Abstracts of Papers Communicated to the Royal Society of London

Abstracts of Papers Communicated to the Royal Society of LondonSource: Proceedings of the Royal Society of London. Series A, Mathematical and PhysicalSciences, Vol. 168, No. 935 (Nov. 25, 1938), pp. S133-S140Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/97260 .

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ABSTRACTS

OF PAPERS COMMUNICATED 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 publication 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".

25 NovEMBBER 1938

Summary of paper on two problems of extensional vibrations due to shocks. By W. T. HOWELL. (Communicated by Sir Robert Pickard, F.R.S. -Received 10 October 1938.)

Heaviside's operational calculus is employed in the treatment of two problems of technical interest whose solutions do not appear to have been published hitherto, viz. (1) a massive paricle is attached to one end of a massive elastic rod, the other end of which is suddenly constrained to move with a constant speed; (2) a massive particle at rest is suddenly attached to one end of a moving massive elastic rod, the other end of which is constrained to move at a constant speed. The conciseness of the method compared with that of the " equation promotrice" of Saint-Venant employed for allied problems is made manifest. Formulae for the velocity of the particle and the extension of the rod at any time are given in each case, and numerical examples illustrated with graphs are worked out for different values of the ratio of the mass of the rod to that of the particle. In particular, it is shown in both cases that the particle may attain a maximum speed considerably greater than that of the other end of the rod.

Summary of paper on diffusion in absorbing media. By P. S. H. HEN1RY. (Communicated by Sir Robert Picka/rd, F.R.S.-Received 10 October 1938.)

When one substance (e.g. water vapour) diffuses through another (e.g. air) in the pores of a solid body, and is at the same time absorbed by the solid, heat will be evolved. This heat will itself diffuse through the body, and will affect the extent to which the solid can absorb the vapour. There are thus two diffusion processes symmetrically coupled by the mutual interaction of the diffusants. The definition

Abstracts [S 133 ]17



S 134 Abstracts of Papers

of diffusion constants in absorbing media is discussed, and consequences of the coupling are worked out subject to certain simplifying assumptions. The general solution is shown to be a linear combination of solutions to the ordinary diffusion equation with the same boundary and initial conditions but different diffusion constants. An analogy with the case of two coupled oscillatory systems is demonstrated. A solution of the ordinary equation for diffusion into a rectangular parallelepiped is given, which is suitable for numerical calculation, and is believed to be new. A table of numerical data for diffusion into a plane sheet is given, from which values for a parallelepiped can quickly be deduced. A numerical example of coupled diffusion is worked out for the diffusion of water vapour into cotton packed at different densities.

The general theory of relaxation methods applied to linear systems. By G. TEMPLE. (Communicated by S. Chapman, FR.S.-Received I 1 October 1938.)

During the last few years Southwell and his fellow-workers have developed a new method for the numerical solution of a very general type of problem in mathematical physics and engineering. The method was originally devised for the deter- mination of stresses in frameworks, but it has proved to be directly applicable to any problem which is reducible to the solution of a system of non-homogeneous, linear, simultaneous algebraic equations in a finite number of unknown variables. South- well's "relaxation method" is one of successive approximation and, in order to complete the previous investigations of this method, it is necessary to prove that the successive approximations do actually converge towards the exact solutions: this proof is given.

Southwell's relaxation methods are not directly applicable to continuous systems, where the number of unknown variables is infinite, but it is shown here that simple extensions and modifications of the relaxation method render it suitable for applica- tion to either discrete or continuous systems.

The general theory of relaxation methods is then developed in terms of the theory of linear operators and sufficient conditions are prescribed for the convergence of the process of approximation.

These general methods are then applied to the solution of non-hiomogeneous linear integral equations and to the solution of non-homogeneous, linear differential equations.

Broadly speaking, it appears that almost all linear systems of equations, algebrai6, integral or differential, can be brought within the scope of relaxation methods, which seem to constitute one of the most powerful methods of computation in mathematical physics and engineering.

The magnetic properties of bismuth. III. Further measurements on the de Haas van Alphen effect. By D. SCHOENBERG. (ComMunicated by P. Kapitza, F.R.S.-Received 11 October 1938.)

The investigation of the field dependence of the susceptibility of bismuth (de Haas-van Alphen effect) has been extended down to lower fields (1500 gauss) at helium and hydrogen temperatures, by measuring the couple on a bismuth crystal



Abstracts of Papers S 135

in uniform magnetic fields. The results are compared with Landau's theory, with which they are in good qualitative agreement.

Detailed examination shows, however, that there are discrepancies as regards (a) the phase of the periodic variation, (b) as regards the details of the envelope curve of the periodic variation and the dependence of its amplitude on the crystal orienta- tion, 'and (c) the temperature variation of the effect, which was not as rapid as predicted by the theory. From the comparison, we obtained the following estimates of the fundamental parameters of the electronic structure; for the "effective" electronic masses,

m2= 1-2 mo, m1/m2=0-01 M3/m2=0-02, and M4/M2=-0O10

(ino is the ordinary electronic mass) and for the degeneracy temperature: Eok= 1400 K. From these data the number of electrons responsible for the effect is deduced as 1-7 x 10-6 per atom. These results are compared with Blackman's estimates, with which they are in agreement as regards order of magnitude, and their bearing on the previous experimental results is also discussed.

The photodynamic activity of the urine of mice treated with blastogenic hydrocarbons. By J. C. MOTTRAM. (Communicated by J. W. Cook, F.R.S. -Received 15 October 1938.)

Several polycyclic hydrocarbons- have been observed to photosensitize the skin of mice, and colloidal suspensions of them to photosensitize protozoa.

This action on protozoa provides a means of detecting them in very high dilution. Using paramoecium, the urine of mice painted with 3: 4-benzpyrene has been examined and found to be photodynamic 1 and 2 days after painting, but not on the third day. On the other hand the urine of inoculated mice continues to be photodynamic for at least a month.

When mice are inoculated with a series of polycyclic hydrocarbons some of which are blastogenic and others inactive in this respect, the urine was fountd to be photodynamic only in the case of the blastogenic hydrocarbons. It appears therefore that mice are able to convert the blastogenic hydrocarbons into water-soluble photodynamic derivatives which are excreted in the urine, but are not able so to convert the non-blastogenic hydrocarbons.

The spectrum of mono-deutero methane in the photographic infra-red. By W. H. J. CHILDS and H. A. JARN. (Communicated by Sir William Bragg, F.R.S.-Received 17 October 1938.)

The preparation of 40litres of mono-deutero methane is described. With it the absorption spectrum in the photographic infra-red has been investigated, and measurements are given of a particularly simple band at 9021 cm.-'. From this band the moment of inertia of the molecule about an axis perpendicular to the




C-D axis can be deduced, and a value of 7-202 x 10-40 g.cm.2 is obtained. This corresponds (assuming a regular tetrahedral structure) to a C-H distance of 1I093 A, to be compared with 1-092 A in the case of CH4. The band is assigned tentatively as the parallel component of 3v2, the second overtone of the perpendicular fundamental at 3031 cm.-'.

Electron transfer in mercury vapour. By F. L. ARNOT and MARJORIE B. M'EWEN. (Communicated by H. S. Allen, F.R.S.-Received 17 October 1938.)

An investigation of the electron transfer process

Hg2++Hg -*Hg++Hg+

has been made using incident Hg2+ ions having energies from 140 to 400 eV. The internal energy set free in the collision by the capture of the electron is 8-28 eV, of which it is found that about 6-3 eV are employed in exciting one of the resultant Hg+ ions, the balance of about 2 eV being shared as kinetic energy between the two Hg+ ions in accordance with the law of conservation of momentum.

The mechanics of the collision process show that the results obtained can be accounted for only by a head-on collision, one of the resulting Hg+ ions remaining stationary and the other carrying off the full kinetic energy of the incident Hg2+ ion plus the total amount of 2 eV internal energy available in the form of kinetic energy.

The cross-section for the process over the energy range of 140-400 eV has been obtained, and this shows an increase of cross-section with energy of the incident Hg2+ ion, the value at the middle of the energy range being of the order of one-tenth of the gas-kinetic cross-section for collision.

Refractive dispersion of organic compounds. X. Refractive indices of pulegone and of m-methylcyclohexanone. Optical exaltation in un- saturated ketones. By C. B. ALLSOPP and D. M. SIMPSON. (Communicated by R. 0. W. Norrish, F.R.S.-Received 17 October 1938.)

Refractive indices over a wide range of visible and ultra-violet wave-lengths, including those covered by a ketonic absorption band, are recorded for pulegone and for m-methylcyclohexanone. The refractivities of the carbonyl radical in each compound are deduced and compared with those previously recorded for C_O in cyclohexanone. An enhanced refractivity in pulegone, which could be described as an "optical exaltation" in view of the conjugation of carbonyl and ethylenic double bonds, can be attributed to the presence of an absorption band which does not appear in the.spectra of the other compounds; but equally abnormal values are obtained for m-methylcyclohexanone for which this explanation cannot be valid. It is con- cluded that these effects result fiom the invalidity of the additive relationship in the presence of the strongly chromophoric radicals, as predicted in a previous paper.




Fused neurons and synaptic contacts in the giant nerve fibres of cephalopods. By J. Z. YOUNG. (Communicated by E. S. Goodrich, F.R.S.-Received 20 October 1938.)

Study of the structure of the system of giant nerve fibres in the squid shows that complete mingling of the neuroplasm of two nerve cells does occur, contrary to the strict tenet of the neuron theory. Such fused neurons, however, always function together in the animal, impulses set up anywhere in them being conducted over the whole continuous neuroplasm. This case, therefore, is the exception to the neuron theory which proves' the rule. It shows that synapses, at which mingling of neuro- plasms does not occur, are necessary, as postulated by the theory, to prevent the indefinite spread of impulses.

Very clear synapses are present in the giant fibre system and are described in detail. The two first order giant nerve cells, which set off the whole system, are activated by numerous end feet scattered over their surfaces. Presumably these neurons only discharge a propagated impulse when a sufficient number (and perhaps a certain pattern) of the end feet are activated. In the stellate ganglion, however, a single impulse in the afferent member of the synapses produces a single impulse in the efferent and at these junctions there is provision for a very large surface of contact between the two fibres.

The significance of the giant nerve fibres in the life of the cephalopods is con- sidered, and the system is shown to one specialized for the production of movement rather than tonus. Contractions are initiated by the action of the minimum possible number of motor units, namely one pair of fused nerve cells. A single impulse set up in this unit can produce a quick twitch of the retractors and expulsion of a jet of water from the mantle. Such a system, though not well suited for the production of finely graded movements, allows the development of few, large and hence rapidly conducting fibres. The combination of speed with fine gradation of movement is only possible in animals, such as vertebrates, in which rapid conduction is obtained by thickness of the myelin sheath, rather than, as it is in the cephalopods, by great diameter of the fibres.

The absorption spectra of carbon dioxide and carbon oxysulphide in the vacuum ultra-violet. By W. C. PRIcE and D. M. SIMPSON. (Communicated by B. G. W. Norrish, F.R.S.-1Received 21 October 1938.)

The absorption spectra of CO2 and COS have been investigated in the vacuum ultra-violet. In the case of C02, the electronic series converging to the lowest 21H state of CO2+ have been identified and the ionization potential corresponding to this state has been established directly as 13-73 + 0 01 V. tThis is in excellent agreement with Mulliken's prediction of 13-72 + 003 V, which is based upon the identification of the 2900 A emission band as being 2Lu + 211, of CO2+, and upon the assumption that the photo-ionization at 685 A is to the 2L: state. Certain weaker bands not of a Rydberg type have also been found. They are attributed to transitions to anti- bonding molecular orbitals.




The spectrum of COS has been found to be intermediate between that of 002 and CS2. Certain differences are attributed to the lack of symmetry of this molecule. The corresponding electronic states of the three molecules are identified by the criterion of the rough agreement of their molecular term values.

Collective electron ferromagnetism. II. Energy and specific heat. By EDMUND C. STONER, F.R.S. (Received 24 October 1938.)

The treatment of collective electron ferromagnetism on the basis of Fermi-Dirac statistics, applied in a previous paper to magnetic characteristics, is extended to energetic characteristics. General expressions are developed for the electronic energy, which may be analysed into a quasi-magnetic and a distributional part. The forms taken by these expressions in the classical and Fermi-Dirac limits are obtained, and general expressions are derived for the specific heat at low temperatures and at the Curie point.

Detailed computations are made of the energy and specific heat over the whole temperature range corresponding to the critical value of the interaction for complete saturation at absolute zero. Computations are also made, for a wide range of values of the effective interaction ratio, of the energy increase between absolute zero and the Curie point, and of the specific heat at low temperatures, and immediately below and immediately above the Curie point.

A brief survey of the specific heat results for nickel indicates that the theoretical treatment provides a satisfactory basis for the analysis and interpretation of experimental results for particular ferromagnetics.

Statistical theory of the adsorption of double molecules. By T. S. CHANG.

(Communicated by R. H. Fowler, F.R.S.-Received 24 October 1938.)

The adsorption of double molecules upon a solid surface with sites of accommodation regularly arranged is studied statistically allowing interactions between adsorbed molecules, by using Bethe's approximation. Kinetic considerations leading to similar formulas are also given.

The isotherms, when compared with those for adsorption of single atoms, seem to be bent towards the axis 0 = 0. When the forces between the adsorbed molecules are attractive, there is also a critical temperature T,, below which the fraction of adsorption 0 may change discontinuously when the pressure is increased. The critical temperature is higher than that for the adsorption of single atoms, if the interaction energy between two atoms belonging to two different adsorbed molecules is the same as that between two adsorbed atoms for the latter case.

It has been found possible by studying the particular case of no interaction, to get roughly the number of ways of arranging -NO double molecules on N sites. The result agrees fairly well with the exact value given by Fowler and Rushbrooke, who




studied the number of arrangements at 0- 0, and l9 1, and further it is found to be the same as the exact value for all 0, for the case in which the N sites are on a line. It is applied when we use Bragg and Williams' approximation in studying the same problem, and gives results similar to those given by Bethe's approximation.

Concerning the scattering of fast electrons and of cosmic-ray particles. By E. J. WILLIAMS. (Communicated by J. Chadwick, F.R.S.-Received 25 October 1938.)

The relativistic theory of nuclear scattering through small angles is discussed, and corrections are applied for the effects of the finite size of the nucleus and the shielding of the nucleus by the atomic electrons. This is preliminary to calculations on the multiple scattering of fast electrons by thin metal foils and of cosmic-ray particles by metal plates. These calculations lead to an accurate estimate of the average theoretical deflexion under the conditions of the experiments, and thereby permit a quantitative interpretation of the observations to be made.

The experimental results of Blackett and Wilson on the scattering of cosmic-ray particles are in good agreement with the theoretical values, especially if the effect of the finite size of the nucleus is allowed for. (The evidence which this agreement provides for the existence of Yukons is discussed.) There is no positive evidence in the experiments for a short-range non-electrical force between the cosmic-ray particles and the nuclear particles of the matter traversed, similar to that between slow neutrons and protons. It is also inferred that the particles whose scattering was observed produced no nuclear disintegrations in the scattering plates, and that the observed anomalous loss of energy by cosmic-ray particles with energy around 109 V is likely to be due to the production of Yukons.

The scattering of fast electrons ( 10 mV) by thin lead foils as recently observed by Fowler and Oppenheimer is much less than the present theoretical values. This discrepancy seems to fall in line with observations by Klarman and Bothe and by Champion on the single scattering in heavy gases of electrons with energy of the order of 1 mV. The scattering of million-volt electrons by a thin aluminium foil recently observed by Slawsky and Crane is in good agreement with the present calculations, so that the above discrepancy if real must be associated with a high atomic number. There is as yet no indication of how the discrepancy could be accounted for theoreti- cally.

Reproduction in the spotted hyaena Crocuta crocuta (Erxleben). By L. H. MATTHEWS. (Communicated by A. S. Parkes, F.R.S.-Received 26 October 1938.)

The external genitalia of the male and female Spotted Hyaena are strikingly similar. Over one hundred specimens of the animal were examined in Tanganyika Territory. The structure of the genitalia is described, and the changes taking place in them during the sexual cycle are recorded.



8 140 Abstracts of Papers

A reinvestigation of turacin, the copper porphyrin pigment of certain birds belonging to the Musophagidae. By C. RIMINGTON. (Communicated by Sir Henry, Dale, F.R.S.-Received 28 October 1938.)

Whilst investigating turacin, prepared from the wing feathers of Turacus corythaix, for possible traces of the III series isomer, it was found that the coproporphyrin obtained by decarboxylation of the uroporphyrin ester appeared to consist almost entirely of coproporphyrin III. A thorough examination has therefore been made of the pigment derived from eleven different species of the Musophagidae, which in- eluded at least one representative of every turacin-bearing genus, except Proturacus.

The turacin was extracted from the defatted feathers and converted into the corresponding uroporphyrin ester. No attempt was made to obtain a pure uroporphyrin ester at this stage. Since the isomeric coproporphyrins are more easily separated than are the uroporphyrins, the entire yield of crude uroporphyrin was decarboxylated in dilute acid under pressure and the resulting coproporphyrin fraction esterified. The coproporphyrin methyl ester so obtained was fractionated by a method which serves to separate the series I from the series III isomer. In every case crystalline coproporphyrin III methyl ester, with the correct double melting point, was obtained, but in no instance was I successful in isolating or detecting the presence of any coproporphyrin I methyl ester. These turacins would appear, therefore, to be, substantially, derivatives belonging to series III, to which the normal porphyrin pigments of animals and plants predominantly belong.

The diffusion of radon gas mixtures. By G. E. HARRISON and W. HIRST.

(Communicated by M. L. E. Oliphant, F.R.S.-Received 28 October 1938.)

Diffusion measurements have been made for gas mixtures containing radon mixed with hydrogen, helium, neon, argon and air. The results of these experiments in the cases of radon-hydrogen and radon-helium mixtures, together with the thermal diffusion experiments already made, suffice to determine the repulsive force between these two pairs of molecules.

It is shown that all previous measurements of the coefficient of diffusion of radioactive gas mixtures are subject to an error due to the adhesion of the emanation to the walls of the diffusion apparatus which always tends to reduce the experimental values obtained for the diffusion coefficient. An experimental study has been made of the means by which adhesion can be made of negligible account in diffusion experiments and an apparatus has been designed which eliminates this disturbing effect. The agreement between the final values obtained for the diffusion coefficient of radon gas mixtures is as good as that between the values recently obtained for the coefficient of diffusion of non-radioactive gas mixtures.

The repulsive force between radon-hydrogen and radon-helium molecules is compared with that between hydrogen-nitrogen, hydrogen-carbon dioxide and helium- argon molecules. The radon molecule is shown to be very "soft"



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Abstracts of Papers Communicated to the Royal Society of London

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