The problem of the influence exerted by the ovary upon metabolism has been studied by a number of authors, but no definite conclusions have yet been reached. In recent years the rôle of the sex-cycle has been considered, and various studies of the relation between the œstrous cycle and metabolism have been undertaken. Apart from the indirect influence, which is due to the increase in the spontaneous activity (Slonaker, 1925), such as is observed in the mouse or rat during œstrus as an effect of ovarian hormone, an influence of the ovarian function upon basal metabolism appears to exist, but nothing definite is known. Since the secretion of “œstrin” from the ovary appears to be periodical (Wiesner, 1926), the question of whether the supposed influence upon metabolism is also of a periodical nature is of particular interest.

In the following pages we propose to clear up certain difficulties which have arisen in the theory of invariants belonging to two quadratic forms homogeneous in n variables x1, x2, …, xn. We denote such a set by a single symbol x, and take it as fundamental that any non-zero set x represents a point in space of n – 1 dimensions. We deal with any number of cogredient sets, x, y, z, x1, x2, etc., each representing a point, of which n at most are linearly independent in this space Sn–1. A prime u is a space Sn–2, lying wholly in the Sn–1, and therefore determined by n–1 linearly independent points.

Certain tentative conclusions may be drawn regarding the relationship between the involution of the thymus gland and the gonads in the fowl.

(1) At maturity the male possesses thymus substance considerably greater in amount than that characteristic of the female.

(2) Successful ovarian grafting in complete males induces a female grade involution of the thymus.

Intermediate grades between male and female thymus follow the implantation of ovary to males in certain cases, although in these no grafts were recovered at the post-mortem examination.

Since only small ovarian grafts have been recovered from males with a female type of thymus, it is evident that the reaction is a delicately balanced one requiring only a relatively small amount of ovarian tissue to determine the degree of involution.

(3) Partial ovariotomy, when performed before sexual maturity, produces no deviation from the female type of thymus.

(4) Castration and ovariotomy cause a delay in the involution of the thymus.

(5) Successful implantation of testes to complete males has no effect on the size of the thymus.

(6) No inference may be drawn from the results of partial castration and the degree of thymus involution.

(7) A definite relationship exists between gonad and thymus involution in the fowl.

1. Endodermal cells frequently show considerable increase in tangential dimension at a late stage in their existence, as a result of which the continuity of the endodermis may be maintained, despite the rapid expansion of the intra-endodermal cylinder following secondary growth.

2. This tangential increase in size of the endodermal cells is usually accompanied by their division. The divisions may actually cause the increase in size of the cells, that is, there is active growth of the cells. Or they may follow a passive stretching. In either case the new walls fulfil a mechanical function, lending added strength to the stretched walls of the original cell.

3. Two types of division are distinguishable:

(a) Those occurring in primary endodermal cells. The new walls soon develop Caspary strips, linking up with those of the parent cells.

(b) Divisions in tertiary endodermal cells. The new walls here show neither Caspary strip nor suberin lamella.

4. It is pointed out that in neither case does the development of new walls interfere with the impermeability of the endodermis.

5. The occurrence of the divisions is considered in relation to the supposed impermeability of the suberin lamella of the secondary endodermal cell, and to the conditions resulting in the deposition of the Caspary strip.

The Old Red Sandstone plane of Caithness, with the geologically associated Orkneys, forms a homogeneous region comparatively isolated from the rest of Scotland by its geographical position and structure and by climatic conditions. Neither the physical geography nor the geology of the region need description here, except to note the absence of metals or similar mineral resources and the influence a stone that breaks easily and naturally along its bedding planes into flat slabs must exercise upon the local architecture. A word must, however, be said about the climate, which has not remained constant in prehistoric times.

The problem of the relation between gonad and the other endocrine glands has, during recent years, attracted much attention. It has been shown that the maturation of the ovary, which is responsible for the other manifestations of puberty, is itself dependent upon the developmental level of its somatic environment rather than upon its own age; that the senescent insufficiency of the ovary is due, not so much to its own inability to elaborate hormones and ova, as to a decrease in the amount of, or deterioration in the quality of, the extra-ovarian substances which are necessary for its proper functioning. Similar evidence has been produced in relation to the testis. It has been shown, further, that the pituitary is intimately concerned in the establishment and maintenance of the œstrous cycle, and also that the placenta exerts an influence upon the structure of the ovary.

The mouse placenta implanted into immature female mice evokes pregnancy conditions in the vaginal epithelium, growth of the follicles in the ovary, and enlargement of the interstitial tissue. It is demonstrated, therefore, that mouse placenta contains an active kyogenic substance.

The Ceylon trotting bull, a small but fast animal, is regarded as a variety of its larger Indian relative, the Zebu, Bos indicus. The case, furnishing the basis of this account, was brought to my notice after the animal had died, so there is no direct evidence regarding its reactions to males and females of the same species. But I am told that although it had been kept for many years in a field with mature cows and bulls it had shown no reaction towards either. Very little is known about the early history of the animal beyond the fact that it was considered to be about seven years old. Nothing is known of its parentage, and as these trotting or racing animals change hands many times in Ceylon, it is impossible to discover whether it had been a twin calf. The animal died of tetanus, and until a fortnight before its death it had been healthy, and, I believe, the winner of many prizes for racing.

(1) An attempt has been made to prove experimentally that there is definite localisation of translocation in the plant.

(2) This localisation is brought about by the almost complete absence of easy cross-transfer of materials in the plant tissues. It affects the movement of both salts and elaborated food-materials.

(3) The fact that movement upwards and downwards is easy while lateral movement is almost completely absent is clearly demonstrated where it is shown that the materials which are elaborated in the leaves on one side of. the swede plant are stored as reserved food-materials in the portion of the bulb on the same side.

(4) It is also shown that this localisation is found in the case of other plants, and that it offers a new method of attacking a variety of problems which at the present time present some difficulty of interpretation.

1. The morphology and anatomy of Trichomanes aphlebioides Christ, a species endemic to New Guinea, is shortly described.

2. The most outstanding feature of the species is the presence of aphlebioid leaves. These latter are shown to be the modified first fronds of the axillary branches.

3. The anatomy of the alphebioid leaves is described. They show great reduction in relation to the humid conditions of the high forests in which the plant grows.

4. The morphology of aphlebiæ and aphlebioid leaves is briefly discussed.

5. No experimental evidence is available with regard to the function of the aphlebioid leaves. Mention is made, however, of the various suggestions which have been put forward in relation to this question.

This investigation is founded upon a long and unique series of readings of deep rock temperature taken at the Calton Hill, extending from the year 1837 to the present time. The thermometers were installed under the direction of the late Professor James Forbes and were described in detail by him to this Society. They were four in number, sunk in the rock at depths of 25·6 feet, 12·8 feet, 6·4 feet, and 3·2 feet, and consisted of large cylindrical bulbs 6 to 8 inches long and 1½ to 2½ inches in diameter, connected by long, fine capillary tubes with the surface of the ground, where they expanded into tubes of wider bore having degrees of convenient length for reading. The bulbs were inserted into tin cylindrical boxes filled with plaster of Paris as a precaution against fracture, and the liquid used was alcohol. Regular weekly readings were commenced in 1837. The thermometer at depth 12·8 feet was broken by frost in 1861, but the readings of the remaining three continued without interruption till the year 1876, when a Portuguese sailor from a ship in Leith scaled the Observatory wall one night and wantonly destroyed all the thermometers and their wooden shelter.

A highly sensitive method of measuring alternating currents of the order of microamperes and of any frequency is described. The current to be measured is passed through the filament of a diode valve. The main heating current of this valve is supplied by an independent oscillator working at the frequency of the current under measurement. The change in the plate current of the valve is measured, thus indicating the amplitude of the alternating current being measured. Theoretical and practical details of the methods of working are given and particulars of the method by which the calibration was tested. It is suggested that the method is particularly applicable to the determination of electro-magnetic field strengths by measuring the currents induced in an aerial.

Three curious types of fossil remains, collected by Mr D. Tait of the Geological Survey (Scottish Office), are here described. They are from the Downtonian (Upper Silurian) of Scotland, and are unknown from rocks of a corresponding age in England. The first type described deserves a name as being characteristic of Scottish Downtonian rocks. The other two forms are very rare, the third one described being represented by a single specimen (and counterpart), and the second by two specimens.

It should be mentioned that the Geological Survey collection contains a specimen of the first type (designated Taitia catena) from the Lower Old Red Sandstone of Tealing Hill, near Dundee. This example (No. T. 1251 h) was presented to the Survey by Mr Macnicol.

Puberty is defined as that stage of individual development characterised by the ability to elaborate functional gametes and by the physical ability to and the desire to play the appropriate rôle in mating. Maturity is defined as that stage of individual development characterised by the exhibition of the maximum fertility ratio and by the ability to produce viable offspring and to rear them.

It is shown that the age at attainment of puberty varies with different stock and with different conditions of husbandry, and that there can be no generally applicable standard. Each worker must standardise his own stock and his own environment.

There are considerable individual differences in the age at maturity, and these are referable to dissimilarities in genetic constitution and to differences in husbandry. In this experiment two groups of animals were involved, coloured and albino. The albinos reached puberty much earlier, showed a longer duration of the cornified stage before mating, a higher proportion of matings at first œstrus, a greater proportion of pregnancies following mating at first œstrus, and a slightly longer interval between first and second œstrus.

Mr President, Ladies, and Gentlemen,—I desire first of all to express my deep gratification at the great honour you have shown me by inviting me to give an address to this renowned Society. Scotland and Norway are closely united by bonds of friendship and also of kinship. There are many Norwegians with Scotch blood in their veins, just as there must be a large number of Scotch people who are descended from the Vikings who came here, long ago, and found the Scotch lassies so charming that they never returned to their own country!

A problem which frequently presents itself to the spectroscopist is that of comparing photographs with a view to detecting differences which are not sufficiently conspicuous to make them obvious by simply superposing the plates. Differences of the kind in question may arise in the spectrum of a particular substance as the result of variations in the conditions of excitation of the spectrum which may produce changes in the distribution of intensities, changes in the nature of the lines, or the emission of new lines.

The discussion of the distribution of the gene ratio of the author's paper of 1922 is amended by the use of a more exact form of the differential equation to be satisfied. It appears that the time needed to halve the variance by random extinction of genes in the total absence of mutations should be 1·4 instead of 2·8 times the number of potential parents in each generation. Either value shows that the loss of variance due to this cause is too trifling to be appreciable in the balance of causes which maintain the actual genetic variability of species.

The same correction alters the distribution appropriate for the maintenance of variability at a fixed level by mutations in the absence of selection. The new solution closely resembles the form previously obtained and now confirmed for the practical case in which selection is present. The method of differential equations, however, fails to deal satisfactorily with these cases, owing to the failure of the integrals to converge at the termini representing cases in which one or other allelomorph is extremely rare.

A method of functional equations is developed for dealing with the termini, and is shown to lead to the same solutions as the amended differential equations in the central portion of the range for which the latter are valid, and further to give the terminal distribution of rare allelomorphs. The method requires the investigation of a continuous function uv of argument v satisfying the recurrence formula

From the asymptotic form of this function its expansion in the neighbourhood of u = 0 is derived, giving the frequencies of the required distributions.

Exceedingly minute values for the selective advantage or disadvantage make a great difference to (i) the chance of success of a mutation and (ii) the contributions of such mutations to the specific variance. The order of magnitude to be considered is the inverse of the population of the species. The neutral zone of selective advantage in the neighbourhood of zero is thus so narrow that changes in the environment, and in the genetic constitution of species, must cause this zone to be crossed and perhaps recrossed relatively rapidly in the course of evolutionary change, so that many possible gene substitutions may have a fluctuating history of advance and regression before the final balance of selective advantage is determined.

It is well known that, if the infinite series

is convergent for any non-integral value of z, it is uniformly convergent in any finite region of the z-plane and represents an integral function C(z), say, such that C(n) = an for n = 0, ± 1, ± 2, … It is called the Cardinal Function of the table of values, and is identical with Gauss's Interpolation Formula (suitably bracketed).

The function C(z) defined by the series (1) has been given two different definite integral representations, due to Ferrar and Ogura respectively.

The processes of long-wave low-temperature radiation in the atmosphere have been studied with a view to investigating the extent to which they may be regarded as diffusion-like; the decrease of water-vapour with height is taken to be exponential, that of temperature to be constant up to the tropopause, and then to be zero. Full allowance is made for the radiation being diffuse, involving the functions ; such properties of these functions as are required in the further work are studied. The expression for the upward flow of radiation is obtained in the form of a power series in the temperature gradient in the troposphere; the coefficient of the first power of the temperature gradient is defined as the “coefficient of radiative diffusion.” There is shown to be a certain amount of ambiguity about the coefficient so defined.

A model atmosphere resembling fairly well the conditions in N.W. Europe is considered: the upward flow of radiation and the coefficient of radiative diffusion are calculated; for this purpose we require Hettner's measurements of water-vapour absorption as modified by Simpson.

The effect of the heating of the ground during the day to a temperature above that of the air near by is then considered; it is shown that the study of the results of this factor which are of importance in the interpretation of continuous temperature records near the ground requires measurements of the absorption of water-vapour for the wave-lengths for which it is particularly opaque; these do not appear to exist.

Certain derivatives of benzacridine and of 4-anilinoquinoline give a blue or red colouration with a solution of iodine in aqueous potassium iodide. In the case of the active anilinoquinoline compounds the colour is usually developed in presence of solutions containing iodine at a concentration of the order of N/10,000, whilst in the case of the benzacridine compounds the colour is still apparent at concentrations of N/100,000 or even less. The effect of variation of concentration of compound, iodine, and hydrogen ions has been investigated in certain instances. The action of certain inorganic salts has also been investigated, but in low concentrations these are without much effect. The methosulphates of the two active benzacridine bases also develop colours with iodine even with very low concentrations of the latter. It is suggested that these methosulphates form micellar, colloidal solutions. The chromogenic property appears to depend not on the nitrogen atom in these compounds but on the structure of the molecule as a whole. The compounds which have been investigated differ from most of those previously known to give colours with iodine, in that they are basic and form colloidal solutions in which the particles are positively charged.