The tow-nettings on which this survey is based were taken mostly from Keppel Pier. The tide as a rule runs down the channel strongly for several hours after high water, and the current is sufficiently strong to hold out the tow-nets more or less horizontal. Owing to some peculiarity in the configuration of the sea-floor at Keppel, the downward current is much the stronger and often begins an hour or several hours before high water. The flood-tide is never strong enough nor constant enough to hold out a tow-net for any length of time, and so most of the observations are based on tow-nettings taken on the ebb. Tow-nettings were taken almost every day and the tow-nets were usually left out for an hour.

The seasons at which the Atlantic salmon ascends rivers differ to a considerable extent in different countries.

In northern Norway and eastern Canada the severe winter conditions compel salmon to ascend from the sea only after the rivers have become free from ice. In one or two of the large rivers of northern Siberia it has been noticed that the salmon are well up into the upper reaches when the ice breaks up, from which it has been argued that they ascend under the ice.

The following pages deal with the simultaneous system of two general quadratic forms in n homogeneous variables. It is a special case of Gordan's Theorem which proves such systems to be finite, for the general projective group of linear transformations. While several works have dealt with the cases when n = 2, 3, or 4, nothing seems to have been written on the general case except a memoir in the year 1908. We continue, and simplify, the results there obtained, and now establish that

(1) All rational integral concomitants of two quadratic forms in n variables and any number of sets of linear variables may be expressed as rational integral functions of (3n + 1) concomitants, and forms derivable by polarisation.

(2) These (3n + 1) forms, called the H system, constitute a strictly irreducible system.

This system is exhibited in §7 as

together with polars.

The work is divided into three chapters: I §§ 1–4 is introductory notation, II §§ 5–17 provides a proof of these theorems, while III §§18–21 gives the non-symbolic and canonical forms of the results.

The following paper is ancillary to certain investigations in stellar photometry which are in progress at the Royal Observatory, Edinburgh, and require the establishment of data relating to the blackening of the plates employed. It describes the laboratory work carried out for this purpose, generally over the very restricted range of exposure times and densities used in the stellar work, but occasionally extended to cover a wider field. The conditions are chosen in order to give the maximum accuracy and range to the stellar work and not with a view to highly accurate laboratory work; on the other hand, the periodical change of emulsion which must occur in any lengthy investigation introduces an element which, though of considerable interest, is lacking in most of the published work on the subject.

The number of writings on compound determinants in the period 1900–1920 is almost identical with the number for the immediately preceding twenty-year period. The languages used by the writers are at least as numerous: but the contributions made by the various nationalities are relatively much altered in amount. The former strikingly high proportion of Magyar work is not at all maintained, and German has somewhat fallen off: on the other hand, English and Italian have increased. Although statements at variance with historical accuracy, and the publication of old results as new, are still more common than they ought to be, pleasing evidence is not awanting of improvement in these respects. There is nothing so glaring, for example, as the fact chronicled against the writers of the two preceding periods that they had unwittingly rediscovered ten times a theorem that had appeared in so well known a journal as Liouville's in 1851.

This paper contains the results of an investigation, on empirical and dynamical lines, into the following matters:—

(1) The origin of surfaces of discontinuity in the atmosphere;

(2) The precise processes occurring at such surfaces in well-defined cases;

(3) The physical processes which lead to the obliteration or movement of the discontinuities;

(4) The part played by the discontinuities in the development of the cyclones of temperate latitudes.