Let f(z) be a single-valued function of z, defined in the domain D given by ; suppose that f(z) is integrable in the general Denjoy sense round all circles with centre ζ lying in D, and along all portions of radial lines intercepted between two such circles.

In various communications published in the Journal of the Chemical Society the author has discussed the effect of different nuclei on the absorption spectra of various compounds. The problem has been further investigated with a number of substances derived from aniline, o-and m-cresols, and α-and β-naphthylamines, and this communication is to give an account of the results. A condensed Cd-spark was used as the source of radiant energy, and alcoholic solutions of the substances were examined in the usual way.

The Mathieu functions of period π and 2π have recently been constructed by the help of analysis similar to that developed by Laplace, Kelvin, Darwin and Hough to find the free tides symmetrical about the axis of a rotating globe. The purpose of this note is to show that a similar construction can be carried out for the second solution of the Mathieu equation, when one solution is periodic in π or 2π, by the help of analysis similar to that used for forced tides. The construction is effected in a form suitable for numerical computation.

It is well known that eclipse observations show that the chief constituents of the higher levels of the sun's chromosphere are ionised calcium and hydrogen. The equilibrium of the calcium has formed the subject of Milne's important researches. The hydrogen presents a rather different problem owing to the large number of possible quantum states that have to be considered.

Where the solutions which carried the lead vein minerals pass along joint planes through the Whin Sill, the dolerite is altered to a white, compact rock for a distance of several feet. The original texture is well preserved in the altered dolerite; the ferromagnesium minerals are replaced by calcium, magnesium and iron carbonate, the feldspars by a minutely crystalline mixture of kaolin and muscovite and the ilmenite by small rutile crystals. The former areas of interstitial quartz are increased and apatite remains completely unchanged. The microscopic evidence that there is neither gain nor loss of alumina during the metasomatism, taken in conjunction with analyses of altered and unaltered rock, may be used to prove that there was a contraction of about 14% during metasomatism. This result is corroborated by the occurrence of cracks which are formed by shrinkage during metasomatism and which are now filled with carbonates.

Most of the results of this paper have been given before by Professor T. H. Havelock, who obtained them by the solution of a difficult integral equation. The method used here is, however, much easier to handle than that given by Professor Havelock.

In two recent papers the writer has given an account of a practical method of finding the characteristic values and functions of Schrödinger's wave equations for a given non-Coulomb central field. For terms of optical spectra the method is effectively the following. We take the wave equation in the form

and require the values of ɛ for the solutions which are zero at the origin and at r = ∞. We consider the result of integrating this equation outwards from P = 0 at r = 0 to a radius r0 at which the deviation from a Coulomb field is negligible, and inwards from P = 0 at r = ∞ to the same radius, with a given value of ɛ; the characteristic values are those values for which these two solutions join smoothly on to one another, i.e. for which they have the same value of η = −P′/P at this radius. For a given ɛ, the solution zero at the origin depends on the particular atom; the solution zero at infinity can be expressed in a form independent of any particular atom.

Surfaces of order n in space of n dimensions, for 3 ≤ n ≤ 9, were discussed by Del Pezzo, who showed that the prime sections of such a surface are represented on the plane by cubic curves through (9 − n) base points.

Gyroscopic effects furnish important instances of dynamical actions, but their general discussion is outside the range of most students reading for Part I of the Natural Sciences Tripos. If, however, we limit ourselves to the case in which the axis of the wheel makes a constant angle with the vertical, the theory becomes elementary and simple devices suffice for recording the movements of the revolving wheel. The recording gyroscope was designed to give students at the Cavendish Laboratory, Cambridge, an opportunity of making practical measurements to verify the theoretical results.

The velocity of bimolecular reaction at a catalyst surface is often proportional to the concentration of either reactant when this is small, but at greater concentrations the rate of reaction falls off considerably, and finally the increase of concentration may actually retard the reaction. The maximum reaction velocity does not occur in general when the partial pressures of the reactants are in the ratios suggested by the chemical equation of reaction.

Sommerfeld has recently made a very important advance in the theory of electric conduction by employing the conception of electron waves and the new mechanics. His theory has been most successful in explaining a large number of phenomena. It treats them, however, from the macroscopic point of view and does not examine the atomic processes involved. The present note, intended to be merely tentative, seeks to attack the latter aspect of the problem.

R. A. Millikan and C. F. Eyring have shown that the auto-electronic emission is independent of the temperature of the cathode up to 1000° K. At higher temperatures a thermionic emission takes place and this masks the auto-emission. W. S. Pforte and the author have recently shown that the thermionic emission is increased by the field in accordance with a relation derived by Schottky, so that when both thermionic and auto-electronic emissions are present it is only necessary to subtract the thermionic current, as given by the Schottky relation, from the total measured current to obtain the value of the auto-emission at the temperature considered. In this way the thermionic and auto-emissions can be separated.

A simple explanation of Pauli's principle was first given with the wave mechanics. Its interpretation in the new theory was that the wave functions of Schrödinger were antisymmetrical in all the electrons concerned. Thus when the interactions of the electrons may be neglected, the wave function (for a system of n electrons) can never be of the form

in nature, but only of the form

Hence σ, τ,…ω must be all distinct.

Equations have been given by Moullin to determine the current in a receiving antenna in wireless telegraphy and they have been discussed and extended by Colebrooke, who in particular considered the reception of a plane polarised wave with its electric vector vertical by an antenna which is partly vertical and partly horizontal. His result shows that the intensity of the received signal is independent of the orientation of the receiver. In practice, however, the incident wave front is not vertical, its tilt depending on the wave length and on the resistance of the earth, as shown by Zenneck, and the purpose of this paper is to investigate the effect of the orientation of a bent antenna in the reception of this type of wave. An approximate theory of the Beverage antenna is obtained by the same method.

In a recent communication to the Society, the author referred to cable-sheath losses, and gave formulae for computing them in certain cases. These appertained to power cables in which were comprised a group of conductors, arranged symmetrically and encased in a single conducting sheath. In some distribution systems, however, the conductors for the several phases are encased in separate lead sheaths, which are either laid in proximity as separate cables, or grouped and comprehended in an outer sheath. The analysis previously given does not include such cases directly. Moreover, it is common practice either to lay the elementary cables with sheaths in contact, or to bond the sheaths together at the ends of suitable sections, in order to prevent differences of potential between them; and, when this is done, a circulating current flows in the circuit of the sheaths and bonds, sufficient to maintain equality of potential between the several sheaths. This current, to which reference was made in the former paper, is additional to the eddy current discussed therein, the integral of which over the cross section of the sheath is zero. It is for convenience here referred to as the “circulating current,” to distinguish it from the “eddy current,” although there is no such distinction between them as the names imply.

A very great deal has been published upon the subject of the electrical counter and its mode of action. Most explanations are incomplete in that they neglect some of the factors involved. The question of the self-restoring property of the system has also received attention, but this property has not been properly related to the general problem of intermittency in discharge tubes.

The use of Pitot tubes in exploring fields of fluid flow is well understood but the limitations of the method have not been very systematically explored.

The heavy elastic structure of a ship possesses many natural periods of lateral vibration, and if any periodic disturbing force within the hull happens to synchronise approximately with any of these natural periods, considerable vibration may result. Experience has shown that the damping of the hull structure is small, and when the rate of revolution of the propeller coincides with a natural period of the ship, a vibration of large amplitude is set up. No doubt reciprocating machinery is competent to produce more violent vibration than turbine machinery, but the inevitable lack of balance of the propeller itself is sufficient to vibrate seriously a turbine-driven ship.

Experiments have been conducted by Gutton, and later by Kirchner, and by Gill and Donaldson upon electrical discharges through gases under the influence of high-frequency oscillations of the order of 107 cycles per second. It was found that the peak voltages required to maintain bright luminous discharges were of the order of 100 volts even when the pressure was as low as that in a soft X-ray tube. The present paper deals with some further studies of these phenomena.

The electron theory of metals revived by Sommerfeld assumes that an electron moves in a metal as though this were an equipotential medium. Considering the nuclei fixed and regularly spaced we obtain a potential periodic in space coordinates. To study the effect of such fields we may simplify the problem so as to contain only one periodic term for each coordinate in its expression for potential. This problem can be reduced further to a one-dimensional one, of which the simplest example is the motion of an electron in a field with potential cos x or sin x. Darwin has shown that a suitable combination or packet of elementary de Broglie waves is capable of moving coherently in several instances. The motion of such a packet is found to be equivalent to that of a particle in classical dynamics with the Heissenberg uncertainty relation. The wave packet is used here for the motion of the electron in a periodic field. The result obtained is equivalent to that of classical dynamics. The wave packet again moves as a particle with an uncertainty relation.