bluuebunny/crossref_metadata_2025 huggingface dataset:
Quantum mechanics as a statistical theory
Authors: Moyal J. E.
Published: November 2008

An attempt is made to interpret quantum mechanics as a statistical theory, or more exactly as a form of non-deterministic statistical dynamics. The paper falls into three parts. In the first, the distribution functions of the complete set of dynamical variables specifying a mechanical system (phase-space distributions), which are fundamental in any form of statistical dynamics, are expressed in terms of the wave vectors of quantum theory. This is shown to be equivalent to specifying a theory of functions of non-commuting operators, and may hence be considered as an interpretation of quantum kinematics. In the second part, the laws governing the transformation with time of these phase-space distributions are derived from the equations of motion of quantum dynamics and found to be of the required form for a dynamical stochastic process. It is shown that these phase-space transformation equations can be used as an alternative to the Schrödinger equation in the solution of quantum mechanical problems, such as the evolution with time of wave packets, collision problems and the calculation of transition probabilities in perturbed systems; an approximation method is derived for this purpose. The third part, quantum statistics, deals with the phase-space distribution of members of large assemblies, with a view to applications of quantum mechanics to kinetic theories of matter. Finally, the limitations of the theory, its uniqueness and the possibilities of experimental verification are discussed.
On the theory of plane strain in finitely deformed compressible materials
Authors: Hill R.
Published: November 2008

In solid mechanics an outstanding lacuna is a general method for solving problems of plane strain for materials other than classically elastic, or visco-elastic, or rigid–plastic. Even with restriction to incrementally linear response, and to infinitesimal deformations superimposed on uniform pre-strains, there is no body of theory with the scope and power of the complex variable approach in isotropic elasticity. This lack has been highlighted recently by the growing interest in bifurcation phenomena in finitely deformed materials. So far, all analytical solutions to plane boundary-value problems with bifurcations (1,2,3,4) have relied on a separation-of-variables technique, which succeeds only for certain types of data.
Piecewise linear immersions
Authors: Smith Anthony
Published: November 2008

0. Introduction. An immersion f of one space X in another Y is a continuous map which is locally an embedding; that is, for any x ∈ X there is a neighbourhood N(x) of x such that f|N(x) is an embedding. Thus the image of an immersion may intersect itself, but it can contain no worse singularities. For example, the well-known model of the Klein Bottle is the image of an immersion into ordinary 3-space; the locus of points of self intersection is a circle, where two distinct circles in the Klein Bottle have their images. This paper obtains a sufficient condition for a map of PL manifolds to be deformable into a PL immersion.
Absolute summability factors of Fourier series
Authors: Sharma P. L. , Kori S. C.
Published: November 2008

1. Let f(t) be a perodic function with period 2π and integrable in the sense of Lebesgue over (–π, π), then its Fourier series is
On functionally constant invariants of the Riemann tensor
Authors: Buchdahl H. A.
Published: November 2008

In any V4 two quadratic invariants of the Riemann tensor, J4 and K4, say, are known which are functionally constant, i.e. the Hamiltonian derivatives of which vanish identically. Certain natural generalizations, J2n and K2n, of degree n of these are considered, J2n being defined in any Vm but K2n only in a V2n. It is shown by methods having purely local character that J2n is functionally constant in any V2n, and that K2n vanishes identically when n is odd or when n is even and the V2n is either conformally flat or admits a hypersurface-orthogonal Killing vector; whilst in a V4n it is functionally constant. These results follow upon a prior spinorial treatment of the special case n = 3 which leads to an explicit expression for a pseudo-vector density of which the scalar density 6 is the divergence. Finally, it is shown that for appropriate values of n there exist functionally constant invariants other than J2n and K2n
Singular numbers of smooth kernels. II
Authors: Oehring Charles
Published: November 2008

Reade[10] has recently improved Weyl's classical estimate λn = o(n−3/2) for the eigenvalues of a symmetric kernel K∈C1 by relaxing the Cl hypothesis to the assumptions that K∈L2[0, 2π]2, that K is absolutely continuous in each variable separately, and that both ∂K/∂s and ∂K/t belong to L2[0, 2π]2. The conclusion of his theorem, that is, of course, stronger than λn = o(n−3/2).
On the Decomposition of an Infinitesimal Group
Authors: Whitehead J. H. C.
Published: November 2008

1. This note contains a second proof of a remarkable theorem, announced by W. Killing and first proved by Eugenio-Elia Levi, according to which any infinitesimal group G, in the sense of Lie, contains a subgroup which is simply isomorphic to the factor group G/Γ, where Γ is the greatest integrable invariant subgroup in G§. Also the theorem is sharpened in that it is proved for groups depending on real as well as on complex parameters. In the final section it is seen that the methods used in proving this theorem can be applied to the problem of solving certain equations which are stated in terms of any semi-simple infinitesimal group of linear operators.
On the solutions of the Low equation
Authors: Lardner R. W.
Published: November 2008

An alternative procedure is developed for examining the solutions of the Low equation. The ambiguities of those solutions which have a finite number of zeros are shown to satisfy the conditions derived earlier by Castillejo, Dalitz and Dyson. The method presented here has the advantage that it makes no special use of the positiveness of the cut-off function, and so can be used when this function changes sign. It is shown that the arbitrariness of the solution increases with the number of these sign changes, but that a completely negative cut-off function still satisfies the CDD conditions.
Approximate integration of rapidly oscillating functions and of periodic functions
Authors: Hsu L. C.
Published: November 2008

The purpose of this paper is to establish a few approximation formulae with error estimates for the integration of rapidly oscillating functions, and to present an expression for the remainder term of an expansion formula obtained previously (see (3)). Moreover, we shall give a certain sharpest possible estimation for the error term involved in the numerical integration of periodic functions. Some results contained in earlier papers ((2), (4), (5)) will be employed and sharpened.
Scalar diffraction by prolate spheroids whose eccentricities are almost one
Authors: Goodrich R. F. , Kazarinoff N. D.
Published: November 2008

The pressure distribution on the surface of a long, thin prolate spheroid is found under the conditions:

(1) The spheroid is illuminated by a harmonic point source of wavelength λ located on the axis of the spheroid.

(2) If a and b are the semi-major and semi-minor axes of the spheroid, then

(3) The boundary conditions on the spheroid are either the Neumann or the Dirichlet conditions.

The distribution is found from the asymptotic solutions of the Helmholtz equation using the inequalities in (2). The distribution is interpreted on certain regions of the surface in terms of travelling waves.
A differential equation for undamped forced non-linear oscillations. II
Authors: Morris G. R.
Published: November 2008

In a previous paper of the same title (1) on

where e(t) is even and has least period 2π, I have shown that the equation has a family of periodic solutions or, equivalently, that a topological transformation T has a family of fixed points. Since much of the detail in (1) is irrelevant here, it will be convenient if the results we must quote about are put into the following form:

Theoerm A. There is a constant integer p such that, whenever k ≥ p, there is at least one solution xk(t) of (1·1) for which

(i) xk(0) > 0, ẋk(0) = 0 and xk(t) has period 2π;

(ii) xk(t) = xk(2π–t);

(iii) xk(t) has, in 0 ≤ t < 2π, k positive maxima, k negative minima and no other stationary points;

(iv)

This except (ii), is a special case of Theorem 2 with the notation x*(t|k, 1, 0) simplified to xk(t) and the constant p introduced to guarantee that (vi) of Theorem 2 implies (iv) above. Finally Lemma 1 of (1), in its original form or as specialized in Theorem B (i) below, gives (ii).

We shall write ak = xk(0) and note, though we do not need to use it here, that, by (v) of Theorem 2, ak = kw + O(k−2) as k→ ∞. If Fk denotes the point (ak, 0) of the (a, b)-plane then Fk is a fixed point of T and we can best state this paper's results in terms of the segment joining a pair of such points.
Note on the heating effect of the γ-Rays from RaB and RaC
Authors: Ellis C. D. , Wooster W. A.
Published: November 2008

Now that the wave-lengths of the main γ-rays of radium B and C are known it has become a matter of some importance to determine their total energy, because from such measurements it is possible to deduce the average number of quanta emitted by each disintegrating atom. If in addition the relative intensities of the different γ-rays could be determined it would be possible to give a complete description of the γ-ray emission.
A ‘Waring's problem’ for homogeneous forms
Authors: Ellison W. J.
Published: November 2008

Professor H. Davenport has raised the following question. Let f(X) be a homogeneous form in n variables X, of degree k, with coefficients in a field K. Is it possible to write f(X) in the form

where the Li(X) are linear forms over K and N depends only on K, n, and k? In particular, what can be said when K = R, the reals; K = Q, the rationals; K = C, the complex numbers ?

We shall show that when k is odd such a representation is always possible and we shall obtain an explicit bound for N. However, if k is even, no such result is possible when K = R or Q, even when we impose the obvious necessary condition that f(X) be positive semi-definite. In fact we shall exhibit a construction for obtaining forms f(X) which are positive definite but cannot be expressed in the form

r even, where φi(X) is a homogeneous form of degree s and sr = k. We shall determine precisely which definite forms can be expressed in the required form. Some natural generalizations of the problem are then considered.
On limiting cases in the flexure of simply supported regular polygonal plates
Authors: Rajaiah K. , Rao Akella Kameswara
Published: November 2008

Limiting solutions are derived for the flexure of simply supported many-sided regular polygons, as the number of sides is increased indefinitely. It is shown that these solutions are different from those for simply supported circular plates. For axisymmetric loading, circular plate solutions overestimate the deflexions and the moments by significant factors.
Approximate solutions of the general relativity field equations with a scalar meson field
Authors: Hyde J.
Published: November 2008

It was shown by Birkhoff ((1), p. 253) that every spherically symmetric solution of the field equations of general relativity for empty space,

may be reduced, by suitable coordinate transformations, to the static Schwarzschild form:

where m is a constant. This result is known as Birkhoff's theorem and excludes the possibility of spherically symmetric gravitational radiation. Different proofs of the theorem have been given by Eiesland(2), Tolman(3), and Bonnor ((4), p. 167).
Preliminary Note on the Masses of the Electron, the Proton, and the Universe
Authors: Eddington A. S.
Published: November 2008

In an investigation which I hope to publish shortly, I think I have been able to improve my theory of the constanthc/2πe2and to bring it at last into a precise form. No alteration is made in the value 137 obtained in the work already published. The recent advance has been mainly due to the fresh light thrown on the foundations of wave-mechanics by Dr Dirac's book. With a fuller understanding of the “theory of 137” it has been possible to discern opportunities for extension in several directions, and it is with these developments that the present paper deals. They are still in a rudimentary state; but since the theory appears to give correctly either accurate or approximate values of the masses of the electron, the helium atom, and the cosmos in terms of the mass of the proton, it would seem to be on the right lines. Moreover the principle of “ignoration of degrees of freedom” on which the numerical predictions depend is strongly suggested by the theory of the constant 137. If my view is right the only arbitrary constant of nature is the number of particles in the universe—if the numberisarbitrary.
The packing of certain sets of cubes
Authors: Steen S. W. P.
Published: November 2008

Let (X1, …, Xn) be the coordinates of the centre of a unit cube C, in n-dimensional space, whose (n − 1)-dimensional faces are parallel to the axes of coordinates. Further let the X's be integers. Let εi = ± 1 for r (≤ n) values of i, 1 ≤ i ≤ n, and let εi = 0 for the remaining n − r values of i. Then (X1 + ε1, …, Xn + εn) gives the centre of a cube C′, which touches the cube C along an (n − r)-dimensional edge or face. The cube C and the cubes C′, for all possible arrangements of the ε's, which are subject to the above conditions, form a symmetrical arrangement of cubes. This paper discusses the possibility of completely filling space by means of the packing together of such sets of cubes.
On the Rotation of Dielectrics in Electrostatic Fields and Related Phenomena
Authors: Vedy L. G.
Published: November 2008

The rotation of a dielectric covered body, suspended between the poles of a Wimshurst machine, is investigated and found to be due to the accumulation of charge on the surface of the body, under the action of the brush discharge, and to the subsequent electrostatic repulsion of this charge. It is shown theoretically, in an appendix, that the rate of rotation is governed by the rate of decay of the surface charge, and is a maximum for a certain value of this rate of decay. The rotation of a chain hanging from an electrical machine into the dielectric layer of a Leyden jar (the inner conducting coating being removed) and similar electrostatic experiments are described, and shown to be due also to the superficial charging of a dielectric body, body, and depends upon the rate of decay of this surface charge. A similar explanation is shown to account for some other electrostatic phenomena.
The Action of the Electrical Counter
Authors: Emeléus K. G.
Published: November 2008

Some previous work on the theory of the electrical counter is extended by a detailed consideration of the ionic process involved. It is shown that with a positive point the total number of ions produced should be proportional to the initial ionisation. Evidence is adduced to show that with a negative point extinction of the discharge is probably brought about by a local increase of pressure, accompanied by an electrical wind along the sides of the point. The latter would bring about the discharge of a definite quantity of electricity, independent of the initial ionisation, provided the initial pressure was not too low. It is shown that these considerations account for a number of other phenomena connected with discharges from small electrodes, and that the quantities involved are of the right order of magnitude.

The experimental work in connection with this paper has been carried out in the Cavendish Laboratory. The author desires to thank Professor Sir E. Rutherford for his continual interest in its progress, and further to thank Professor Appleton, and Dr Chadwick for much helpful discussion of several of the points involved.
The theory of the influence of magnetic fields on the stopping power of gases for α-particles
Authors: Kronig R. de L.
Published: November 2008

The purpose of this note is to calculate, on the basis of the assumptions which underlie the theory of the stopping of α-particles by matter, the influence of space quantization on this phenomenon. The results arrived at may be capable of an experimental test and will serve to illuminate these assumptions and to indicate their limitations.
A series of rational loci with one apparent double point
Authors: Babbage D. W.
Published: November 2008

1. A locus Vn, of dimension n, in [2n + 1], for example a curve in [3] or a surface in [5], has ∞ 2n chords, of which a finite number pass through a general point of the space.
Recombination of Ions in the Normal Arc
Authors: Bramhall E. H.
Published: November 2008

The rate of recombination of ions in the copper arc is studied by means of the probe, the post-arc ion density being obtained directly as a function of time. Experimental results agreeing with the theory are obtained, and a coefficient of recombination, α = 5·7 × 10−9, is found. If the temperature of the gas in the path of the arc immediately after extinction is 2500°C., a comparison between the above value and that accepted for normal conditions shows that α varies approximately as the 2·5 power of the temperature, which is in agreement with the existing data.
Concerning the success of the absorption method of investigating the high velocity limits of continuous β ray spectra
Authors: Feather N.
Published: November 2008

Experience has shown that simple absorption measurements lead to quite trustworthy estimates of the maximum energies represented in the continuous spectra of many β ray bodies. For the interpretation of these experiments the range-energy relation for homogeneous particles is apparently all that is necessary. In the present paper a detailed analysis is given of the various factors which conspire to this useful result. Analytical simplifications are possible when the energy distribution in question extends beyond about 7 × 105electron volts energy. Under this limitation it is shown that the empirical result follows from the known form of the absorption curve for homogeneous particles and the most general considerations regarding the characteristics of such measuring instruments as are regularly employed. From the analysis in one case, however, it appears that, despite numerical agreement between the results of different methods of investigation, caution is still necessary in any statement concerning the absolute nature of the high energy limits of continuous β ray spectra.
Wave Functions of Many-Electron Atoms
Authors: Lennard-Jones J. E.
Published: November 2008

1. The wave function of an atom containing many electrons has not yet been solved completely, even that of helium being as yet unknown. In the absence of a direct solution of the Schrödinger equation for the electrons in an atom, various attempts have been made to devise approximate methods of solution in particular cases. The particular case of helium, being the easiest, has received considerable attention and a number of approximate wave functions appropriate to the normal state have been constructed. These functions usually contain empirical constants which are adjusted to make the energy of the system a minimum. Zener has attempted the more ambitious programme of finding the wave functions of all the atoms in the first period of the Periodic Table (Lithium to Neon), and has made interesting discoveries as to the way in which the wave functions differ from atom to atom. This work also is based on the variation of parameters.
On the Riemann zeta-function
Authors: Titchmarsh E. C.
Published: November 2008

It was proved by Littlewood that, for every large positive T, ζ (s) has a zero β + iγ satisfying

where A is an absolute constant.
The general surfaces in four dimensions with one or two apparent triple points
Authors: Archbold J. W.
Published: November 2008

1. Let F be an irreducible surface in [4] with apparent triple points, t in number; let P be an arbitrary point in the space and p1,…,pt the trisecant lines which can be drawn through P. Then, if F lies on at least ∞1 cubic primals, any one of these which passes through P will contain p1,…,pt in consequence and the linear system will be compounded of the congruence of trisecant lines of F. By a well-known theorem it follows that the grade of the system is zero. The free surface of intersection Φ of two cubic primals will be ruled, having t generators, each a trisecant of F, passing through every point on it.
On the non-linear difference equation Δxn = kΦ (xn)
Authors: Haldane J. B. S.
Published: November 2008

1. Among the equations arising in the theory of natural selection is the finite difference equation

where k is a constant which may have any value between 1 and − ∞ inclusive, but is often small. Its solution is discussed in the accompanying paper(1). It is a particular case of the equation

where Φ(x) is a known one-valued function of x. When k is small this may obviously be solved approximately by treating it as a differential equation

whence
The effect of the orbital velocity of the electrons in heavy atoms on their stopping of α-particles
Authors: Thomas L. H.
Published: November 2008

Henderson proposed a theory of the stopping of swift α-particles by matter. He treated the electrons in the atoms as free and at rest and ignored all collisions of the α-particle with them except those in which the electron would on that assumption gain sufficient energy to leave the atom. Fowler has shown that Henderson's theory gives stopping-powers only of about 60% of those observed. Fowler also made a calculation of the stopping-power of hydrogen by combining the effects of close collisions treating the electron as free and slight collisions as perturbations of the electron's motion in a circular orbit. He obtained much better agreement. This method is, of course, the natural extension of Bohr's original theory to that model.
Asymptotic expansions of the expressions for the partition function and the rotational specific heat of a rigid polyatomic molecule for high temperatures
Authors: Viney Irene E.
Published: November 2008

The partition function F(θ) is of fundamental importance in the theory of the specific heat of gases. Once it is known, the rotational specific heat of a perfect gas is given by

where R is the gram-molecular gas constant, and θ bears the relation

to the absolute temperature T, k being Boltzmann's constant.
The equilibrium of atoms and ions adsorbed on a metal surface
Authors: Evans R. C.
Published: November 2008

The theory of the evaporation of adsorbed atoms and ions of the alkali metals from a hot metal surface has been developed from somewhat different viewpoints by Langmuir and Kingdon and by Becker. These two treatments, which yield essentially the same results, are applicable only when equilibrium conditions obtain on the surface, so that the surface concentration is not changing. It is the purpose of the present note to extend Becker's treatment to take account of the rate of attainment of equilibrium on the surface, in order to lead to an interpretation of some experiments on the rate of evaporation of the alkali metals adsorbed on hot tungsten.
The Compton Effect in Wave Mechanics
Authors: Dirac P. A. M.
Published: November 2008

The problem of the scattering of radiation by a free electron has been treated by the author on the basis of Heisenberg's matrix mechanics, which was first modified to be in agreement with the principle of relativity. The main point of this modification is that, whereas in the non-relativity theory one deals with matrices whose elements vary with the time according to the law eiwt, in the relativity theory the elements of the matrices must vary according to the law eiwt′ where t′ = t − (l1x1 + l2x2 + l3x3)/c if they are to determine correctly the radiation emitted in the direction specified by the direction cosines (l1, l2, l3), x1x2 and x3 being the coordinates of the electron at the time t. These matrices were obtained by writing the Hamiltonian equation of the system in the form

where W′ is a variable canonically conjugate to t′ and H′ commutes with t′, and then using H′ as an ordinary Hamiltonian function of a dynamical, system that has W′ for its energy and t′ for its time variable.
The application of the method of the magnetic spectrum to the study of secondary electronic emission
Authors: Sharman C. F.
Published: November 2008

There are two ways of investigating the velocity distribution of an electronic emission—the retarding potential and the magnetic deflection methods. These have been applied to the case of the photo-electrons by Millikan and Ramsauer respectively. On one important point the results disagreed; Millikan found a definite maximum velocity, while Ramsauer obtained an asymptotic falling off of the number of electrons with increasing velocities. In a critical discussion of the two methods Klemperer has shown that they agree when photoelectric activity of the collecting electrode in the first, and when electronic reflection at the walls and slits in the second, are eliminated.
The Pure Archimedean Polytopes in Six and Seven Dimensions
Authors: Coxeter H. S. M.
Published: November 2008

An Archimedean solid (in three dimensions) may be defined as a polyhedron whose faces are regular polygons of two or more kinds and whose vertices are all surrounded in the same way. For example, the “great rhombicosidodecahedron” is bounded by squares, hexagons and decagons, one of each occurring at each vertex. Thus any Archimedean solid is determined by the faces which meet at one vertex, and therefore by the shape and size of the “vertex figure,” which may be defined as follows. Suppose, for simplicity, that the length of each edge of the solid is unity. The further extremities of all the edges which meet at a particular vertex lie on a sphere of unit radius, and also on the circumscribing sphere of the solid, and therefore on a circle. These points form a polygon, called the “vertex figure,” whose sides correspond to the faces at a vertex and are of length 2 cos π/n for an n-gonal face. Thus the vertex figure of the great rhombicosi-dodecahedron is a scalene triangle of sides .
The ionisation curve of an average α particle
Authors: Feather N. , Nimmo R. R.
Published: November 2008

Photographs have been taken under controlled illumination of the tracks of α particles in a cloud expansion chamber and a calibration of the photographic plates employed has been carried out. Systematic photometry of the track images has made possible the calculation of the variation of the light scattering power of an α particle track over the last two centimetres of its length in standard air, and the variation of this quantity has been identified with the variation of ionisation along the track.

Photographs of tracks in air, helium and hydrogen have been examined. In these three gases the maximum ionising efficiency of the α particle occurs when it possesses the velocity respectively appropriate to the distances 3·0, 2·55 and 2·25 mms. from the end of its path in standard air. This common velocity parameter has been employed throughout the discussions which are appended to the experimental results.
The Interference of Light in a Wedge
Authors: Arnot F. L. , Rutherford E.
Published: November 2008

Briefly summing up we see that when a point source is employed the slit of the spectroscope is illuminated by light coming from one point only in the wedge, and consequently clear distinct bands will be obtained in the spectrum irrespective of which end of the wedge is towards the source, and irrespective of the angle of incidence or of the distance between the wedge and spectroscope.

With a large source, however, the slit of the spectroscope receives rays coming from many different points in the wedge. The path difference between the interfering components of each of these rays is in general different. Therefore each ray will produce a complete set of interference bands in the spectrum. These sets of bands are relatively displaced, the superposition of all causing uniform illumination.

It has been shown, however, that there is one special case in which the path difference for the interfering components of all rays is the same. In this case, each ray still produces, a complete set of bands in the spectrum but these sets are no longer relatively displaced; bright bands are superimposed on bright bands and dark bands coincide with dark bands. There is thus both an increase of intensity and definition.

It has been shown that the conditions necessary for this special case are:

(1) The thick end of the wedge is towards the source.

(2) The slit of the spectroscope is placed at a distance of

from the wedge, the distance being measured along the central ray entering the slit of the spectroscope.

The case of an air wedge has been discussed, and a possible advantage to be gained in using such for spectroscopic purposes in place of parallel plates has been mentioned.
Over-tension in a Condenser Battery during a sudden discharge
Authors: Kapitza P.
Published: November 2008

In the recent experiments on the Zeeman effect in strong magnetic fields made by Mr H. W. B. Skinner and myself for obtaining an intense source of light for a small fraction of a second, we have been discharging a condenser battery consisting of 32 Leyden jars connected in parallel with a capacity of one-tenth of a microfarad. The discharge was made through a small spark gap by means of an oil immersed switch (the details of this arrangement are to be found in the above-mentioned paper). When the discharge was produced a curious phenomenon was sometimes observed. After the battery had been charged to its maximum tension, and the switch had been put into operation, only a small spark occurred in the spark gap, and the main part of the discharge went over the top of the insulators of one of the Leyden jars.
Metallic Complexes with the Aliphatic Poly-Amines
Authors: Mann F. G. , Pope William J.
Published: November 2008

The existence of complex compounds of metallic salts with ammonia was recognised in the early years of last century. Platinum in particular readily unites with ammonia, and the early chemists, when studying the general chemistry of ammonium platino-and platini-chlorides, soon discovered highly crystalline ammonia derivatives of platinum which contained an unusually high proportion of the metal. In the formulation of such compounds difficulties at once arose. Thus Peyrone in 1844 knew three distinct compounds of the composition PtCl2N2H6, a pale lemoncoloured compound known as the second chloride of Reiset, an orange-coloured compound discovered by Peyrone himself, and finally a dark green insoluble substance known as Magnus' green salt, discovered by the latter in 1828. The existence of these three compounds, now known as trans and cis dichloro-diaminoplatinum [Pt(NH3)2Cl2], and as tetramino-platinous platinochloride [Pt(NH3)4]PtCl4 respectively, could not be satisfactorily explained on current theories of salt formation. Similar compounds in which aliphatic and cyclic mono-amines replaced the ammonia groups were discovered later, but it was not until 1889 that Jörgensen introduced the use of the simplest stable aliphatic diamine, viz. ethylene diamine.
On the regularity of surfaces
Authors: Roth L.
Published: November 2008

The general theory of surfaces has been developed without much attention to the simpler aspects of the subject and, in particular, to the problem of determining some elementary criteria of regularity or referability; there is, in fact, only one well-known criterion of this kind, due to Castelnuovo and Enriques. (Theorem 2 of the present work.) It seems desirable, therefore, to establish some tests which require no more knowledge of a surface than its order, sectional genus and normal space. A number of such tests is given in the present paper. Before it was written the author had the advantage of consulting an unpublished manuscript by Professor Comessatti on the classification of surfaces in S4; in this work the regularity of surfaces of order eight is considered and, in part, those of order nine; the four-dimensional case of Theorem 11 and a particular case of Theorem 6 and Theorem 14 are given. Theorems 4 and 5 are also proved by Comessatti. For permission to publish these results and for the help derived from them the author's grateful thanks are due.
The action of β and γ rays on rock salt crystals
Authors: Burbidge P. W.
Published: November 2008

1. Many insulating crystals, such as rock salt, after exposure to high energy radiation, e.g. X-rays, β-rays, ultra-violet light or γ rays, acquire, as a result of this treatment, two new properties: (i) a new absorption band, usually situated in the visible spectrum, well separated from the continuous absorption in the far ultra-violet, and, when intense, giving visible coloration to the crystal in ordinary light; (ii) the power of showing what has been termed the inner photo-electric effect, i.e. when subjected to an electric field and then illuminated with light in the region of the new absorption band, the “activated” crystal gives an instantaneous response in the form of a small electronic conduction; in the dark or for light outside this band it is still non-conducting (Fig. 1).
An attempt to detect radiation in thunder clouds
Authors: Macky W. A.
Published: November 2008

An account is given of attempts to detect radiation in thunder clouds by means of photographic plates attached to balloons. Eleven balloons were sent up and the plates attached to ten were recovered and examined.

The result was negative in every case.

A small ionisation chamber with quartz condenser intended for detecting radiation in thunder clouds is described.

These observations were made at the Solar Physics Observatory, Cambridge, and I have to thank the Director for giving me every facility.

I am also greatly indebted to Professor C. T. R. Wilson for his continued advice and interest.
A hydrogen discharge tube for spectrographic work
Authors: Braddick H. J. J.
Published: November 2008

The hydrogen discharge has for some time been established as a convenient source of continuous spectrum in the ultra-violet. The continuum extends from nearly 4000 Å. to the limit of a quartz spectrograph and provides a very good background for absorption measurements. A number of tubes have been described for producing this spectrum, but the following advantages are claimed for the form here described.
The Cantor manifolds lying on a closed surface
Authors: Kaufmann Boris
Published: November 2008

In recent years Cantor manifolds have assumed great importance in topology. This is due chiefly to the work of Urysohn and to the later work of Alexandroff. Urysohn, in the paper in which he introduced the theory of dimensions, showed that a 2-dimensional closed surface is a 2-dimensional Cantor manifold. Alexandroff has not only extended this result to n dimensions but has also established the existence on the cutting set Z of the surface F of generalized cycles homologous to zero on the various parts of F − Z. These results show that the deepest structural characteristics of the closed surface come to light when one dissects it.
The disintegration of boron by α-particles
Authors: Miller H. , Duncanson W. E. , May A. N.
Published: November 2008

The protons emitted from boron, when it is bombarded by α-particles from radium C′ and polonium, have been examined. All have been ascribed to the disintegration of the B10 isotope following the capture of an α-particle. Four energy changes with values 3·1 m.v., 0·4 m.v., − 0·1 m.v., and − 1·0 m.v. are necessary to explain the range distribution observed. Experiments with α-particles from polonium also show that penetration through the top of the potential barrier stops at an energy of 3·6 m.v. and that below this there is a resonance level at about 2·9 m.v.
Some Theorems on Abelian Integrals Associated with an Algebraic Variety
Authors: Hodge W. V. D.
Published: November 2008

1. In some recent papers I have developed the theory of what I have called harmonic integrals associated with an algebraic variety. My object has been to provide an apparatus with which to investigate the properties of the classical integrals

of total differentials which are finite everywhere on an algebraic variety Vm of m dimensions

These integrals are referred to in what follows as “Abelian integrals”, as it is desirable to have a single name to denote all integrals of this type. The usual qualification “of the first kind” is omitted, and is always to be understood. In the present paper it is shown how the theory of harmonic integrals can be applied to deduce certain results concerning Abelian integrals, and a number of interesting problems are suggested by these results.
On a Class of Irregular Surfaces
Authors: Pedoe D.
Published: November 2008

1. Let P = 0, Q = 0, U = 0, V = 0 represent four independent quadric surfaces, and consider the equation
A Note on Creation and Annihilation in Statistical Assemblies
Authors: Sterne T. E.
Published: November 2008

The statistical method described in 21·4 of Fowler's Statistical Mechanics was devised to deal with assemblies in which the total numbers of elementary physical systems remained constant. The same method is applicable, with no formal changes, to assemblies in which elementary physical systems of two different sorts can be created and annihilated in pairs, like the negative and positive electrons in the theory of Dirac.
The Gliding of a Plate on a Stream of Finite Depth
Authors: Green A. E.
Published: November 2008

We have examined the two-dimensional gliding of a semi-infinite plate on the surface of a stream of finite depth. We have calculated the lift L in terms of the ratio D/H, where H is the depth of the stream at infinity up-stream, and D is the height of the trailing edge of the plate above the surface of the stream.

In particular we have found that the trailing edge cannot be at a height of more than 0·07H approximately, above the up-stream fluid surface.

In conclusion, the writer would like to thank Prof. G. I. Taylor, F.R.S., for suggesting this problem and for his continued interest in it.
A differential retarding potential method for the study of the energy distribution of slow electron emissions
Authors: Sharman C. F.
Published: November 2008

The method described gives the differential energy distribution curve directly from readings of a galvanometer and a voltmeter. When adjusted, the arrangement is convenient in operation and very good “resolution” can be obtained. The existence of a maximum frequency of secondary electrons at a finite small energy has been established, and its position is shown to be independent of the energy of the primary beam over a fairly wide range. The effect of deposition of tungsten on a clean copper surface is studied with respect to the secondary emission properties of the surface. From these experiments some interesting conclusions concerning the mechanism of the process may be drawn.

I am very grateful to Prof. Sir Ernest Rutherford for the encouragement he has given and the interest he has taken in this work.
Systems of Double Rows of Line Vortices in a Channel of Finite Breadth where the Axis of the Row is Parallel to the Axis of the Channel
Authors: Rosenhead L.
Published: November 2008

The stability and the stream lines of the symmetrical and unsymmetrical double rows in a channel have already been discussed by the author. It is the object of this paper to investigate the possibility of the existence of a double row whose axis is parallel to, and not necessarily coincident with, the axis of the channel. It will be seen that, if the system of vortices is to move forward as a whole, then the only possible types of double row are those that have been discussed previously, that is, the symmetrical and unsymmetrical systems, and in both of these cases the centre lines of the row and channel are coincident. It was shown previously that the symmetrical row is always unstable and that the unsymmetrical system is stable within a particular domain of stability.
An Optical Interference Method of Measuring Young's Modulus for Rods
Authors: Searle G. F. C.
Published: November 2008

The general arrangement of the apparatus is shown in Fig. 1. A vertical steel rod AA of circular cross-section is fixed to a heavy cast-iron base Z shown diagrammatically in the figure. The rod AA is bent by a load applied to the end of the horizontal bar BC carried by the upper end of A A. The point of application of the load is defined by a transverse groove cut in the bar. The rod AA passes through the two metal plates DD, FF, which are soldered to the rod, the faces of these plates being horizontal.
The β-Ray Spectrum of the Natural L-Radiation from Radium B
Authors: Black D. H.
Published: November 2008

It has been observed by various workers that, in addition to particles ejected from the various atomic levels of the atoms concerned, some are ejected by rays which correspond to the natural K X-radiation of those atoms. It has also been shown that some radioactive substances emit β particles of comparatively low energy. Therefore it was thought advisable to make an attempt to see whether this “soft” radiation has a line spectrum; for one would expect to find traces of the natural L-radiation, just as one finds evidence of the K-radiation, provided that the effect is sufficiently intense.
The Natural X-ray Spectrum of Radium B
Authors: Rutherford Ernest , Wooster W. A.
Published: November 2008

It is now well known that radium B is an isotope of lead of atomic number 82 with a mass 214, and consequently, if the atoms of radium B are bombarded by an external source of electrons, the spectrum excited in it should be identical with that of lead atomic number 82. A very interesting question arises with regard to the L radiation emitted by a source of radium B during its spontaneous transformation. At the moment of the expulsion of the disintegration electron from radium B, the internal atomic structure of radium B corresponds to an element of number 82, but an instant later, when the electron has escaped from the nucleus, the charge on the latter is 83 and there must follow a reorganisation of the external electrons. Under these conditions, we cannot be certain whether the L spectrum of radium B should correspond to an element of number 82 or 83. Since the excitation of the L spectrum is for the most part due to the action of the rays from the nucleus, the spectrum should correspond to number 82 if the emission of the γ-ray precedes the escape of the disintegration electron and number 83 if it is subsequent to this process.
Assemblies of Imperfect Gases by the method of Partition Functions
Authors: Fowler R. H.
Published: November 2008

In a recent series of papers analytical methods have been introduced which allow of a mathematically simple treatment of the theorems of statistical mechanics for the usual assemblies of isolated or effectively isolated systems. By this we mean that the individual component systems may be treated for energy content as if they were never interfered with. It is only then that energy can be assigned to systems rather than to the assembly as a whole, and it is on this partition of energy among the systems that the analysis is based. When this independence, for example between separate atoms, breaks down as in a molecule, and still more in a crystal, we can take the whole complex to be a system. The analysis will still apply, and if we can formulate the dynamical motions of the complex system, we can still make progress. The essential step for any system is to construct its partition function. Examples of such constructions for molecules and crystals will be found in the papers quoted, and are of course otherwise well known.
The lateral vibration of non-uniform bars, with application to ships
Authors: Moullin E. B.
Published: November 2008

The heavy elastic structure of a ship possesses many natural periods of lateral vibration, and if any periodic disturbing force within the hull happens to synchronise approximately with any of these natural periods, considerable vibration may result. Experience has shown that the damping of the hull structure is small, and when the rate of revolution of the propeller coincides with a natural period of the ship, a vibration of large amplitude is set up. No doubt reciprocating machinery is competent to produce more violent vibration than turbine machinery, but the inevitable lack of balance of the propeller itself is sufficient to vibrate seriously a turbine-driven ship.
The Production of High Speed Electrons by Indirect Means
Authors: Walton E. T. S.
Published: November 2008

The present paper contains an account of some work done in an attempt to produce high speed electrons, using an indirect method suggested by Sir Ernest Rutherford. Although it was not found possible to make the method work, yet a description of it may be of interest on account of the importance attached to any method of obtaining fast electrons.
The Fields Close to a Radiating Aerial
Authors: Moullin E. B.
Published: November 2008

This paper is concerned with the electric and magnetic field close to conductors which carry an alternating current. Hertz's famous solution of Maxwell's equations gave the field at a great distance from a magnetic or electric dipole whose moment was alternating harmonically: but from its very character it could not describe the field at points which were insufficiently remote from the origin for the source to appear as a dipole. The great development of radio communication has made important certain problems about the field in the vicinity of wires which are carrying an alternating current. Thus imagine that an aerial of some thousand feet in height and very many acres in extent has been erected. Before the designer of this vast and costly structure can calculate the rate of energy output, he must suppose himself so far removed that the aerial has dwindled to a mere speck in the aether. Such a process must seem both unsatisfactory and unsatisfying to those who take the responsibility of obtaining radio communication. It is already known that the field at any point can be expressed formally when the distribution of current and charge in the source is postulated: it is shown in this paper that the field at all points very near to the source can be expressed by simple formulae. Of course it is not an exact solution for the field due to a conductor of specified shape, because the postulated distribution of current and charge is incorrect.
Representation of the planes of five-dimensional space
Authors: Rao C. V. Hanumanta
Published: November 2008

The planes of a given S5 can be represented by the points of a locus V9 in space of nineteen dimensions. This locus is a double locus on a certain other manifold V14, and the tangent spaces of the V9 generate a W18. Segre has a memoir on the subject of these loci, in which he arrives at his results by a series of short steps, the argument being mainly geometrical.
On the Quantum Theory of the Problem of the Two Bodies
Authors: Oppenheimer J. R.
Published: November 2008

The problem of the two bodies has been treated on the new mechanics by Dirac, Pauli, and Schrödinger, who have independently derived the Balmer terms. The present paper is an attempt at a more complete solution. In particular, formulae are derived for the line intensities of the hydrogen spectrum, for the photoelectric effect and its inverse, and for the continuous absorption spectrum in the ultraviolet and in the X-ray regions. Also the probabilities of transition, deflection and capture are computed for the collision of an electron and an ion. Numerical values are only obtained, however, for the simplest line intensities. It is hoped to treat the problem in greater detail.
The law of stifling of sound by curtains or cushions
Authors: Larmor Joseph
Published: November 2008

The intensity of stifling is estimated. Under ideal conditions the absorption should vary as the secant of the angle of incidence of the sound.