Vol. 6, No. 2 (1946)
1946-01-20
目录
1946, 6 (2): 79-85.
doi: 10.7498/aps.6.79
Abstract +
In estimating the frequency of oscillation of a positive-grid oscillator, it is usually. assumed that the space charge effect is negligible. Under this assumption, the potential distribution in the space between the plane-parallel electrodes is linear. Thus the electric field in the space is uniform and the average velocity of electron flight can be used to evaluate the frequency of oscillation. The presence of space charge affects the potential distribution in space so that the electric field in this region is no more constant. Hence more exact formula must be used to compute the frequency of oscillation. The calculation is further complicated by the fact that the anode potential is usually made slightly negative with respect to the cathode. In this case, the location of the virtual cathode at which the electrons turn back does not coincide with that if a straight line potential distribution were assumed. The predicated frequency of oscillation is about 10-20 percent lower than that if space charge were neglected.
1946, 6 (2): 86-99.
doi: 10.7498/aps.6.86
Abstract +
The main purpose of this paper is, after making some necessary preliminaries on the theory of linear differential operators in one real variable, to obtain the explicit condition that such an operator of any order be a Hermitean operator, and as application of the result point out various quantum-mechanical instances.
1946, 6 (2): 100-107.
doi: 10.7498/aps.6.100
Abstract +
A simple problem in thermodynamics is considered with a view to emphasizing that the application of the adiabatic law pVY=const. for a gas is permissible only when the process is quasistatic.
1946, 6 (2): 108-111.
doi: 10.7498/aps.6.108
Abstract +
An investigation of the numbers of isotopes of some particular elements seems to lead to the assumption that there is a simple numerical relationship among the number of isotpopes, the atomic number, and the period. If the atomic number of an element is divisible by the square root of twice the actual number(1) of elements which are contained by the same period that includes the element under consideration, the quotient, a whole number, will be equal to the number of naturally occurring isotopes of the element.
