perturbations, such that the energy lies close to one permitted band in one region of the crystal and close to a second permitted band in another, is developed. The theory is then applied to a one-dimensional crystal in a uniform electric field, using the narrow band approximation; the probability for an electron to cross a forbidden energy band is calculated. These results are considered in connection with the interpretation of the current-voltage characteristic of an N -P junction of germanium at high electric fields.

A quantum-mechanical theory of the thermal accommodation coefficient is discussed for a diatomic gas whose molecules can possess internal energy of rotation as well as translational energy. Expressions are obtained, in terms of transition probabilities, for ai, the accommodation coe~cient associated with the change in translational energy of a beam of gas molecules reflected from a solid surface, and ai, the accommodation coefficient associated with the change in internal energy of the gas molecules. The gas molecules are considered as rigid plane rotators; and, on striking the surface, a gas molecule experiences a change in rotational and translational energy, while an atom of the solid loses or gains vibrational energy. Some general conclusions are drawn concerning a, and ai and their relation to each other, and a special case is considered.

The vibrational energy transfer between an atom and an atomic oscillator is considered for a Morse potential interaction, from the point of view of thermal accommodation coefficient theory. An expression is obtained for the transition probabilities for the exchange of one quantum of energy. A comparison is made with the semiclassical theory. Inconsistencies in the literature are noted and discussed.

Exact quantum-mechanical transition probabilities for the collision of an atom with an atomic oscillator for the case in which the interaction has the form of a Morse potential are obtained by numerical integration of the relevant close-coupled scattering equations. These transition probabilities are compared with approximate ones calculated from distorted-wave theory over a range of parameters which have been of interest in examining the collision of helium atoms with a tungsten surface. Some information is obtained concerning the range of validity of the first-order theory, and certain suggestions that have appeared in the literature for correcting the distorted-wave results are found to be inadequate.

Solutions of the one-dimensional Schrodinger equation for a periodic potential modified by a perturbing potential are expressed as yp(x) = 2& <£(#&) a(x-Xk). The function a(x-xu) is a Wannier function localized around the &th atom of the crystal and associated with a particular permitted band; the coefficients satisfy a differential equation of infinite order. W.B.K. solutions of the equation for are obtained. In the permitted band, is oscillatory; in the neighboring forbidden bands decreases exponentially with distance from a band edge. Various types of perturbing potentials are considered and quantum conditions are derived for impurity states and for states in which the permitted band is crossed.