In a recent paper, Fowler discusses the adsorption isotherm for a monatomic layer, assuming an interaction between neighbouring atoms in this layer. In this paper we do not intend to give a contribution to the physical problem, but merely to show how the statistical problem involved can be solved by a method due to Bethe.

1. In a recent note I showed that Langmuir's adsorption isotherm

where θ is the fraction of the surface covered by adsorbed gas, p the gas pressure in equilibrium with it, and A (T) a specified function of the temperature, can be derived as a theorem in statistical mechanics without any appeal to the mechanism of deposition and re-evaporation. Necessary and sufficient assumptions for the truth of (1) are that the atoms (or molecules) of the gas are adsorbed as wholes on to definite points of attachment on the surface of the adsorber, that each point of attachment can accommodate one and only one adsorbed atom, and that the energies of the states of any adsorbed atom are independent of the presence or absence of other adsorbed atoms on neighbouring points of attachment. Under these assumptions the explicit form of (1) is

where m is the mass of the adsorbed atom or molecule, bg(T) the partition function for its internal states in the gas phase, and vs(T) the partition function for its set of adsorbed states. These sets of states are to be so specified that the energy zero is assigned tot the lowest state of each set in constructing bg(T) and vs(T), and then X is the energy required to transfer a molecule from the lowest adsorbed state tot the lowest gas state. Quite another adsorption isotherm was shown to hold when adsorption of a molecule takes place as atoms and requires two or more points of attachment.

It is a well-known fact that the non-conservation of energy during β decay may be explained by assuming the existence of light neutral particles, neutrinos, which are ejected from the nucleus at every act of β emission and which enable all the conservation laws to be fulfilled. A study of the energy distribution of recoil atoms during β decay might furnish some data for testing this hypothesis. However, in order to determine the energy distribution of recoil atoms consider-able experimental difficulties have to be overcome. The energy of recoil atoms of ordinary radioactive substances is of the order of magnitude of 1 volt, i.e. of the same order of magnitude as the adsorption energy of atoms on a surface. Thus, on escaping from the'surface on which they are adsorbed, they will lose an amount of energy of the same order of magnitude as that which they possess, and their velocity distribution will therefore be completely distorted. This difficulty may be met by employing an artificial, light radioactive substance, whose recoil atoms may have energies some ten times greater than 1 volt. For this reason active carbon C, obtained by bombarding boron with deuterons according to the reaction 10B+2H→11C+n, was employed as a radioactive substance. Moreover, the fact that the emission of positrons from 11C is not accompanied by the emission of γ-rays has the advantage of simplifying the interpretation of the results.

The fact that the rate of production of atomic hydrogen at a tungsten surface at a given temperature is proportional to the square root of the hydrogen pressure means either that the important process is the evaporation of atoms from an adsorbed film which over the whole range of experimental conditions is sparsely occupied, or that the production of atoms is in the main due to a process in which a hydrogen molecule strikes a bare tungsten atom in the surface, one atom being adsorbed and the other evaporating and the surface being almost completely covered over the whole range of experimental conditions. Either process leads to a temperature variation in the rate of atom production in agreement with experiment. A definite decision between the two processes cannot yet be made.

The results of experiments on the diffusion of hydrogen through metals from a pressure p on one side to a vacuum on the other show that at high pressures the amount diffusing varies linearly with p½ but that at low pressures it varies more rapidly. The difficulty usually encountered when diffusion from an adsorbed layer into the solid is considered theoretically is that the theory indicates that saturation should be reached. In this paper it is shown that this difficulty is due to the omission of an important process at the surface and that by including this process the experimental results can be explained.

The various processes occurring at the surface when hydrogen is adsorbed on tungsten are considered together with the dissociation equilibrium of hydrogen in the gas phase. The form of the adsorption isotherm is deduced from the principle of detailed balancing and is in agreement with that obtained by Fowler using a statistical method. A detailed interpretation of the experimental results now available shows that either (a) measurements of the rate of removal of the adsorbed film of oxygen on tungsten do not measure the rate of evaporation of oxygen atoms or (b) it is not possible to obtain a general first approximation formula giving the rate of evaporation of adsorbed atoms in terms of the heat of desorption. The desorption of hydrogen from tungsten is discussed and it is shown that the agreement between the temperature at which the film evaporates at an appreciable rate and that deduced from a desorption formula of the type mentioned in (b) assuming that the hydrogen evaporates as atoms must at present be regarded as a coincidence.

Ising discussed the following model of a ferromagnetic body: Assume N elementary magnets of moment μ to be arranged in a regular lattice; each of them is supposed to have only two possible orientations, which we call positive and negative. Assume further that there is an interaction energy U for each pair of neighbouring magnets of opposite direction. Further, there is an external magnetic field of magnitude H such as to produce an additional energy of − μH (+ μH) for each magnet with positive (negative) direction.

Some apparent anomalies in oscillograms obtained in the course of electrical impulse tests of a material used in the construction of lightning arresters have led to a fuller investigation of the behaviour of the test circuit as applied to the study of a material with a non-linear voltage-current characteristic.

This investigation has been carried out by evaluation of solutions of the equations of a simplified form of the circuit numerically and by means of the differential analyser, and by further oscillograms taken under conditions suggested by the behaviour of these solutions.

The apparent anomalies which originally gave rise to the investigation have been shown to be a real feature of the response of the circuit, and not a spurious effect due to the recording apparatus, and the study of the initial response of the circuit to the impulse leads to the interpretation of another feature of the oscillographic records which had been previously regarded as an instrumental error.

When an electron makes a transition from a continuous state to a bound state, for example in the case of neutralization of a positive ion or formation of a negative ion, its excess energy must be disposed of in some way. It is usually given off as radiation. In the case of neutralization of positive ions the radiation forms the well-known continuous spectrum. No such spectrum due to the direct formation of negative ions has, however, been observed. This process has been fully discussed in a recent paper by Massey and Smith. It is shown that in this case the spectrum would be difficult to observe.

We shall discuss the annihilation of positrons by a process in which only one quantum of light is emitted. The positive electron is regarded as a hole or unoccupied state in the distribution of electrons in negative energy states, and is destroyed by an atomic electron jumping down into it with the emission of a single quantum. This process is only possible in the presence of a nucleus, which can take up the momentum liberated, and is therefore most probable when the atomic electron is a K-electron.

In automatic temperature-controlling apparatus a temperature-sensitive element, commonly called a thermostat, serves to increase or decrease a supply of heat to the body or oven whose temperature is to be prevented from changing. The thermostat and heating elements are commonly both electrical, the thermostat comprising a “master coil” whose resistance changes with temperature, the heating element consisting of a “slave coil” carrying the heating current. The temperature of the master coil is made to control the current in the slave coil, usually by the interposition of some form of relay with the appropriate translating and amplifying apparatus. Since every form of relay exhibits “backlash”—the critical values of the operative signal at make and at break are not exactly equal—such a system necessarily oscillates or “hunts” through a range at least as great as the backlash of the relay; and since further there is thermal separation between the master coil and the slave coil, the hunting has a range exceeding the backlash of the relay. It is a common experience with such thermostatic apparatus that, owing to this action, continued improvement towards constancy of temperature is not attainable by increasing the delicacy with which the temperature of the master coil controls the current in the slave coil.

1. Let f(x) be a complex function belonging to LP (−∞, ∞); i.e. let f(x) be measurable, and |f(x)|p integrable, over (−∞, ∞). The function

is called the Fourier transform of f(x), if the integral on the right exists, in some sense, for almost every value of y. It is well known that, if 1 ≤ p ≤ 2, the integral (1) converges in mean, with index p′ = p/(p – l)† i.e. that

where

The errors occurring in a large number of Jeffreys's phases for neutral chlorine have been determined. A discussion of the source of these errors is given, from which it appears that errors in the phases of zero order and of order unity are due to a cumulative error over the range of integration. A method of correcting for this error is obtained. This method is of easy practical application, and it reduces the error almost to zero for phases of these orders.

The error occurring in higher order phases is found to be mainly due to errors in the two π/4 terms, which take into account the exponential tails of the waves in the totally reflecting region. For phases of high order these errors in the two π/4 terms cancel each other, and consequently the total error in phases of high order is practically zero.

A correction graph for the zero-order phase is given from which the error in this phase for atoms of atomic number up to 36 can be read off. The graph is such that an extrapolation to higher atomic number would not involve much error.

1. Ellis(1) has proposed energy level systems for the bodies of the Thorium series, but the values of the γ-ray intensities forming the basis of this system fail to account satisfactorily for the total energy of the γ-rays emitted by Th C and its products. This is a serious discrepancy which needs examination. Since the publication of these level systems, we have obtained new values for the intensities of the γ-rays from Th C and Th Pb. The details of these measurements are given in the second part of this paper. These γ-ray intensities are, of course, deduced from the intensities of the discrete β-groups by dividing by the appropriate internal conversion coefficient. The changes which we have made in the γ-ray intensities are due first to revised values of the β-ray intensities from Th Pb and secondly to a revised set of values of the internal conversion coefficient (2). We have not however found it necessary to make any change in Ellis and Mott's (3) allocation of lines to dipole or quadripole type. The contributions of the two factors are made clear in Table I.

Experiments are described in which observations were made of the motion of electrically charged cloud particles past a sphere. The cloud particles were moving vertically up in an air stream, and there was a vertical electric field. This gave conditions similar to those surrounding a falling rain drop in a thundercloud, and the observations are in accordance with the theory proposed by Wilson to account for the mechanism of thunderclouds.

Recent reports contain tables of a parameter K required in calculating the performance of an airscrew by a new method.

The method of calculating K (due to Goldstein) is unsuitable for large values of the pitch especially near the tip of the airscrew.

In the case of infinite pitch we fall back, for a two-bladed airscrew, on the problem of a rotating lamina in two dimensions.

The solution for a cross lamina (corresponding to a four-bladed propeller) is given below and the tables of K for four blades are completed.

A formula for the limit of K/Kp at the airscrew tip is given for a propeller with any number of blades, where Kp is an approximate value of K due to Prandtl.

K for any number of blades is given in the form of an infinite series. The case of three blades is discussed in detail.

The very small water drops which are considered in this note are as a rule met with in the form of clouds with a high numerical density of drops. The interior of such a cloud will never be in temperature equilibrium with the walls of a containing vessel, and under these conditions measurements of the rate of fall of the top of a cloud are not measures of the Stokes free fall of a single drop. Optical methods of measurement assume, therefore, a particular importance. The angular diameter of the diffraction halo has long been used as a measure of drop size in clouds; the applicability of this method for small drops will be considered. The criterion of “Rayleigh scattering” has also been employed as showing that the diameter of the drops in question was very much smaller than the wave length of light. A third method which may be applied to drops of diameter of the order of one wave-length will be discussed.

These experiments were performed at the Cavendish Laboratory with the high voltage apparatus of Cockcroft and Walton and may be considered as a continuation of the experiments of Cockcroft, Gilbert and Walton on the production of induced radioactivity by high velocity protons and deuterons.