This paper considers the stability of a valve amplifier which has an oscillatory circuit in the grid and in the anode circuit. An exact condition for stability is obtained for circuits which have no resistance, and it is shown that when both circuits have the same natural frequency instability is then impossible if the anode inductance exceeds μ times the grid circuit inductance. This condition is believed to be new; in practice it is unnecessarily severe, but it is believed that stability should be sought by increasing the anode inductance and the grid circuit capacity. The stability of circuits which have resistance is too cumbersome to express generally, but it is discussed on broad principles; the stability and amplification of multistage amplifiers are also considered briefly. The following papers should be compared with the present one.

Absorption curves in paper have been obtained for the β-rays of actinium (B + C) and actinium C′. Some inferences regarding the shape of their energy distribution curves have been drawn, and the ranges of the β-rays of actinium B and actinium C′ fix their maximum β-ray velocities at Hρ 3430 and 6140. The potency of the method is emphasized for elements which cannot be easily investigated directly in a magnetic spectrograph.

The γ-ray ionizations of actinium B and actinium C′ have been compared under the same conditions with the β-ray ionization of actinium C′.

In conclusion, the writer wishes to thank Professor Sir Ernest Rutherford for his kind interest in the work. Thanks are also due to Dr J. Chadwick and Dr C. D. Ellis for many valuable suggestions and discussions.

It is shown that a quartic equation may be found which expresses the grid characteristic of a valve accurately over a considerable range, and that for modern dull filament valves the grid current curve is exponential over only a very restricted length.

Expressions are given for calculating rectified current and the amplitude of harmonics produced by a simple grid rectifier when voltages of the following wave-forms are applied: E sin pt, (A + B sin nt), and (A + B cos mt + C cos nt)sin pt. Further, a formula is given from which we may calculate the rectified current produced by a cumulative grid rectifier when a voltage E sin pt is applied.

All these formulae are applicable if the grid characteristic, is parabolic, cubic, quartic or quintic in form.

It is also shown that when an acoustically modulated radio frequency voltage is applied to a cumulative grid rectifier, even if the valve has a parabolic grid characteristic, an infinite number of harmonics of the modulation frequency are produced. These harmonics are due to the. action of the grid leak and condenser. It appears, however, that in practice the amplitude of these harmonics will be very small compared with those produced, primarily, by the curvature of the grid characteristic.

A preliminary investigation is described in which a type of gold leaf source suitable for use with an expansion chamber is developed. Such a source is necessary for the detailed examination of β particles of energy less than about 50,000 electron volts by the Wilson method. Some results obtained with sources of radium D and thorium B + C of this type are presented in outline.

The writer would like here to acknowledge the help and encouragement he derived from many discussions with Professor Sir Ernest Rutherford and with Dr J. Chadwick during the course of the investigation, and further to express his thanks to Mr G. R. Crowe for assistance in the preparation of some of the sources.