Wilson's cloud method, provides a means of measuring the ranges of β-rays which is free from any uncertainties arising from the scattering of the rays, and for this reason it is an invaluable method for obtaining the true rate of loss of energy of β-rays as they traverse matter. Thetrue rate of loss of energy or ‘stopping power’ is defined as the quantity , where is the mean energy lost by β-rays of energy T in travelling a distance dx measured along their paths. The cloud method of course enables one to observe only the total ranges of β-particles, and in deducing the stopping power from the mean range it is necessary to bear in mind that owing to ‘straggling,’ which in the case of β-rays is large, the differential coefficient , where is the mean range of particles of energy T, is not exactly the same as the stopping power . is however the quantity which the cloud method enables us to observe. It is the purpose of this note to consider the exact relation between these two quantities so that the information provided by the cloud method may be rigorously interpreted.

Photographs have been taken under controlled illumination of the tracks of α particles in a cloud expansion chamber and a calibration of the photographic plates employed has been carried out. Systematic photometry of the track images has made possible the calculation of the variation of the light scattering power of an α particle track over the last two centimetres of its length in standard air, and the variation of this quantity has been identified with the variation of ionisation along the track.

Photographs of tracks in air, helium and hydrogen have been examined. In these three gases the maximum ionising efficiency of the α particle occurs when it possesses the velocity respectively appropriate to the distances 3·0, 2·55 and 2·25 mms. from the end of its path in standard air. This common velocity parameter has been employed throughout the discussions which are appended to the experimental results.

Briefly summing up we see that when a point source is employed the slit of the spectroscope is illuminated by light coming from one point only in the wedge, and consequently clear distinct bands will be obtained in the spectrum irrespective of which end of the wedge is towards the source, and irrespective of the angle of incidence or of the distance between the wedge and spectroscope.

With a large source, however, the slit of the spectroscope receives rays coming from many different points in the wedge. The path difference between the interfering components of each of these rays is in general different. Therefore each ray will produce a complete set of interference bands in the spectrum. These sets of bands are relatively displaced, the superposition of all causing uniform illumination.

It has been shown, however, that there is one special case in which the path difference for the interfering components of all rays is the same. In this case, each ray still produces, a complete set of bands in the spectrum but these sets are no longer relatively displaced; bright bands are superimposed on bright bands and dark bands coincide with dark bands. There is thus both an increase of intensity and definition.

It has been shown that the conditions necessary for this special case are:

(1) The thick end of the wedge is towards the source.

(2) The slit of the spectroscope is placed at a distance of

from the wedge, the distance being measured along the central ray entering the slit of the spectroscope.

The case of an air wedge has been discussed, and a possible advantage to be gained in using such for spectroscopic purposes in place of parallel plates has been mentioned.

The absorption curves and the photo-ionisation experiments agree to give a value for the molecular photo-electric threshold of λ 2555 ± 20 a.u. If our view of the ionisation process is correct, the energy of dissociation is 0·505 ∓ ·01 volts. If the picture of the ionisation process is wrong, the energy of dissociation may be a little lower (a few hundredths of a volt). The corresponding heat of dissociation is 11400 calories. In the range of temperature (200° C. to 500° C.) generally used in experiments on potassium vapour, the fraction associated varies from 10−4 to 10−2. An equation for calculating the fraction associated at any temperature is given by the writer in an earlier paper.

The interferometer designed by Michelson has been adapted in recent years to the testing of various types of optical systems, one form being used for the testing of prisms and another form—the “lens interferometer”—for the examination of the symmetrical optical system. The details of the instrument may be found in a paper by Mr F. Twyman, in which are given some photographs of the results of its application to certain lenses of known aberration. Essentially the interferometer ensures that a plane and undistorted wave of light falls upon the lens or system to be examined, after refraction through which it falls upon a convex mirror whose centre is at the focus of the converging wave; by which, therefore, the wave is returned through the optical system and emerges as a plane wave if the system under examination be ‘perfect,’ or free from aberration. Otherwise the final wave is not plane, but is distorted by the aberrations impressed upon it by the system under test—through which, it will be noticed, it passes twice; and this emergent wave is superposed upon a portion of the incident (plane) wave, obtained by previous passage through a partly silvered mirror; with which, therefore, interference effects are observed. And these effects depend only upon the aberrations produced by the system under examination, for they measure, in fact, the departure of the finally emergent wave from the ideal plane form. Various interference contours are obtained in this way, and their form and size enable the observer to deduce the aberrations of the system and to measure their magnitude.

In a recent communication to this Society Dr Hartree has put forward a method for calculating the field of anatom containing many electrons. Each orbit—to borrow a metaphor from the old quantum theory—is related to a wave-function Ψ which obeys Schrödinger's equation. The potential energy used in this equation is due partly to the field of the nucleus, and partly to the fields of the electrons in the other orbits. The latter are calculated upon Schrödinger's interpretation of the wave-function, that |Ψ|2 is the density of charge, measured in electronic charges per unit volume. It is not the purpose of this paper to discuss the practical methods of obtaining wave-functions which reproduce the fields from which they are derived; but to relate these wave-functions and their energy parameters to those of the accepted theory.

Duane's quantum theory of diffraction is applied to the reflexion of electrons by crystals and to the spatial distribution of photoelectrons and fluorescent radiation from a crystal.

Two alternative criteria for coherence are given. According to the second of these there is coherence provided that the momentum imparted to the components of a system during the process concerned is insufficient, owing to quantum restrictions to their motion, to change their energy. Calculations made on this supposition show that in the case of the scattering of radiation by a crystal there is complete coherence for the lower orders, while for higher orders this ceases to be the case and the reflected intensity is reduced as the result of incoherent scattering. The specular reflexion by gases is also considered.

Duane's theory of diffraction has not been placed on a rigorous basis and the solutions which have been proposed here for various problems may be incorrect. Even so the theory has at least served to bring to light several points of theoretical and experimental interest which deserve consideration.