The lines of a double-six will here be represented by the usual notation

where two lines whose symbols are in the same line or same column of this scheme are non-intersectors and all other pairs of lines intersect. Any six of the lines, no two of whose symbols are in the same column, and just three are in the same row, are generators of a quadric, and the actual position in space of each of the other six is determined by the two points in which it intersects this quadric.

The present work is the outcome of a study of the special type of (3, 2) correspondence on a circle, namely that between a point and the extremities of its pedal line. This led to considering correspondences in general, and to the formulation of concepts which are believed to be new, for example the Canonical Forms, § 1 (2), and Multipliers, § 1 (3). The case of the (n, 1) correspondence has already been given by the author.

For a strut under thrust when buckling is resisted by a force proportional to the displacement, it is shown that for both a clamped and a pinned strut there is stability for any length when the thrust is less than a certain critical value; and the relation is found between the length and the first value of the thrust above this that will give buckling. A notion of the wave-length and number of nodes after buckling is obtained.

The results are applied to the theory of the formation of mountains by horizontal compression, and it is shown that the crust of the earth would be able to transmit, without buckling, stresses right up to the breaking stress across regions of continental extent, unless the depth down to the level of no strain were less than 16 metres.

An attempt is made to employ the results also to consider the stability of solid surface films under compression, and it is seen that other factors, making for stability, must enter besides rigidity and gravity. This is supplied by surface tension, and it then appears that collapse due to a weakness in the film must precede buckling.

A rough calculation is given of the frequency of vibration of an atom in a solid film.

A century ago geodetic and gravitational universal surveys were mainly concerned with determining the effective (gravitational) ellipticity of the Earth, after due allowance had been made for local anomalies, with especial view to the exact purposes of physical astronomy. One of the chief of these anomalies was exhibited by a remark of Airy, after scrutiny of the available data in his treatise (1830) on “Figure of the Earth” in the Encyclopedia metropolitana, that the observations show gravity to be abnormally in excess on island stations. It appeared, for instance, that this cause might make the mass of the Moon uncertain up to 2 per cent. A very refined explanation of this anomaly of island stations (which will be seen presently to be only partially effective) was offered by Sir George Stokes, from whom this last remark is quoted, in the course of a memoir, fundamental for theoretical geodesy, in which he demonstrated that no outside survey could lead to any certain knowledge of the distribution of mass inside the Earth, even in its outer crust, except as a matter of probability when backed up by geological knowledge.

The following gives a brief summary of a paper, which it is hoped to publish in extenso later. It is a contribution to the theory of ferromagnetic crystals, and contains in particular a theoretical explanation of Webster's experimental results.

In the recent experiments on the Zeeman effect in strong magnetic fields made by Mr H. W. B. Skinner and myself for obtaining an intense source of light for a small fraction of a second, we have been discharging a condenser battery consisting of 32 Leyden jars connected in parallel with a capacity of one-tenth of a microfarad. The discharge was made through a small spark gap by means of an oil immersed switch (the details of this arrangement are to be found in the above-mentioned paper). When the discharge was produced a curious phenomenon was sometimes observed. After the battery had been charged to its maximum tension, and the switch had been put into operation, only a small spark occurred in the spark gap, and the main part of the discharge went over the top of the insulators of one of the Leyden jars.

Measurements of the saturation currents produced between two parallel plates by a source of radium C of carefully tested purity have been performed by an accurate galvanometer method. From the results a transformation constant

has been assigned to radium C corresponding to a half-value period of 19·72±·04 minutes.

Similar measurements with radium active deposit have enabled a value to be estimated for the period of radium B between 26·7 and 26·8 minutes, which is the limit of accuracy of the experimental data.

An interpretation of ultra-short wave wireless phenomena is given which indicates that the maximum number of electrons per c.c. in the atmospheric ionized layer is of the order 105 to 106.

It has been found that illumination of a mercury surface by ultraviolet light strong in the line λ=2536·7 Å., exerts a marked influence on the photochemical union of hydrogen andgases such as oxygen, ethylene, and carbon monoxide. The rate of reaction is proportional to the first order to the area of surface exposed.

The formation of a mercuric oxide film has been shown to occur only in the presence of a mixture of hydrogen and oxygen, and alternative mechanisms for its formation are suggested.

In the case of nitrogen-hydrogen mixtures, hydrazine and ammonia have been identified in the reaction products, and in the case of hydrogen and oxygen, hydrogen peroxide and water have been found, and it is suggested that the reactions proceed in steps.

The catalytic efficiency of the surface depends on its cleanness and is cut down by poisons, such as the reaction products in the case of the combination of hydrogen and carbon monoxide.

The theory of catalytic action recently advanced qualitatively by Pease, Taylor, Armstrong and Hilditch, Constable, which the author has endeavoured to treat quantitatively, is extended in this paper to the explanation of the effect of pressure and inert diluents on catalytic action on saturated surfaces. The results are shown to be in agreement with experiment, and further inferences may be made concerning the relative mean lives of the reactant and the diluent on the surface.

The existence of complex compounds of metallic salts with ammonia was recognised in the early years of last century. Platinum in particular readily unites with ammonia, and the early chemists, when studying the general chemistry of ammonium platino-and platini-chlorides, soon discovered highly crystalline ammonia derivatives of platinum which contained an unusually high proportion of the metal. In the formulation of such compounds difficulties at once arose. Thus Peyrone in 1844 knew three distinct compounds of the composition PtCl2N2H6, a pale lemoncoloured compound known as the second chloride of Reiset, an orange-coloured compound discovered by Peyrone himself, and finally a dark green insoluble substance known as Magnus' green salt, discovered by the latter in 1828. The existence of these three compounds, now known as trans and cis dichloro-diaminoplatinum [Pt(NH3)2Cl2], and as tetramino-platinous platinochloride [Pt(NH3)4]PtCl4 respectively, could not be satisfactorily explained on current theories of salt formation. Similar compounds in which aliphatic and cyclic mono-amines replaced the ammonia groups were discovered later, but it was not until 1889 that Jörgensen introduced the use of the simplest stable aliphatic diamine, viz. ethylene diamine.

It is well known that charcoal possesses catalytic properties. It accelerates the decomposition of hydrogen peroxide, the removal of bromine from ββ-dibromo propionic acid and enables certain oxidations to take place in air at ordinary temperatures.