The MSS. here calendared were presented to the Royal Society of Edinburgh by David Hume the Younger, nephew of the philosopher and Baron of the Scottish Exchequer.

The editors desire gratefully to acknowledge a grant made by the Research Committee of Armstrong College, Newcastle-upon-Tyne, in the University of Durham, to assist them in the work of compiling the Calendar.

The efficacy of intracardiac injection of adrenaline to assist recovery from asphyxia having been recently disputed, we have instituted a number of experiments with the object of determining what effect, if any, is produced by such injection in asphyxiated animals in which the respirations and/or the heart had entirely stopped, and the blood-pressure had become reduced almost or quite to zero.

The ultra-violet absorption spectra of C2N2, CNCl, CNBr and CNI have been photographed.

Measurements are given of band edges of the C2N2 absorption spectrum in the region 2380 A–1850 A. The influence of temperature on the relative intensities of the bands has been studied.

The long wave-length limits of the regions of continuous absorption due to the cyanogen halides are: CNCl, 2240 A; CNBr, 2540 A; CNI, 3100 A and 2150 A.

We desire to thank Dr Baker, of the Royal Observatory, Edinburgh, for making photometer records of several spectra, Dr Ludlam for his helpful interest in our work, and Imperial Chemical Industries, Ltd., for a grant towards the cost of quartz apparatus.

1. Reference is made to experiments conducted by Flaskämper as a result of which he stated that the removal of the cotyledons at an early stage from seedlings of Phaseolus sp. and of Vicia Faba resulted in an elimination of the pith from the subsequently formed part of the root in both species, and further induced a reduction in the number of poles in the root of the second species.

2. The significance of such observations in a consideration of the theory of the Size Factor is pointed out.

3. The experiments have been repeated. The malnutrition resulting from the decotylation affected the varieties employed in the present work more adversely than with Flaskämper, and usually caused the death of the seedling after a shorter or longer period.

4. Sufficient evidence has been obtained, however, to throw very serious doubt on Flaskämper's conclusions. The two reduction phenomena he described are now shown to occur in the normal development of the roots of these species, and there is no indication that their occurrence is affected by decotylation.

5. A teleological explanation, based on the theory of the Size Factor recently advanced by Bower, is made of this reduction in the number of protoxylem poles which occurs in the normal development of the roots of these plants.

6. The significance of the appearance of a pith in the basal parts only of these roots is discussed.

In conclusion, I desire to express my indebtedness to Professor F. O. Bower, F.R.S., for his constant interest in this work, and to thank Dr S. Williams and other members of the Botany Department for much valuable help. Also my best thanks are due to the Executive Committee of the Carnegie Trust for a grant towards the expense of the illustrations both of the present work and those of a recent paper on “The Stem-Endodermis in the Genus Piper,” published in the Transactions of the Royal Society of Edinburgh.

The orthogonal properties of the Hermite polynomials, their relation to the normal frequency function, and the part they play in expressing the more general frequency function of Type A, are matters of common knowledge in mathematical statistics. Less well known are the very similar properties of a class of polynomials related in the same kind of way to Poisson's frequency function of rare events and to the function of Type B which generalizes Poisson's function. These polynomials have been interestingly studied during the last few years by Ch. Jordan and by H. Pollaczek-Geiringer. (References are given at the end of this paper.) In preparation for our main object we shall gather together the principal results concerning these polynomials, together with a few others not mentioned in the extant literature.

In a recent paper, Professor E. T. Whittaker discussed the problem of defining, in a general riemannian space-time, the concept of spatial distance between material particles. It is the object of this paper to give an alternative definition, and to compare the new formula with that of Whittaker.

This communication extends the method of classifying carbonaceous minerals already introduced in order to include the three components of common coal. The existence of the three constituents has long been recognised, but their close study, and the nomenclature now generally accepted, date from 1919, when Dr M. C. Stopes described their salient characteristics in a paper to the Royal Society. In that paper she gave the name durain to the hard, lustreless constituent, that of vitrain to the lustrous part, and borrowed the French miner's name fusain for the charcoal-like material commonly found between the bands of a coal seam. A bright variety, called clarain by Dr Stopes, is now usually regarded as a blend rather than as a separate substance, and may be disregarded in a classification such as this.

Vertebraria is one of the commonest and most characteristic fossils in those Upper Carboniferous and Permian strata in which Glossopteris is the dominant fossil plant. It has been found in the form of coaly incrustations, impressions, and casts, and accounts of these various forms have been given by Arber and Seward. In view of our very inadequate knowledge of Vertebraria and Glossopteris any information about them is of importance. The genus Vertebraria Royle was founded on impressions of plant axes, some of which, from the evidence of the attachment of roots, must be judged to be roots or rhizomes. Vertebraria axes are usually found lying in the plane of the bedding of the matrix (Pl. I, fig. 2) and less frequently at right angles to the plane of bedding (PL I, fig. 3).

The analysis of the performance of an internal combustion engine, based upon the indicator diagram, for the purpose of investigating such matters as the cyclical changes of temperature and internal energy content of the charge, and the heat flow between the working agent and the cylinder walls, is of considerable importance.

1. A description of the mammalian pigmentary system is given together with an outline of the mechanism of melanin production and those factors which influence or control it.

2. The production of melanin by chemicophysical interaction between circulating 3-4-dihydroxyphenylalanine (dopa) in the blood-stream and an enzyme or enzymes of intracellular origin is accepted, but it is emphasised that in the interaction there are numerous opportunities for physiological interference which inhibit melanin formation.

3. The current theories of the origin of melanin are discussed and evidence supporting the nuclear origin of oxidising enzymes is given.

4. It is suggested that in the sheep some epidermal cells are more potentially pigment-producing than others, and that a gradation exists between the cell which cannot produce pigment and that which produces it to a maximum degree.

5. It is postulated that only one pigment exists, and that all animal colours are the result of a modification of this one pigment.

6. The results of staining sections of lamb and adult sheep skin with dopa are given.

7. A series of in vitro experiments planned to standardise the dopa reaction is described.

8. It is suggested that the dopa reaction may be used as a simple chemical test in genetic analysis whereby the pigmentogenic potentialities of a particular sheep may be analysed.

The elliptic integral of the second kind

can, by substitution, be made to depend upon

Writing E(K) = E, Jacobi's Zeta function is defined by

where

Z(u) is an odd function of u with period 2K.

0.1. In Max Brückner's discussion of isohedral (gleichflächig) and isogonal (gleicheckig) polyhedra (Vielecke und Vielflache, pp. 140 ff.) two faces of a polyhedron are defined to be equal when they are either directly or inversely congruent, and the dihedral angles at corresponding edges are equal; two vertices are equal when the spherical polygons, which they form on unit spheres with centres at the vertices, are either directly or inversely congruent, and the lengths of corresponding edges are equal. With these definitions he shows that all possible isogonal polyhedra are obtained by truncating the corners and edges of the regular n-sided prism, the octahedron and hexahedron, and the icosahedron and dodecahedron, in a manner similar to that in which the semi-regular polyhedra are obtained from the regular polyhedra. The semi-regular or Archimedean bodies are indeed just special varieties of the more general isogonal polyhedra. The isohedral polyhedra are the polar reciprocals of the isogonal polyhedra, and are obtained from the regular double-pyramid and the regular polyhedra by the reciprocal constructions, “pointing” the faces and edges.

1. The overwhelming majority of cases of alkaptonuria are consistent with the hypothesis that this disease is determined by a single autosomal recessive gene substitution.

2. The observed proportion of alkaptonurics in recorded fraternities with two normal parents and the incidence of consanguineous parentage conform quantitatively to the requirements of Mendelian hypothesis in a system of random mating.

3. There appears to be an alternative form of alkaptonuria which is dominant.

Grateful acknowledgment is made to Sir Archibald Garrod for advice regarding the sources consulted.

As far back as 1678 Martin Lister, in his Historiæ Animalium Tractatus, has noted that, in the case of certain Molluscs, the fæces are of a regular form, and that their shape differs according to the species; he deduces from this that the intestine must show a corresponding difference in the various species.

1. A reagent (p-cresol) has been used to determine the activity of tyrosinase in the potato tuber.

2. The course of the reaction tyrosinase-p-cresol has been shown to be mono-molecular, with a short linear period at the commencement. From observations of this period, constants for the enzyme activities have been obtained and a temperature coefficient deduced.

3. The enzyme activity has been shown to depend upon stage of maturity of tuber, variety of tuber, and disease infection, but to be independent of tuber weight, environment, season, and storage conditions.

4. The probable significance of the results has been discussed.

The writer wishes to thank the Department of Agriculture for Scotland for a Grant which enabled the work to be carried out, and also Dr A. Lauder and Dr A. M. Smith of the Edinburgh and East of Scotland College of Agriculture for their interest and assistance throughout the course of the work.

This paper is an account of an experimental investigation which was made on the behaviour of the secondary spectrum of hydrogen as affected by the pressure of the luminous gas. It was conjectured that the classification of the lines of the spectrum according to their behaviour in this respect should be of value in the problem of accounting for their origin in terms of the quantum theory. There can be no doubt, on the evidence given below, that the method is of some importance. For this reason it has been considered worth while bringing the results already obtained to the notice of workers in this field by publishing tables of intensities.

1. The adrenal gland of Xenopus is essentially similar in distribution and structure to the adrenal of Urodeles.

2. In addition, adrenal tissue occurs in the walls of the renal veins, inferior vena cava, aorta and renal arteries, a condition similar to that found in some Cyclostomes and Fishes.

We wish to thank Mr B. McManus for his assistance in the preparation of sections.

§1. Einstein has shown that the gμv giving the metric, ds2 = gμvdxμdxv, for a unified field theory can be expressed in terms of the two tensors ahμahv by

The results obtained may be summarised in the following table comparing the filial and fraternal coefficients for autosomal and sex-linked variation. When dominance is complete the values given are referred to equal frequency of the allelomorphic genes, i.e.p = ½ = q.

Briefly, then, the contribution of sex-linked genes to the observed variance will tend to lower the correlation between father and son and between brother and sister. It will raise the correlation between father and daughter or between sister and sister conspicuously. These considerations emphasise the interest attaching to a separate investigation of fraternal correlation for sibs of all three sex classes in connection with studies on twins. If the correlation for dizygotic twins of like sex is higher than for dizygotic twins of unlike sex, the difference might be due to the greater similarity of environment for two individuals of the same sex, or it might be due to the contribution of sex-linked genes to the observed variance. In the latter case the correlation for boy pairs should be significantly lower than the correlation for girl pairs. The wide discrepancies in recorded data for fraternal correlations with respect to intelligence quotients might be re-examined from this standpoint. If an appreciable proportion of the total variance is due to sex-linked genes, it is of more importance that a boy should have a clever mother than a clever father.

A brief history of the measurement of diffusion of gases (excluding “effusion,” “transpiration,” and other processes from which data for the calculation of the diffusion coefficient may be obtained) is given.

A visual method of following the diffusion of a strongly coloured vapour (bromine) into colourless gases is described.

The diffusion coefficients calculated from the observed data are in good accordance with those obtained theoretically.

The authors desire to thank Miss Netta Macnaughton for valuable assistance in the experimental work.