The connexion between the conditions for five lines of S4

(i) to lie upon a quadric threefold,

and (ii) to be chords of a normal quartic curve,

leads to an apparent contradiction. This difficulty is explained in the first paragraph below and, subsequently, two investigations are given of which the first uses, mainly, properties of space of three dimensions.

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.

The stability of a charged raindrop has been discussed mathematically by Lord Rayleigh. The case of an uncharged drop in a uniform electric field is perhaps of more meteorological importance but a mathematical discussion of the conditions for stability turns out to be very much more difficult in this case, owing to the fact that the drop ceases to be spherical before it bursts. Moreover it does not seem possible to express its geometrical shape by means of any simple mathematical expressions. On the other hand, by using a soap bubble instead of a water drop it was found possible to carry out experiments under well-defined conditions in this case, whereas experiments with Rayleigh's charged drop would be difficult.

Radiologists have often had cause to note certain apparent anomalies in the behaviour of their apparatus. It is quite well known that different X-ray tubes, excited by different kinds of high tension apparatus, yield X-radiation of markedly varying quality and quantity even under conditions which, as measured by spark gap and milliammeter (the usual measuring instruments of the radiologist), are apparently identical. These anomalies seemed to offer an interesting field for investigation, and one which might not be without value on the practical side.

In the year 1663 John Wallis, Savilian Professor of Geometry in the University of Oxford, delivered a lecture in which he claimed that he had proved Euclid's Postulate of Parallels according to the strictest laws of demonstration after Euclid's manner.

The velocities of electrons emerging through an aperture in an anode to which they were accelerated have been investigated.

The velocity distribution of electrons passing through holes ranging from 0·13 mm. to 3·24 mm. in diameter in a thin copper sheet is shown in Fig. 2. In this case the accelerating field between filament and anode was 204 volts.

Corresponding results for a capillary tube 0·40 mm. in diameter and 16 mm. long are shown in Fig. 3, where the curves are plotted for different accelerating potentials. Experiments were also made with shorter lengths, down to 5 mm., and with a tube 1·25 mm. in diameter. All the tubes investigated gave the same distribution of velocities of the electrons in the emergent beam, within the limits of error of the experiments.

In conclusion the authors wish to express their thanks to Sir Ernest Rutherford for his interest and advice during the course of the work.

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.

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.

The two letters now communicated are from G. G. Stokes to W. Thomson, of dates Dec. 12–13, 1848, three years after Faraday's great magneto-optic discovery. They formulated already the permissible types for general equations of propagation, virtually on the basis of the very modern criterion of covariance,—relative to all changes of the spatial frame of reference in the case of active fluids, but having regard to the fixed direction of the extraneous magnetic field in the Faraday case. Their form was elucidated in each case by correlation with a remarkable and significant type of rotational stress in a propagating medium.

1. Changes in the relative intensities of the lines in the fluorescent L-spectrum of Cerium excited by radiation of various wave-lengths have been observed.

2. These results imply a change in the relative absorbing powers of the three L-levels as the wave-length of the absorbed radiation diminishes from a value just below the absorption wave-length of the L-levels to a value considerably below. The absorbing power of the LI-level becomes increased relative to the absorbing powers of the other L-levels as the wave-length diminishes. The results agree with those published by H. Robinson in a recent paper.

3. These results imply a breakdown of the law that μ/λ3 is a constant (where μ is the absorption coefficient of X-rays of wave-length λ) as applied to the individual L-levels of an element.

4. A comparison is made between the above results, and some results on the relative absorbing process of the L-levels obtained by Ellis and Skinner from β-ray spectra.

(1) An apparatus has been devised in which the composition of the vapour phase passing over the catalyst can be varied at will, or two vapours can be used alternately as reactants.

(2) By using ethyl alcohol, and amyl alcohol from fusel oil alternately as reactants, the poisoning of a very active copper gauze catalyst has been followed and the temperature coefficient of the dehydrogenation of ethyl alcohol by the copper has been measured during the poisoning.

(3) The activity of the catalyst, poisoned by amyl alcohol, fell in accordance with the simple logarithmic law

(4) Confirmation was obtained that the rates of dehydrogenation of ethyl and amyl alcohols were equal.

(5) The temperature coefficient of dehydrogenation on the catalyst was unchanged throughout the poisoning, though the reaction velocity was reduced 30 times.

(6) The temperature coefficient was also shown to be unchanged during sintering, the reaction-velocity having been reduced 10 times.

(7) Equations are derived for the rate of poisoning of an exponential distribution of centres of activity when the poison attacks the more active centres selectively.

(8) The relation deduced

cannot usually be distinguished (except with special relations between the constants) from the simple logarithmic law of poisoning.

(9) Thus the exponential distribution normally poisons like a surface composed of homogeneous centres, the temperature coefficient being unchanged by the poisoning.

(10) The equation

describes the reaction-velocity as a function of time, and temperature, and gives adequate explanation of previous experimental results on the forms of the heating and cooling curves with “poisonous” alcohols.

(11) Frenkel has shown , where τ0 is the vibration frequency of the molecule perpendicular to the surface, and μ0 is the heat of desorption of one gram molecule. Thus if the heat of desorption is not small compared with the energy necessary to cause chemical disruption of the molecule, the previous equation becomes

the form of the equation being unaltered.

1. The following are well-known theorems of elementary geometry: Given any euclidean plane triangle, A0 A1 A2, and any pair of points, X, Y, isogonally conjugate q. A0 A1 A2; then the orthogonal projections of X, Y on the sides of A0 A1 A2 lie on a circle, the pedal circle of the point-pair. If either of the points X,- Y describe a (straight) line, m, then the other describes a conic circumscribing A0 A1 A2, and the pedal circle remains orthogonal to a fixed circle, J; thus the pedal circles in question are members of an ∞2 linear system of circles of which the circle J and the line at infinity constitute the Jacobian. In particular, if the line m meet Aj Ak at Lt (i, j, k = 0, 1, 2), then the circles on Ai Li as diameter, which are the pedal circles of the point-pairs Ai, Li, are coaxial; the remaining circles of the coaxial system being the director circles of the conics, inscribed in the triangle A0 A1 A2, which touch the line m. If Mi denote the orthogonal projection on m of Ai, and Ni the orthogonal projection on Aj Ak of Mi, then the three lines Mi Ni meet at a point (Neuberg's theorem), viz. the centre of the circle J. Analogues for three-dimensional space of most of these theorems are also known ‖.

1. The conductivity of liquid sulphur is found to vary with the temperature in a similar manner to that in which the viscosity varies.

2. The conduction is electrolytic in character.

3. There is a definite E.M.F. of polarisation.