A rough periodicity may sometimes be seen in the progress of Science. After a stirring time of advance may come a period of lethargy, or even of negation, followed again by some fresh spurt of activity. At the present moment we seem to have reached a phase of negation in respect of the achievements of phyletic Morphology, and in conclusions as to Descent. This is suggested by the Presidential Address in Section K at the British Association at Liverpool. Already Professor Seward in the Hooker Lecture, 1922, had said, “It may be that we shall never piece together the links of the chain of life, not because the missing parts elude our search, but because the unfolding in all its phases cannot be compared to a single chain. Continuity in some degree there must have been, but it is conceivable that plant life viewed as a whole may best be represented by separate and independent lines of evolution, or disconnected chains which were never united, each being initiated by some revolution in the organic world.”

Although a study of the photo-electric activity of metals in air can contribute little to the scientific interpretation of the phenomenon, yet it acquires a greater interest and some practical importance in connection with the physiological effect of ultra-violet light. In employing such light for therapeutic purposes, it is necessary to know which are the effective rays for the treatment under consideration, and how different sources vary as regards intensity of radiation. As the primary cause of the physiological change produced by light is probably photo-electric action, it is not surprising that several investigators have suggested the use of the photo-electric activity of a metal plate in air as a means of estimating the quality and intensity of the radiation.

According to the quantum theory of the production of spectra the lines Hα and Hβ of the Balmer series in the hydrogen spectrum may be produced in six and eight different ways respectively. This general conclusion, however, has to be modified. The mass of an electron in its elliptical orbit is not constant but depends upon its velocity. Consequently, the total energy of an electron in its orbit must be expressed in the form

where na and nr are the azimuthal and radial quantum numbers and where , and the other symbols have their usual meaning.

1. I define the X-determinant in the following manner. It is of order n.

where x denotes any numerical quantity, and observe that it becomes a determinant or permanent according as x takes the value −1 or +1.

I should like to take this opportunity of thanking the Committee of the Carnegie Trust for the Universities of Scotland for their courtesy in furthering and facilitating the work, the results of which are submitted in the following pages.

(1) If note be taken that, when k in the title is 0, there is only one such determinant, namely the adjugate, it will be seen that what we are about to consider is a family of compound determinants which includes the adjugate as a very special case. Such determinants have not altogether escaped study, but until recently the attention paid to them has been incidental and fragmentary.

The following paper is one member of a series designed to elucidate the circumstances of correct time-keeping, the first two of which were published in 1918.

The problem has in the meantime gained appreciably in interest. It was known that time-determinations from night to night at the same observatory were liable to discrepancies, which were presumed to have an accidental character and would be eliminated by grouping. Now, comparisons by the aid of wireless telegraphy of determinations made at different observatories, and grouped with the intention of eliminating accidental error, exhibit like discrepancies, of a more systematic character, with a range certainly not less than 0s·3. The search for the cause of this fault is engaging the attention of astronomers. It is a larger fault than is found in any other region of their science; and as its source is obscure, additional value attaches to any collateral investigation bearing upon it.

The mathematical theory of graduation or adjustment, which hitherto has been developed chiefly in connection with the needs of actuarial science, centres round the following problem: A set of numbers u1, u2, u3, … un is supposed to have been obtained from observations or statistics of some kind. These numbers would represent the values of a variable ux corresponding to the values 1, 2, … n of its argument x, were it not that they are affected by accidental irregularities due to errors of observation, or to the imperfections of statistics. It is desired to construct a set of numbers , which represent the most probable true values of the variable ux corresponding to these values of x, so that the “graduated” numbers differ as little as possible from the “ungraduated” numbers u1, u2, … un, but are freed from the accidental irregularities, and thus form a “smooth” sequence, i.e. a sequence from which a regular difference-table can be formed for use in various calculations.

Ewing's theory of the construction of a magnetic atom separates the atom into two portions: (a) the Weber element, possessing constant magnetic moment and capable of turning in response to an applied magnetic field; and (b) an outer (or inner) group of fixed “magnets” (i.e. electrons moving in orbits), which have like poles all directed towards the centre of the atom. Owing to the want of symmetry of the elements composing the group or shell, there are several magnetic fields, each of different direction, acting in the neighbourhood of the Weber element, and the direction of each of these represents a position of stability of the Weber element.

It has long been known that a bituminous coal seam is not a homogeneous bed, but is made up of a number of parallel bands. For example, Karsten in 1826 observed and described three banded constituents of such a seam, viz. Faserkohle, Matt Coal, and Glanz Coal, corresponding respectively to mineral charcoal, dull coal, and bright coal, and he gave some chemical details of their composition. Bowman, 1841, stated “there is a peculiarity in the texture of coal which has not received the attention it deserves. If it be clearly examined it will be found to consist of a series of parallel horizontal layers varying in thickness, these laminæ being best observed in the cross fracture, and often exhibit considerable difference in compactness and lustre. This structure, though in coal seams indistinct, is so general that it seems to point to some law which the chemical geologist might advantageously investigate.” Again, Wethered in 1884 observed that a coal seam is separated by partings into many beds differing in quality as in structure while in 1885 he pointed out the advisability of studying the different bands of a seam, and of recording details of its dull and bright portions.

In 1916, in a paper on the size of the particles in deep-sea deposits, Odén showed that the distribution by mass of a suspension into classes of particles of different size could be inferred from a study of the course of sedimentation of such a suspension from a state of uniform dispersion in water. The experimental data required constitute the “sedimentation curve ” of the suspension, showing the total weight deposited, at a fixed depth, at the end of any assigned length of time.

Helium, with atomic number 2, stands second only to hydrogen in interest for the theoretical physicist. The atom would have to consist of a doubly charged positive nucleus and two electrons. “Here,” as Sommerfeld puts it, “we stumble over the three-body problem.” In Bohr's original model of the neutral helium atom the two electrons rotate about the nucleus at opposite ends of a diameter of a circle. The work necessary to detach both electrons, or the second order ionisation potential (if it is expressed in equivalent volts), comes out too great, 82·9 volts instead of 78·6 volts. Later models conceived by Landé and by Bohr clear up some of the difficulties of explaining the separate sets of series described as the parhelium (singlet) and the orthohelium (doublet) series, but according to the calculations of Kramers, the ionisation potential of the crossed orbit model comes out 3·8 volts less than the value experimentally determined. Summing up the present position in his Presidential Address to Section A, at the Liverpool meeting of the British Association, M'Lennan says: “Although real progress has been made, it cannot be said that finality has been reached in the determination of the form of a completely satisfactory model of the atom of so simple an element as helium.”

Most of the work which has been done directly on the cathode fall of potential refers to discharges where the potential difference applied was less than 1000 volts. In view of the large amount of work which has been done with discharge tubes worked from an induction coil at voltages of the order of 30,000, it seems of interest to consider how far the results obtained at the lower voltages can be applied to this case.

When potassium acetate and trichloracetate are electrolysed together, mixed compounds are formed, but only to a very slight extent. A small quantity of trichlormethyl acetate is to be found among the reaction products. The presence of either salt affects the reactions of the other by diminishing the yields of the normal products and by promoting the production of substances like trichlormethyl alcohol and ethylene which result from the oxidation of single molecules of each acid. A short explanation of this phenomenon has been given. No methyl alcohol appears among the final products, but formaldehyde is found in considerable quantities. This oxidation is connected with the production of an oxidising agent such as chlorine at the anode. Hexachlorethane and methyl chloride are also produced during the electrolysis of this mixture.

The author desires to take this opportunity of thanking Professor Sir James Walker, F.R.S., upon whose suggestion this work was begun, for his helpful advice and criticism during its execution.

The sulphur bacteria are found in shallow waters, both marine and fresh, and play an active part in the decomposition of animal and vegetable matter. They require for their full development an abundant supply of oxygen and of sulphuretted hydrogen. They do not thrive unless the water is periodically renewed, or else is so shallow that oxygen is obtainable to a fairly large extent from the atmosphere. When the oxygen is used up their development rapidly comes to an end, and in some cases, as is described below, the organisms disappear completely. They derive their supply of sulphuretted hydrogen from the decomposition of the protein molecule of vegetable and animal matter. Usually a growth of sulphur bacteria is visible to the naked eye as a greyish or reddish mantle covering the surface of a mass of decomposing organic matter. If, for some reason or other, the supply of oxygen is not plentiful at the bottom of the pool, the mass of growth leaves the surface of the decomposing matter and moves nearer the surface of the water.

It is well known that the value of a cubic (or odd-dimensional) determinant |aijk| (i, j, k = 1, 2, … n) will reduce identically to zero, if exactly similar rôles are assigned to all the suffixes in determining the signs of the terms. To escape this difficulty, the usual theory of determinants of higher dimensions assigns a special rôle to the first suffix i, and considers that the class of the permutation of the values of i in any term makes no contribution to the sign of the term. This is, in effect, to make the suffix i non-determinantal in character.

Most of the work on the emission spectra of the halogens has been confined to the visible or near ultra-violet regions: but, in view of the characteristic chemical and photo-chemical properties of these elements, it has become increasingly important to make a general survey extending well into the ultra-violet. The emission spectra of chlorine and bromine in the visible and near ultra-violet up to about 370 µµ have been described by Eder and Valenta as consisting of lines, chiefly in the green and blue. For bromine, a continuous spectrum was also observed, starting at about 490 µµ; this rapidly falls off in intensity, but at about 420 µµ a second continuous band commences, extending with increasing intensity to the limit of their photograph about 370 µµ. Quite recently the investigation of the quartz ultra-violet region of chlorine has occupied several observers, chiefly from the physical point of view; Jevons has measured the ultra-violet line spectrum from 335 µµ to 207 µµ, and a communication on the same subject has appeared from Angerer.

A very considerable amount of careful work has been devoted to the investigation of the phenomenon, first noticed by Budde (1), that when light falls on chlorine an immediate expansion takes place, followed by an equally rapid contraction to the same, or very nearly the same, volume when the light is obscured. Light in the visible region is effective, but the shorter the wave-length the greater was found to be the expansion; the infra-red had no effect; the ultra-violet has not been carefully explored. The temperature of the gas rises during the expansion and corresponds to the increase in the volume (2). However, Baker (3), and also Shenstone (4), and Pringsheim (5), found that very pure dry chlorine did not give the effect at all.

Breathing, in normal conditions, is regulated by the concentration of carbon dioxide in the blood; the “respiratory centre” of the brain, which directs the movements of the lungs, controls matters with a highly delicate degree of regulation so as to maintain that concentration at a fixed level. When, through hard exertion or through the influence of carbon monoxide poisoning, the organism becomes seriously affected by want of oxygen, that deficiency itself begins to influence the respiratory centre and to stimulate breathing. During the course of poisoning by carbon monoxide, then, the lung-ventilation increases; the increase accelerates the rate of saturation of the blood by the gas, which in turn reacts in intensifying the oxygen-shortage. A consequence of the hyperpnœa which thus progressively develops is the washing out of much of the carbon dioxide in the blood.

The investigations described in this paper dealt with the behaviour of specimens of specially pure nickel under various conditions and in varying magnetising fields. Several experiments were carried out.

I. The specimen being in the form of a bar about 30 cms. long and the purpose of the experiment being to find the nature of the curve of magnetisation at low magnetic fields, Lord Rayleigh's magnetometric arrangement (Scientific Papers, vol. ii) was used.