1. The pregnancy rate of primiparæ, suckling their young, was, in this experiment, 24·1 per cent.; that of multiparæ suckling their young, 50 per cent. It is shown that this difference is not due to differences in the incidence of ovulation associated with postpartum œstrus. The suggested explanation of this difference between puberal and adult groups is that a certain level of somatic maturity is a prerequisite for full reproductive activity.

2. In all cases the duration of pregnancy was prolonged. The degree of prolongation was variable and could not be related to the number of young in the uterus or suckling. The results provide no support for the suggestion that this prolongation, due to delayed implantation of the fertilised ova, is to be referred to an inhibitory action on the part of the mammary gland. The suggestion is made that the delayed implantation and prolonged pregnancy are due to inability on the part of the corpus luteum to cater adequately for implantation and lactation synchronously.

The growth of the finger nails has been investigated, and the rate on the right side as compared with the left, and in summer as compared with winter, determined for each finger. In nearly every case the rate is faster in summer than in winter.

In nearly every case also the rate is faster on the right hand than on the left. A notable exception is presented by the thumb nails, which have grown faster on the left hand than on the right both in summer and winter. The slowest rate of growth occurred in the nail of the little finger of the left side. The cutaneous nerves (ulnar) of this finger had been severed, and, with the exception of those which subserve pain, had not shown functional recovery. It is therefore probable that a trophic influence is exercised through the nerves upon the growth of the nail; the probability being supported by the fact that the little-finger nail on the left or de-nervated side not only exhibits a slower rate of growth but is distinguished from the corresponding nail on the normal side by being more flattened in form, rougher on the surface, and more brittle in texture.

Consider a system of “orthogonal polynomials”

P0, P1 (x), P2(x), …

possessing the property

x1, x2, …, xr being real given numbers, and p (x) a given “weight” function.

1. The observations of rock temperature on the Calton Hill have recently been analysed by Mr R. W. Wrigley, with a view to the discovery of changes going on gradually and independent of weather conditions. Mr Wrigley took groups of years, such that the mean air temperature was the same for each group, and found the mean rock temperature for like periods. He trusted that in this way he would be able “to get rid of the surface temperature variations.” The result of the calculations was that for different periods in which the mean air temperature was the same the temperature of the rock might vary by half a degree Fahrenheit. The rock temperature had a maximum about 1856, fell until 1892, and rose after that date.

The data which are available do not seem very suitable for Dr Whipple's method of analysis. As explained in my original paper, the groups into which the rock-temperature observations were divided depended entirely upon the method adopted to get rid of the effect of variations of air temperature at the surface, and the resulting means were for dates which had no connection with the long-period temperature fluctuations which were later disclosed. A series of observations extending over nearly a hundred years was thus reduced down to eight mean temperatures for periods of various lengths.

The late Dr R. Kidston proposed the name Lyginorachis to include isolated petrified petioles which exhibited a structure so similar to the petioles of the well-known Lyginopteris (Lyginodendron) oldhamia (Binney) as strongly to suggest affinities with that plant.

Two species of Lyginorachis are known, both from the Lower Carboniferous rocks of Britain. In 1923 Dr D. H. Scott gave an account of L. papilio from the Cementstone Group (Calciferous Sandstone Series) of Norham Bridge, Tweedside, and briefly referred to a second species, L. taitiana, from the Carboniferous Limestone Series. Kidston had passed on these sections to Dr Scott for description.

It is known (cf. Charlier's statistical memoirs, passim) that the frequency function of Type A can be written compactly in symbolic form,

where r! ar is equal to kr, the rth seminvariant of the distribution, D = d/dz and

For most purposes it is convenient to take the mean, k1 as origin and the standard deviation, as unit. The function of Type A then becomes

where φ(x)=(2π)−½e−x2, and Ar is the coefficient of (−)rtr in the expansion of exp

One of the main objects of the study of animal distribution is to determine the probable areas of origin and dispersal—Osborn's Centres of Radiation—of the different families and genera of the various classes of animals. This is not an easy matter, and, as reference to any standard work on molluscs would show, the questions of the origin, in time and space, of the various families of molluscs, as also their relationships, are often severely left alone. The classification is, as a result, often quite arbitrary and does not show the genetic relationships of the different members. In dealing with families with a world-wide and, more particularly, a discontinuous distribution, it is a matter of grave doubt whether several of the families, as defined, are homogeneous units which originated in any one area of the globe and spread to other regions.

In this investigation a graphical method, based on the ultimate analysis, is applied to the classification of the carbonaceous minerals of organic origin. It is necessary in any such study to disregard those ingredients (e.g. ash-forming compounds, sulphur, nitrogen, and free moisture) whose presence, while greatly influencing the commercial value of a carbonaceous mineral, has no significance in regard to its classification. These extraneous or adventitious ingredients have therefore been eliminated by calculation, so as to reduce each analysis to terms of its essential elements—carbon, hydrogen, and oxygen.

In 1862 Anderson described a parasite of Cancer pagurus from the Firth of Forth, which he named Sacculina triangularis. The species differs from Sacculina carcini in its external form and the shape of the testes, particulars of which are described in Anderson's paper in sufficient detail to prove that the parasite is specifically distinct from Sacculina carcini. In a paper dealing with the European species of the Sacculinidæ (Boschma, 1927) I mentioned Sacculina triangularis as a distinct species, basing this statement on Anderson's description and figures. Afterwards I had the opportunity to study the anatomy of the species, owing to the kindness of Professor J. H. Ashworth, who sent me nine specimens of Sacculina on Cancer pagurus from the Firth of Forth. The following description of the characters of the species is based on this material.

In two recent papers Professor E. T. Whittaker has solved the electromagnetic equations for the case of a uniform gravitational field. The fundamental tensor associated with such a field makes the Riemannian tensor vanish, since such a field can be transformed away by a suitable choice of coordinates. This property enables us to find the electromagnetic field in a uniform gravitational field without solving Maxwell's equations, but by a mere transformation of co-ordinates.

In a former paper on the same subject the writer pointed out that the sequence used by D. Bernoulli for approximating to the greatest root of an algebraic equation could be further utilised in such a way as to give all the roots. It is suggested in the present paper that there is really no need to compute a first Bernoullian sequence at all, but that by the theory of dual symmetric functions the coefficients in the given equation may be used with equal convenience. In a practical respect this simplifies the technique of root-evaluation.

The homogeneous linear equation of the second order may be solved by means of a, continued fraction whose elements are coefficients in the equation. The two dimensional continued fraction is generalised to m dimensions and yields the solution of the equation of the mth order.

1. From the above it is therefore justifiable to conclude that Sirex cyaneus is typically hymenopterous, in that:

(a) the ripe male reproductive tissue is haploid (8 chromosomes), while the female oogonia are diploid (16 chromosomes);

(b) the abortive character of the first spermatocyte division is evidence that chromosome reduction does not occur during the maturation of the male gametes.

2. Support is thus afforded to the hypothesis commonly held, that the male hymenopteron is a haploid organism and is the product of an unfertilised (haploid) egg, while the female is a diploid organism arising from a fertilised egg.

3. Feulgen's “Nuclealreaktion” holds for the chromatin involved in the abortive division and for the chromosomes of the second spermatocyte; but the large chromatoid body and cytoplasmic granules seen in these same stages by the iron hæmatoxylin technique did not give the chromatin reaction. The nature of these chromatoid bodies remains to be discovered.

The fossil cuticles of the paper-coal from the Moscow Basin in Central Russia were first described and figured by Auerbach and Trautschold in 1860. Since then these cuticles have been the subject of much discussion, especially with regard to the interpretation of their numerous regularly disposed perforations. According to the various views of previous investigators, several generic and specific names have been assigned to these cuticles. Auerbach and Trautschold, regarding the perforations as the result of the fall of the leaf-cushions as well as the leaves, considered the cuticles to belong to the genus Lepidodendron, and named the plant to which they belonged Lepidodendron tenerrimum.

1. Fourier's Integral Theorem.—In a former paper it was shown that certain formulæ, usually obtained by means of Fourier's Integral Theorem, could also be proved by contour integration: and, indeed, Fourier's Integral Theorem can be established by this method. The functions involved must be holomorphic, so that the proof does not justify the application of the theorem to such wide classes of functions as the usual proof by means of Dirichlet Integrals. In what follows it will be assumed that all the integrals are convergent, and the changes of order of integration justified. Fourier's Integral Theorem will be proved in the following form.

Experiments are described, the aim of which is the determination of the energy spent in producing one pair of ions when electrons of velocity corresponding to 50–270 volts are totally absorbed in air. It is found that this energy varies with the initial speed of the electron, but that it asymptotes to the value 37 ± 2 electron-volts when the energy of the electron is very great.

This value of the “volts per ion pair” is compared with those found by other experimenters. A correlation of the three electronic “constants,” the range of the electron, the ionization per unit path, and the total ionization is attempted. It is concluded that, unless in the case of very fast cathode rays or β-particles, the “ionization per unit path,” as measured by ionization chamber experiments, has no meaning.

In a paper recently read before this Society the ultimate analysis was used as a means of distinguishing between the various species of carbonaceous minerals, it being shown that, by a simple graphical method, these minerals could be classified in five groups, viz.: coals, sub-cannels, cannels, parafila shales, and torbanites. Minerals from all these groups are past, present, or prospective raw materials for oil-distillation, for which purpose, indeed, the oil shales and torbanites are especially suitable. It is therefore of interest to inquire whether their yield of crude oil and the composition of these substances are related in a manner sufficiently definite to serve as a guide to those concerned in this branch of technology.

(1) A year's measurement of the light-intensity in an exposed site (“mbuga”) and in a Berlinia woodland community, Kikori (4° 21' S.), Tanganyika, by means of the Eder-Hecht Graukeilphotometer is described.

(2) The Bunsen-Roscoe units per second are shown to be very high, even under canopy of the Berlinia; they are very much greater than measurements recorded by Dorno for Assuan and Rio de Janeiro.

(3) While there is a positive correlation between the B.-R. values and the hours of direct sunshine, it is also clear that during cloudy periods (less than 50 per cent, of possible sunshine is experienced at Kikori and on the Central Plateau of East Africa generally) the B.-R. values are also very high.

(4) There is a positive correlation between the values of the Eder-Hecht photometer (in terms of blue-violet-ultraviolet rays), and the readings of the Livingston radio-atmometer measuring the total light-intensity of the same stations in terms of cubic centimetres of water.

(5) In virtue of the peculiar effects of the light of Tropical Africa upon the European nervous system, it is urged that quantitative and qualitative studies of the light in those regions should be investigated.

(6) Field biologists should make greater use of this efficient, cheap, simple, and portable instrument.

1. The given set of equations in question is

and the problem was solved by Cayley in the Quarterly Journal of Mathematics, viii, pp. 183–185. The method was peculiar and is still interesting. He introduced three additional unknowns, deduced a fresh set of five equations, from which he then proceeded to eliminate four unknowns, namely, the new three and x/y.