(1) The conditions of dissociative equilibrium in an external gravitational field have been given by Willard Gibbs, as follows: If the state of a system is such that it is in (mechanical and thermodynamic) equilibrium when the constituents are taken to be independent, and if a condition of dissociative equilibrium is satisfied at one point, then the same condition is satisfied at all points, and the state is one of equilibrium if the constituents are actually capable of dissociating.

(2) In particular, the constituents of a column of dissociating gas under gravity settle out according to Dalton's law; if the condition of dissociative equilibrium is satisfied at one height it is satisfied at all heights.

(3) The conditions of equilibrium are generalised so as to take account of external electric fields and of the possibility of the products of dissociation being charged. Result (1) is shown to be unaffected.

(4) The theory is applied to the equilibrium of an ionized gas such as a stellar atmosphere under gravity. Whatever the charge on the star, the tendency of the light electrons to diffuse away from the heavy ions is almost entirely prevented by the electrostatic forces between them, and the result is the production of a field in the interior capable of supporting half the weight of the positiveions (Pannekoek, Rosseland). For the purposes of this statement the “interior” may be taken to commence at a pressure of 10−24 atmos. It is only above the level corresponding to 10−34 atmos. that electrons and ions separate out according to Dalton's law.

(5) The theory is applied to the equilibrium of an ionized gas under an external electric field. An external applied field of the order of 40,000 volt cm.−1 cannot give rise to potential differences exceeding about 1 volt under the conditions of a typical stellar atmosphere.

Now that the wave-lengths of the main γ-rays of radium B and C are known it has become a matter of some importance to determine their total energy, because from such measurements it is possible to deduce the average number of quanta emitted by each disintegrating atom. If in addition the relative intensities of the different γ-rays could be determined it would be possible to give a complete description of the γ-ray emission.

It is shown that, assuming conservation of energy and momentum in individuai transitions, radiation must be regarded as propagated by linearly directed quanta. Evidence is brought forward in favour of the view that these quanta are spatially localised longitudinally as well as laterally. As these conclusions seem unavoidable, an attempt is made to see if there is any possibility of accounting for interference effects in terms of quants possessing periodic properties.

The idea that a single quantum can produce interference effects is untenable. The conception of the phase of a quant is introduced, and it is supposed that atoms may absorb a quant in a given phase provided they are in a “state” corresponding to that phase. Considering radiation emanating from a point, it is shown that a tentative explanation of interference may be obtained if the quants have a constant phase at emission, and if they give atoms at any point an impulse towards the state corresponding to their phase at the point. According as these impulses reinforce or oppose each other, bright or dark parts of a fringe System are obtained. Practically the whole nomenclature and method of the wave theory may be taken over and applied to the quant phase field surrounding an emitting source. Essentially, on this view, an explanation of interference is sought in terms of different quants, and the dark and bright parte of a fringe system are to be explained, not in terms of different numbers of quante arriving at them, but in different phase relations of quante which do arrive.

Quante are characterised by a magnetic and electric vector, whose magnitudes and directions define the state of polarisation and the phase. Electron orbite may also be regarded as characterised by two vectors in terms of which it seems as if the “state” may be specified.

The relation between transition character and type of radiation emitted is finally considered and it is shown that the evidence so far available renders plausible an explanation of interference of the kind put forward. Much further experimental work, particularly in connection with the Stark and Zeeman effects, is, however, necessary, before sufficient precision can be given to the views put forward to make them satisfying. On the other hand, it seems premature to suppose that only a formal treatment is possible of the physical phenomena involved.

The sensitivity of photographic plates to mass rays bears practically no relation whatever to their sensitivity to light. A short account is given of tests on the relative merits of different brands of plates since the first experiments on positive ray analysis. The process of improving the qualities of plates by schumannising is discusseci and details are given of the process found likely to give the best results. Success cannot be guaranteed even with the most careful manipulation, but if achieved yields plates of outstanding value for use in such methods of analysis as the mass-spectrograph.

1. The kinetic theory of metallic conduction is usually supposed to lead to formulae for the conductivity coefficients which in some respects are very much at variance with the actual phenomena. In spite of the important successes achieved by the theory, which in themselves are almost sufficient evidence that the fundamental basis is correct, these discrepancies are regarded in some quarters as so serious as to warrant the complete rejection of the theory as beine inadequate to account properly for the facts.

Mystery has remained attached to the transmission of free electric rays a long way round the protuberant curvature of the earth, which has recently developed into the greatest sudden practical evolution in signalling since the telephone. The difficulty was already emphasised by the late Lord Rayleigh, as soon as the first signs of transmission across the Atlantic had been detected by the Marconi operators. The effect has been sometimes supposed to be accounted for by a hypothesis that the rays are turned downward by an upper conducting layer in the atmosphere. But conduction, as usually understood, involves dissipation, and thus loss of energy of the rays by absorption: so that a train of radiation travelling along a layer sufficiently conducting to bend the rays could not go far. In fact, by a well-known dynamical principle, if the absorption is small of the first order, the resulting decrease of velocity of the train is small of the second order and so of no account for bending rays in a varying field.

As is well illustrated by photographs of their tracks, the majority of β-particles of given initial velocity bave approximately the same range, measured along the path. When the track shows a visible branch, indicating that an exceptionally close encounter has resulted in the ejection of an electron with kinetic energy amounting to an appreciable fraction of that of tbe primary particle, the main track is naturally of less tban tbe average range. A diminution of range may also be expected to follow such of the nuclear deflections as result in the emission of X radiation; this decrease in range indeed affords a possible method of measuring the energy of the radiation emitted in individuai cases and so testing theories such as that of Kramers as to the nature and origin of the continuous X-ray spectrum.

The propagation of electric currents through long cables has often been treated theoretically and the solutions, first obtained by Kelvin and by Heaviside, have moulded the development of transcontinental telegraphy and telephony. These solutions presume that the source of electrical disturbance is situated at one point in the cable and this is the condition appropriate to wired communication, but in the more recent process of wireless communication we have an analogous problem which requires different terminal conditions.

Many investigations bave sbown the presence of a “continuous” β-ray spectrum accompanying tbe β-ray lines in tbe naturai spec-trum of Ra B and Ra C. The existence of sucb a spectrum is not easily accounted for if one is to regard the nucleus as existing in sharply quantised states. It has been pointed out that this spectrum may be a spurious effect, arising from scattering from the walls of the apparatus and not from within the atom itself. Therefore it is of importance to obtain accurate information regarding the continuous spectrum and its relation to the line spectrum.

Since the publication of a previous paper on chemical constants, some further experimental data upon the dissociation of chlorine by Wohl have appeared, from which a new and rather more satisfactory value of the chemical constant of diatomic chlorine can be calculated. Wohl concludes that Q0, the heat of dissociation at absolute zero, is – 57,000 calories. This is in good agreement with Henglein's value – 54,000 but differs from that of Trautz and Stackel, namely – 71,000, which is the value adopted in the previous paper. Q0 is necessarily an adjustable constant, and since Wold's value gives results which are a good deal more concordant with each other and with the theory, we now take Q0 = − 57,000. Wohl also uses hv0/k = 902 instead of 1093, but as the difference made by this change is very small compared with other disagreements, we retain the value 1093. The following table gives the new values of Γ (Cl2), calculated in the same way as before. The initials at the heads of the columns refer to the results of Henglein, Trautz and Wohl respectively.

The general arrangement of the apparatus is shown in Fig. 1. A vertical steel rod AA of circular cross-section is fixed to a heavy cast-iron base Z shown diagrammatically in the figure. The rod AA is bent by a load applied to the end of the horizontal bar BC carried by the upper end of A A. The point of application of the load is defined by a transverse groove cut in the bar. The rod AA passes through the two metal plates DD, FF, which are soldered to the rod, the faces of these plates being horizontal.

In Chapter v of his Les Méthodes Nouvelles de la Mécanique Céleste Poincaré proves a theorem which he calls The non-existence of Uniform Integrals. This theorem is as follows:

Let

be a system of equations in which the characteristic function F is expanded in a series

convergent for sufficiently small values of | μ |, for all real values of y1, … yn, and for values of x1, … xn within certain finite real intervals; while F0, F1; … are analytic functions of x1, … xn, y1, … yn, of which F0 is independent of y1, … yn and Fl, F2, … are periodic with respect to these variables with period 2π.

Let

be a system of differential equations in which X1, … Xn are analytic functions independent of t, expansible in convergent series of powers of x1, … xn. Suppose further that not all the functions X1, … Xn vanish when x1 = … = xn = 0. It will be shown in §§ 1–3 that these equations possess (n — 1) independent integrals independent of t, expansible in convergent series of powers of x1, … xn; i.e. functions

such that

identically. In § 4 it is shown how the series for ϕ1,…ϕn−1 may be most directly constructed, and in § 5 is briefly considered the corresponding problem when the origin is a singular point of the equations, i.e. when the expansions of X1,…Xn all begin with terms of the first or higher degrees.

Let

be a system of differential equations of Hamiltonian form, the characteristic function H being independent of t and expansible in a convergent series of powers of x1, … xn, y1, … yn in which the terms of lowest degree are

During the last six months we have succeeded in achieving two of the improvements which were foreshadowed in a former paper on this subject.

Many years ago Rutherford remarked that the high energy lines of the radium C β-ray spectrum showed the existence of γ-rays of very high frequency, and later he pointed out that their frequencies must be closely connected with the β-ray energies through the quantum relation. Although the truth of Rutherford's point of view has become more and more obvious, no advance in the detailed knowledge of these lines has been made in the last seven years. This spectrum is very complicated and the lines faint.

Experiments with a helical method of focussing β-rays are described. Although the method does not appear to be so generally useful for obtaining ordinary β-ray spectra, it possesses certain advantages, of which may be mentioned:

(1) Large dispersion;

(2) Greater intensity;

(3) Good screening.

The method produces some evidence on the question of the continuous background, and experiments with it in this connection are described.

Experiments carried out with the aim of elucidating the action of the α-particle counter are described. A normal counting circuit including an ionization chamber with point and plane electrodes was used. The “wave-form” and intensity of the transient impulses resulting from discharges stimulated by single electrified particles have been determined using a cathode-ray oscillograph. It is found that the nature of the impulse is determined largely by the capacity and resistance of the system, and not by the nature of the electrical stimulus. The potential impulse normally detected by string electrometer methods is shown to be proportional to the current responsible for the recharging of the electrostatic capacity of the counter after the rapid discharge of the capacity initiated by the electrified particle.

I have collected in the present note some theorems regarding the solution of a certain system of linear equations with an infinity of unknowns. The general form of the equations is

the numbers a1, a2, … c1, c2, … being given. Equations of this type are of course well known; but in studying them it is generally assumed that the series depend for convergence on the convergence-exponent of the sequences involved, e.g. that and are convergent. No assumptions of this kind are made here, and in fact the series need not be absolutely convergent. On the other hand rather special assumptions are made with regard to the monotonic character of the sequences an and cn.