Abstracts of Papers Communicated to the Royal Society of LondonSource: Proceedings of the Royal Society of London. Series A, Mathematical and PhysicalSciences, Vol. 177, No. 971 (Mar. 18, 1941), pp. S29-S36Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/97477 .

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ABSTRACTS

OF PAPERS COMMUNIJCATED TO THE ROYAL SOCIETY OF LONDON

In accordance with a resolution of Council, summaries or abstracts of papers are to be published as soon as practicable. The publica- tion of such abstracts in no way indicates that the papers have been accepted for publication in any fuller form. These abstracts are issued for convenience with the " Proceedings of the Royal Society of London" but do not form a part of the "Proceedings".

12 JUNE 1940

The wave-form of atmospherics at night. By J. S. ELDER, D. B. HODGES, W. E. PHILLIPS, B. F. J. SCHONLAND, F.R.S. and J. W. VAN WYK. (Received 5 February 1940.)

The wave-form for all atmospherics received at night from sources within 2000 km. can be accurately described as a ground-pulse followed by a series of sky-pulses produced by successive reflexions between the ionosphere and the earth, 30 such reflexions being frequently recorded. The time separation between the peaks of these pulses is determined by the distance travelled and the height of the layer. The primary pulse emitted by the source is usually a single complete oscillation of period ranging from 50 to 400# gsec. At distances greater than 500 km. the ground-pulse

and the first sky-pulse merge owing to the shortness of the time-interval between

them. Differences of amplitude, form and phase between pulses can arise from

differences in angle of emission from the parent lightning channel.

The height of the reflecting layer can be determined within + 1 km. It ranged

from 85-5 to 90*5 km. during two winter months, with a mean of 88-0 km. The

distances of the sources as found by analysis of the pulse series were corroborated by

independent location with cathode-ray direction-finders. The reflexion-coefficient of

the layer for the pulses of longer period exceeded 0-80. The velocity of the ground-

pulse where it can be tested is within 0 7 % of that of light.

Abstracts [ S 29 ] 7

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S 30 Abstracts of Papers

Operator calculus in the electron theory of metals. By K. FucHs. (Comn- municated by M. Born, F.R.S.-Received 28 March 1940.)

An operator calculus is developed applicable to problems in the electron theory of metals. It differs from the common operator calcuLlus of the quantum theory in the fact that the wave ftnction is defined in a finite space (the atomic polyhedron) bounded by a finite surface. This leads to the introduction of surface operators.

The position operator x cannot be developed with respect to the proper functions of the Hamiltonian. Instead, an operator 6 is introduced, which is essentially tho Fourier development of x.

Thus there are three fundamental types of operators: The differential operator p, the multiplication operator 6, and the surface operators. It is shown that with the lielp of these a consistent calculus can be developed.

The reversible formation of starch from glucose-l-phosphate catalysed by potato phosphorylase. By C. S. HANES. (Communicated by F. F. Blackman, F.R.S.-Received 29 March 1940.)

An enzyme (phosphorylase), which catalyses the reversible conversion of starch and inorganic phosphate to glucose- I -phosphate, has been found to occur in a number of higher plants. A method is described for obtaining from potato tubers highly active preparations of phosphorylase which are free from certain enzymes which catalyse alternative reactions.

The reversibility of the transformations: starch + inorganic phosphate=glucose-l-

phosphate, is shown by the fact that the reaction proceeds in either direction until the ratio of inorganic orthophosphate/glucose-l-phosphate attains a value which is iiot significantly altered by wide variations in the concentrations of the reactants or the enzyme. The equilibrium value of this ratio is not detectably affected by altera- tions in the concentration of starch but varies considerably with alterations in the concentration of hydrogen ion. This is shown to be due to the effects upon the extents of dissociation of the inorganic and esterified phosphate, the di-valent ions alone determining the equilibrium; thus the ratio (HPO4)=/(C6H105. 0. POO3)= remained approximately constant at a value of 2-2 when the pH value was varied from 5 to 7. When glucose-l-phosphate is added to the enzyme there is an initial lag in the liberation of phosphate and the formation of starch. This induction phase is abolished, and the reaction velocity greatly increased, by small additions of starch or maltose.

The preparation on a large scale of glucose-l-phosphate (in the form of the crystalline potassium salt) by allowing crude potato juice to act in starch is described.

Observations on the polysaccharide formed from pure glucose-l-phosphate under the action of purified phosphorylase indicate that it resembles closely the so-called amylo-amylose fraction of natural potato starch.

The mechanism of this reversible interconversion and its bearing on the problems of carbohydrate metabolism in the plant are considered.

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Abstracts of Papers S 31.

The effect of field size and pattern on the change of visual sensitivity with time. By B. H. CRAWFORD, M.Sc. (Communicated by Sir John Parsons, F.R.S.-Received 29 March 1940.)

Results are recorded showing the effect of size of a circular conditioning field on brightness threshold measurements made at the centre of the field, firstly, with the field steadily exposed and viewed, secondly, when the conditioning field has been cut off and the eye is returning to a state of dark adaptation. Conditioning and test fields are both illuminated by white light. No field size effect is detectable over the range 600 diameter down to 30 diameter. Below 30, for a steady state of adaptation, various rather complex effects of interference between the conditioning fields are shown; these are explained in terms of the effect of distant parts of the conditioning field in raising the threshold and a perceptual interference between the patterns of conditioning and test fields. For changing states of adaptation the effect of field size cancels out- xcept in an isolated case-if the initial conditioning field brightnesses are adjusted to give the same steady value of threshold: then, after cutting off these various conditioning fields, the decrease of brightness threshold follows the same course. However the test patch of retina be brought to a given steady state of adaptation, as measured by the brightness threshold, it will recover its dark adaptation in the same way. These considerations apply both to foveal vision and to vision in the parafovea at 80 from the fovea.

The pressure of water waves upon a fixed obstacle. By T. H. HAVELOCK, F.R.S. (Received 29 March 1940.)

The diffraction of plane water waves by a stationary obstacle with vertical sides is examined, in particular the variation of amplitude along the sides and the average steady pressure due to the wave motion. Results similar to those in other diffraction problems are obtained for an infinite plane and for cylinders of circular or parabolic section, and approximations are made for sections of ship form. The examination was made in view of possible applications in the problem of a ship advancing through a train of waves, and the results are discussed in relation to the average additional resistance in such circumstances. It appears that the mean pressure obtained on diffraction theory from the second order terms can only account, in general, for a small proportion of the observed effect; the motions of the ship, and in particular its oscillations, are essential factors in the problem.

Ionic regulation of Carcinus maenas. By D. A. WEBB. (Communicated by J. Gray, P.R.S. -Received 1 April 1940.)

Analyses have been made, with respect to the principal inorganic constituents, of the blood and urine of Carcinus, when living in normal sea water, diluted sea water, and sea water modified by the addition of magnesium sulphate.

The composition of the blood of individuals living in normal sea water is as follows (the concentration of each ion being expressed as a percentage of the concentratioin

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S 32 Abstracts of Papers

that would be expected if the blood were in dialysis-equilibrium with the external medium): Na 1 10 %, K 118 %, Ca 108 %, Mg 34 %, Cl 104 %, S04 61 %.

This ionic regulation is the resultant of the following processes: active absorption by the gills of sodium, potassium, calcium and chloride at a rate greater than that at which they are lost by diffusion; differential excretion by the antennary gland-, which tends to conserve potassium and eliminate magnesium and sulphate; inward diffusion across the gills of magnesium and sulphate in accordance with the concentration gradient.

In normal conditions there is active absorption of water. In dilute media, when osmoregulation begins, this is suspended, and possibly there is a fall in the passive permeability of the gills to water. In other respects osmoregulation is brought about by an intensification of the processes responsible for ionic regulation.

The permeability of the cuticle under physiological conditions is such that it does not affect the salt and water exchange of the animal, which is controlled by the branchial epithelium.

The structure of the gills of four species of Decapoda is described and correlatod with their powers of osmotic and ionic regulation.

The anatomy of ineffective nodules and its influence on nitrogen fixation. By H. K. CHEN and H. G. THORNTON. (Communicated by Sir John Russell, F.R.S.-Received 4 April 1940.)

The anatomy and cytology of nodules produced on clover, peas and soy beans by "effective" and "ineffective" strains of Rhizobia were investigated, with especial reference to the changes in volume of the active infected tissue during the life of the nodule. In clover the mean volume of this active bacterial tissue is about three times as great in "effective" as in "ineffective" nodules. This is due to an early arrest of growth in nodtules produced by ineffective strains. In all nodules the active bacterial tissue eventually disintegrates, but in effective clover nodules it remains without disintegration for about six times as long as in ineffective nodules.

In an experiment to test the nitrogen fixation by clover inoculated with an effective and an ineffective strain, the differenice between the strains in the amounts of nitrogen fixed could be accounted for by the differences in volume and in duration of the active bacterial tissue. In peas, nodules produced by an effective strain were nearly twice the length as those produced by an ineffectivo strain and their bacterial tissue remained without disintegration for about twice as long. In soy beans the mean volume of bacterial tissue was 4-75 times as great in effective as in ineffective nodules and the percentage of that volume composed of infected cells was twice as great. In ineffective soy bean nodules disintegration of the bacterial tissue began when the plant was four weeks old and was practically complete by the twelfth week, at which time no disintegration could be found in effective nodules. The difference in amount of nitrogen fixed by soy-bean plants bearing each type of nodule could be accounted for wholly by the factors mentioned above.

Thus in both clover and soy-bean nodules the volume and duration of the active infected tissue are the main, if not thc only, factors determining differences in nitrogen fixation, amongst the strains teste(d.

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Abstracts of Papers S 33

The soft X-ray spectroscopy of solids. II. Emission-spectra from simple chemical compounds. By H. M. O'BRYAN and H. W. B. SKINNER. (Com- municated by A. M. Tyndall, F.R.S.-Received 9 April 1940.)

K- and L-emission bands emitted in the soft X-ray region of the spectrum by atoms in a number of chemical compounds have been investigated. The substances for which such spectra are available through the present or previous Work are: fluorides, chlorides, bromides, iodides, oxides, sulphides, boron nitride and other boron compounds; and carbides. In the cases of SiC, BN and a number of oxides, spectra from both the component atoms forming the compound have been obtained.

The results are interpreted, as those for metals and element insulators have been in a previous paper, to give the characteristics of the bands of levels which exist for the valence-electrons in the normal state of the substance. In the case of the halides, data on the p- and s-levels of the negative ions are given, and it is shown that, even in this case, the crystal structure leaves its mark on the form of the bands of levels. The 2p bands of oxygen in the oxides are more spread-out on an energy scale, thus showing that the interaction between electrons in neighbouring atoms is considerable. The spectra of the metal ions in oxides are very complex, and an attempt is made to disentangle the factors which lead to this complication. In doing so, it is hoped that we may have thrown some light on the difficult subject of the structure of semi-polar compounds in solid form.

The strains produced by precipitation in alloys. By F. R. N. NABARRO. (Communicated by N. F. Mott, F.R.S.-Received 15 April 1940.)

If the process of diffusion in metals results simply in the interchange of pairs of atoms, large strains must be set up when a new phase precipitates in an alloy. The strain energy involved is calculated for particles of precipitate of various shapes, and is found to be least if the precipitate forms thin plates. The shape of the particle actually formed is influenced by this energy, by the degree of supersaturation of the solid solution, and by surface effects; the calculated shape is shown to agree reason- ably well with that observed experimentally.

The fine structure of phloem fibres in untreated and swollen jute. By B. C. KUNDU and R. D. PRESTON. (Communicated by V. IH. Blackman, F.R.S.--Received 16 April 1940.)

Studies of the optical properties of jute suggest that the wall is composed of chains of cellulose forming a single, fairly steep spiral. During growth the wall spiral becomes steeper up to the onset of wall thickening.

This fibre provides a study complementary to that of hemp. The outer layers have the least resistance to swelling and the phenomenon of "ballooning" is therefore never observed. For similar reasons transverse cracks never develop during swelling.

The results fully confirm the conclusion that swollen material cannot safely be used in determining wall structure.

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S 34 Abstracts of Papers

Plant pigments in the Galipagos Islands. By T. W. J. TAYLOR. (Com- municated by Sir Robert Robinson, F.R.S.-Received 18 April 1940.)

The Galapagos Islands were visited by the Lack-Venables Expedition during the winter 1938-39, and analyses were made of the anthocyanin pigments contained in the characteristic and largely endemic plants of Indefatigable Island. The methods used for anthocyanin identification under camp conditions are described. No new pigments were found, but a high proportion of the plants were found to contain nitrogenous anthocyanins. This provides powerful support for the views already put forward as to the distribuition of such pigments, although slight modification of these views is needed.

Isomorphous replacement and superlattice structures in the plagioclase felspars. By S. H. CHAO and W. H. TAYLOR. (Communicated by W. L. Bragg, F.R.S.-Received 19 April 1940.)

From X-ray oscillation-and rotation-photographs of a limited number of plagioclase felspars it seems probable that the structure-type depends upon the chemical composition in the following way. From pure soda felspar to at least 22 % lime felspar there extends an isomorphous series with the albite structure, based on a unit cell with linear dimensions 8 x 13 x 7A approximately and containing four molecules of NaAlSi3O8 or the equivalent when (CaAl) replaces (NaSi). There is probably a similar range of isomorphism, near pure lime felspar CaAl2Si2O8, with thc anorthite structure which has axes 8 x 13 x (2 x 7)A, but is of coourse very similar to the albite structure. The characteristic features of the photographs of the inter- mediate plagioclases can be explained, with the help of an optical model, in terms of a structure in which sheets with the albite structure and sheets with the anorthito structure alternate, but n4ore experimental data are needed for the complete elucida- tion of the problem.

The base-catalysed prototropy of substituted acetones. By R. P. BELL and 0. M. LIDWELL. (Communicated by C. N. Hlinshelwood, F.R.S.-Receivedl 23 April 1940.)

Kinetic measurements have been made at 250 on the catalysed halogenation of the following ketones: acetone, acetonylacetone, monochloroacetone, monobromo- acetone, as. dichloroacetone and acetylacetone.

In all cases the reactions are of zero order with respect to the halogen and exhibit general basic catalysis. For the first two ketones general acid catalysis is also detectable. For each ketone the catalytic constants kB of four carboxylate anions are related to the dissociation constants KA of the corresponding acids by an equation of the type kB =G(I/KA),, where G and a are constants for a given ketone. The catalytic constants measured cover a range of about 1OW.

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Abstracts of Papers S 35

Examination of tho results (together with thoso of Pederson for the bromination of acetoacetic ester and acetoacetic acid) shows that the exponent ac decreases steadily from 0-88 to 0-48 as the reactivity of the ketone increases.

The catalytic coefficients of the water molecule are given approximately by tho e(uations valid for the carboxylate anions, but the hydroxyl ion is in each ca-so a much less efficient catalyst than these equations predict.

A thermodynamical theory of the tensile strength of isotropic bodies. By F. FURTH. (Communicated by M. Born, F.R.S.-Received 24 April 1940.)

By thermodynamic considerations a new formula connecting the tensile strength of an isotropic body with its melting energy and Poisson's elastic constant is developed and found in good agreement with experiments.

General bi-harmonic analysis for a plate containing circular holes. By A. E. GREEN. (Communicated by G. I. Taylor, F.R.S.-Received 24 April 1940.)

A general solution is given for problems of generalized plane stress distributions in an infinite plate which contains circular holes of varying sizes in any positions, subject only to certain conditions of convergence of the solution. The method for extending the results to allow for the effect of one or two straight boundaries is indicated.

As a particular case of the general solution the problem of the stress distribution in an infinite plate under tension containing three holes in a row is discussed, and a few numerical results are given. These results are compared with experiments which were carried out by Mr P. L. Capper. The comparison is incomplete as the experi- ments were done for a finite plate and the influence of the edges of the plate on the numerical values of the stresses is considerable. Agreement, however, is found for the general character of some of the stresses.

Smoking and tobacco pipes in New Guinea. By A. C. HAIDDON, F.R.S. (Received 25 April 1940.)

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8 36 Abstracts of Papers

The combustion of aromatic and alicyclic hydrocarbons. V. The products of combustion of benzene and its monoalkyl derivatives. By J. H. BUR- GOYNE. (Communicated by A. C. C. Egerton, Sec.R.S.-Received 25April 1940.)

The progressive formation of products in the combustion of benzene and its monoalkyl derivatives has been studied by analytical methods, and the characteristic features of the isothermal reactions at various temperatures have been established.

A cool-flame reaction of n-propylbenzene has also been investigated, and by comparison with corresponding isothormal combtistions, it is concluded that the propagation of cool-flames is conditioned by the accumulation of a phenylalkyl hydroperoxide.

The results are interpreted in the light of the theory of the two-stage process, and a schematic mechanism for the main combtustion reaction is outlined. This comprises degradation of the side-chain (if present) andl rupture of the benzene nucleus, followed by rapid degradation of the higher aliphatic aldehyde thtus formed, yielding finally formaldehyde and the ultimate combustion products C02, CO and

H20.

The mechanism of the semicircular canal. A study of the responses of single-fibre preparations to angular accelerations and to rotation at con- stant speed. By 0. L6WENSTEIN and A. SAND. (Communicated by S. W Kemp, F.R.S.-Received 3 May 1940.)

Single-fibre discharges havo been recorded from the horizontal ampulla of the isolated labyrinth of Raja. Responses to different speeds of angular acceleration and to rotation at constant angular velocity are described. The existence of a spontaneous rhythm of discharge which is increased by ipselateial, and inhibited by contralateral rotation is confirmed.

During uniform angtular acceleration the freqtuency of impulses increases or de- creases gradually in a linear manner, and the rate of irncrease or decrease is propor- tional to the speed of acceleration. The threshold speed of acceleration is in the region of 30 per sec.2. During prolonged rotation at constant speed the frequency of discharge, having attained a maximum or minimum co-incidentally with the initial acceleration, gradually returns to the spontaneous value over a period of about 20-30 sec. These results are interpreted in terms of the physical properties of the cupula as described by Steinhausen.

The spontaneous discharge, and its excitation and inhibition by ipsilateral and contralateral rotation provide a basis for the interpretation of labyrinthine tone, and of the reflex responses to rotation in both directions of unilaterally operated animals. The sensory activity of the semicircular canal, interpreted in terms of the physical properties of the cupula, provides a framework which is adequate to account for the time relations of nystagmus and after-nystagmus.

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