1. Appleton and van der Pol have shown that in a simple Triode or Dynatron generating circuit the anode potential v is related to the time t by a differential equatior of the type

where f (v) is a power series in v, and may be written

1. There seems to be little doubt that the detailed mechanism of ionisation or excitation by electron impact will not admit of description, even to a first approximation, by the system of classical mechanics. However the experimental work of Franck and Horton and their collaborators, has shown that, within the limits of the error of experiment, an electron is able to impart the whole or part of its kinetic energy to the atom it excites. When its initial energy is greater than the excitation energy, the electron, instead of being brought to rest, retains the excess as kinetic energy.

The object of this note is to correct an error in my paper “Extensions of a theorem of Segre's…,” the notation used being the same. The curve C4 dealt with is regarded as given by its canonical representation

and at one point in the paper we sought the locus of the lines analogous to the line A2A4 of the figure of reference for each of the ∞2 representations of this type (p. 671, small print). In the space representation of the locus there is an additional principal curve

and the order of the locus must be reduced by that of the form corresponding to the points of this conic. The locus sought is in fact none other than the cubic form, locus of chords of C4, the present system of lines being the directrix systemt†. This follows at once from the following results, which can be shown immediately using the above representation:

(1) The space joining such a line g to any tangent cuts the curve again in coincident points, and thus contains a second tangent;

(2) The line joining the points of contact of these tangents meets g, and the points give the involution

I have to correct the proof of the assertion on p. 471 of my paper that if f (t) is integrable over (0, a) and ν ≥ – ½, then

1. Geodesic curves, even of simple surfaces such as quadrics, are almost always transcendental: occasionally they are algebraic: still more rarely do they belong to simple and familiar types. The form of the differential equation referred to proves conclusively that even such integrals as are expressible by elementary functions must be quite exceptional.

The object of this note is to direct attention to an entirely false inference which was drawn from the analysis given in my previous paper with the same title.

The problem of finding the number of r-dimensional regions which are situated in a space Sn of n dimensions, and which satisfy a suitable number of conditions of certain assigned types (called “ground-conditions”) has been investigated by Schubert. A special class of such problems arises when the r-dimensional region is merely required to intersect k regions Pλ of rλ dimensions (λ = 1, 2 … k) situated in general position in Sn where for the finiteness of the sought number we must have

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. The plane quartic curves which pass through twelve fixed points g, of which no three lie on a straight line, no six on a conic and no ten on a cubic, form a net of quartics represented by the equation

In a previous paper it has been shown that the corrosion of zinc, cadmium, iron and lead is connected with electric currents set up through unequal distribution of oxygen; the currents have been measured and compared with the weight of metal corroded away. The “unaerated” areas are anodic, and thus the attack tends to become concentrated upon the points relatively inaccessible to oxygen. When a drop of salt water is placed on an iron sheet, the central part of the drop suffers anodic corrosion, giving rise to ferrous salts, whilst the marginal ring over which oxygen has ready access to the metal becomes cathodic, alkali being produced there. Where the ferrous salt and alkali come into contact, ferrous hydroxide is precipitated, which oxidises to ferric hydroxide; after a few hours we get a membrane of brown ferric hydroxide extending right over the drop, but surrounded by a ring of clear alkaline liquid. All the actual corrosion of the metal is confined to the area within the membrane; the metal below the external ring of clear liquid, to which oxygen has access, suffers no attack.

1. Mr J. P. Gabbatt has discussed in the most recent Part of the Proceedingsof this Society the Pedal locus of a simplex in hyperspace. It is, however, possible to regard the pedal property of the circumcircle somewhat differently and so to seek other extensions. Given a circle, any three points on it are vertices of an inscribed triangle, and the feet of the perpendiculars on the sides from any fourth point of the circle are collinear. Is there any curve in space on which an analogous property holds for any five points, viz. that the feet of the perpendiculars from any one upon the faces of the tetrahedron formed by the other four are coplanar?

It will be shown that curves of order n exist in Euclidean space of n dimensions on which any n + 2 points have such a property; but that the curves cannot be real if n is odd.