bluuebunny/crossref_metadata_2025_split huggingface dataset:
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.
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 integralsof total differentials which are finite everywhere on an algebraic variety Vm of m dimensionsThese 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.
A Note on Creation and Annihilation in Statistical Assemblies
Authors: Sterne T. E. 
Published: November 2008

ABSTRACTThe 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.
A Microcalorimeter
Authors: Ward A. F. H. 
Published: November 2008

A microcalorimeter is described accurate to 0·0005 cal. The elevation of temperature was measured by a series of iron-constantan thermo-couples, with one set of junctions making good thermal contact with the tube-where the heat was liberated and the others in a brass ring outside, kept in a thermostat. They were connected in series with a very sensitive moving coil galvanometer. The Tian multiple walled thermostat was used—three concentric copper cylinders insulated with kapok, the inner filled with water and the outer controlled by a mercury regulator. The constancy of temperature in the inner vessel was rather better than 1/500,000° C.Continuous heat evolutions could also be measured by passing a current through another set of thermo-couples, when the Peltier cooling compensated for the heating and the temperature was kept down to its original value, thus avoiding cooling corrections.
A Method of Generalising the Law of Mass Action for Heterogeneous Surface Reactions
Authors: Constable F. Hurn 
Published: November 2008

To the conditions of reaction in homogeneous systems is added yet another condition, the adsorption of the reactants on the centres of activity of the surface. The surface is treated as if it were homogeneous, reaction taking place as if those centres on which the heat of activation is smallest were alone responsible for chemical change.The general equation is worked out in terms of the rate of bombardment, and the mean lives of the molecules on the surface. It is incidentally shown that the same areas associated with the forward reaction must inevitablycatalyse the backward reaction.The general solution is impracticable, so the special cases of irreversible synthesis and decomposition are considered and results are obtained.
The Petersen-Morley theorem, II
Authors: Frith R. 
Published: November 2008

In a paper by Mr Lyons and myself an elementary proof of the following theorem was given:Given three lines a, b, c in space, if a′ is the line of shortest distance of b and c, b′ that of c and a, and c′ that of a and b; and if x is the line of shortest distance of a and a′, y that of b and b′, and z that of c and c′, then x, y, z have a common line of shortest distance.
Contributions to the theory of Ramanujan's function τ(n) and similar arithmetical functions
Authors: Rankin R. A. 
Published: November 2008

Suppose that is an integral modular form of dimensions − κ, where κ > 0, and Stufe N, which vanishes at all the rational cusps of the fundamental region, and which is absolutely convergent for The purpose of this note is to prove thatThe notation employed is that of my second paper under the same general title* I refer to this paper as II.
The adsorption of dipoles
Authors: Miller A. R. 
Published: November 2008

The following correction has to be made to my recent paper on the adsorption of dipoles. Equation (10) and the sentence immediately preceding it are to be replaced by the following paragraph:In the polynomial expressions for f1(x) and f2(x) the coefficients of the powers of x depend on η2 and η3 which are functions of T.
Momentum distribution in molecular systems
Authors: Duncanson W. E. , Coulson C. A. 
Published: November 2008

Theoretical calculations on the mean radial momentum distribution of the electrons are made for the molecules CH4, C2H6, C2H4 and C2H2; from these distributions the profiles of the Compton line are deduced. It is assumed that each electron acts as a single scattering centre so that the mean radial distribution for the molecule is just the sum of the various “partial distributions” for each electron separately. The electrons are supposed to be paired together in the formation of localized bonds, and the contributions from each type of bond have to be separately determined. When superposed, these give the momentum distribution for the whole molecule. Such distributions are similar in shape, but the peak value of the momentum curves moves to higher values of p as the C—C bond becomes more saturated.A comparison of the various partial distributions for C2H4 shows that the C—H bond is an important factor in the momentum distribution of such molecules. In other hydrocarbon molecules, we may presume that the proportion of C—H bonds will be very significant in determining the breadth of the momentum distribution curve, and hence of the width of the Compton line; in fact the half-width of the Compton line decreases both with an increase in the number of the C—H bonds, and with increased saturation of the C—C bonds.In the only case where experimental results are available, CH4, the discrepancy between theory and experiment amounts to about 30%. Reasons for this discrepancy are discussed; in part the discrepancy may be attributed to the approximations used in the wave functions; but reasons are given for supposing that in part also it arises from an incorrect interpretation of the experimental results.
A theorem on finite differences with an application to the theory of Hausdorff summability
Authors: Fuchs W. H. J. 
Published: November 2008

1. It is trivial thatfor all integers n ≥ 0 implies sn = 0 (n = 0, 1, 2, …). This conclusion is no longer true if it is only known that (1·1) is true for an infinity of n. But we shall show that the truth of (1·1) for, roughly speaking, one-half of all positive integers, together with an order condition on the magnitude of sn, ensures sn = 0 for all n. This follows fromTheorem 1. Let a1 < a2 < … be positive integers, n(R) the number of a's not exceeding R, sn a sequence of complex numbers. If(ii) sn = ο(nK)as n tends to infinitythen sn = P(n), where P(x) is a polynomial of degree less than K.
Sufficient statistics and intrinsic accuracy
Authors: Pitman E. J. G. 
Published: November 2008

It is proved that if there exists a sufficient statistic for the estimation of an unknown parameter of a population, the frequency function of the population must be of a certain type.It is shown that some modification of previous theory of the intrinsic accuracy of statistics is necessary when the range of the population sampled is a function of the parameter to be estimated.Finally, the theory is extended to sufficient sets of statistics, i.e. sets of statistics which together contain all the information provided by a sample about an unknown parameter.
The eigenvalues of electromagnetic angular momentum
Authors: Pryce M. H. L. 
Published: November 2008

It is shown that the eigenvalues of the angular momentum of the electromagnetic field containing a number of charged particles, apart from spin angular momentum, are only the integral multiples of ħ. This is shown by using cylindrical polar variables, and taking a particular choice of the vector potential in which the radial component is zero, defined explicitly in terms of the magnetic field strengths. By expanding in terms of the Fourier functions einθ, the angular momentum is separated out into terms independent of one another, each taking on only integral values in units of ħ.The arguments all apply equally well to a modified field theory such as that of Born and Infeld.
The envelope of the subspaces of the polyhedra of an involution on a rational curve
Authors: Baker H. F. 
Published: November 2008

The following note was suggested by an interesting paper written by F. P. White, where many references are given. It refers to a theorem given by W. F. Meyer, by whom the proof is indicated as possible by generalization of an intricate analytical proof given by him for a simple case. His result is that if on the rational curve of orderr, in space [r], say the curvecr[r], there be an involution ∞k, of sets ofmpoints, expressed, suppose, by an equationthen the spaces [r− 1], formed fromrpoints of any one of the polyhedra ofmpoints, are an aggregate ∞kof primes of this space [r], which is of class (m−k,m−r), the notation (p, q) meaning the binomial coefficientp! /q!(p − q)!. By Meyer, the conditionsk<r≤mare supposed to be satisfied. But there is a theorem forr<k≤m− 1, relating toselected[r − 1], formed fromrpoints of any one of the polyhedra ofmpoints. The general theorem may be formulated thus: In a space [r], the equation of any prime may be expressed by λu+ μv+... + ρw= 0, whereu= 0,v= 0, …w= 0 are any r + 1 given independent primes, and λ, μ, …ρ are coefficients which may be described as prime coordinates of the [r].
Proof of a theorem of Paley
Authors: Zygmund A. 
Published: November 2008

1. Let f(x) be a real function of period 2π, integrable L over (0, 2π), and letBy sn(x) and σn (x) we denote respectively the partial sums and the first arithmetic means of the series (1·1). Similarly, by and we denote the partial sums and the first arithmetic means of the seriesconjugate to (1·1). By we mean the function conjugate to f(x), that iswhere the integral is taken in the principal-value sense.
Concerning the velocity and temperature distributions in plane and axially symmetrical jets
Authors: Howarth L. 
Published: November 2008

The calculations of the velocity and temperature distributions for the turbulent flow in axially symmetrical and plane jets are described.For axially symmetrical jets Tollmien's results derived from calculations based on the momentum theory are stated; the calculations on the basis of the modified vorticity transfer theory and on the vorticity transfer theory with symmetrical turbulence are carried out. Unfortunately it seems to be true that none of these theories provides results in good agreement with experiment for both the velocity and temperature distributions.For plane jets the results obtained by Tollmien and based on the momentum transfer theory are stated; the calculations on the basis of the vorticity transfer theory are carried out. The velocity distributions on both theories are identical and in fair agreement with experiment. In order to test the validity of the theories it is necessary to compare the theoretical results for the temperature with experiment. No results for the latter seem to have been published.
The disintegration of boron by slow neutrons
Authors: Bower J. C. , Bretscher E. , Gilbert C. W. 
Published: November 2008

Photometrical measurements of the photographic images of cloud tracks of the disintegration of boron by slow neutrons,have enabled the ranges of both the He and the Li particle to be determined. We find that the He particle has a range of 7·0 ± 0·3 mm. and the Li particle a range of 4·3 ± 0·2 mm. in standard air.We deduce that the 7Li nucleus is usually formed in an excited state, with energy of excitation of either 0·5 or 0·8 M.e.V. The wide latitude in excitation energy is due to the uncertain state of our knowledge of the energy-range relation for α-particles.
On the stability of nuclei against β-emission
Authors: Fuchs K. 
Published: November 2008

By means of purely qualitative arguments which do not depend on any particular model, the general scheme of stable nuclei and the isotopic breadth of nuclei with odd charge number are explained.The breadth of the isobaric region can be obtained if the numerical values of certain energies are known. Though these can be estimated only very roughly, the values for the breadth of the isobaric region obtained in this way are in good agreement with the experimental values. The increase in the breadth of the isobaric region from light nuclei to heavier nuclei can be explained, but no plausible explanation has been found for the fact that the breadth decreases again for the heaviest nuclei.
The energy levels of ‘holes’ in liquids
Authors: Auluck F. C. , Kothari D. S. 
Published: November 2008

SummaryThe Schrödinger equation for a ‘hole’ in the hole-theory of liquids is constructed and solved by the B.W.K. method. The energy levels are found to be discrete, and the eigenvalues are obtained in terms of the density and surface tension of the liquid. The relation between the energy of the ground state and the temperature of melting is considered.
The yield of 139Ba in the fission of natural uranium by fast and slow neutrons
Authors: Broda E. , Kowarski L. , West D. 
Published: November 2008

ABSTRACTThe yields of 139Ba per fission in natural uranium by unslowed neutrons from a mixed radium-beryllium source and by C-group neutrons were compared. In each case the fission rates measured with an ionization chamber were correlated with the β-ray activity of 139Ba, chemically extracted from a mass of uranium oxide exposed to an identical neutron spectrum. The ratio of the two fission yields is found to be 0·84 ± 0·03. The possibility of using 139Ba as a local or integrating indicator of fission in extended uraniferous media, and of distinguishing between the contributions by fast neutrons and by slow neutrons is discussed.
On one-dimensional regular assemblies
Authors: Rushbrooke G. S. , Ursell H. D. 
Published: November 2008

The grand partition function of any statistical assembly may be defined by the equationwhere E denotes any value of the energy of the assembly, k is Boltzmann's constant, T the thermodynamic absolute temperature and λi a parameter which is later to be connected with the chemical potential, μi, of the ith species in the assembly by the simple formula
Quantum mechanics of the anharmonic oscillator
Authors: McWeeny R. , Coulson C. A. 
Published: November 2008

SummaryA method is presented for the accurate numerical treatment of molecular vibration problems in which the potential energy function is of the formThe treatment is carried through in detail for the case V(q) = Aq2 + Bq4, which, in most instances affords an adequate description of the potential. There is no restriction on the relative magnitudes of quadratic and quartic terms so that the method is equally applicable to the purely anharmonic oscillations occurring in types of ring bending (1), where V(q) = aq4.An approximate formula is derived for the energy levels in the general case. The case V = aq4 affords an illustration of the accurate treatment; the first five eigen-values and eigen-functions are computed and from them the associated transitionprobabilities. Numerical results are presented in a form convenient for further application. On comparison the approximate formula is found to yield results in error by approximately 1 %, the error decreasing for the higher levels for which the formula tends to a B.W.K. expression. In conclusion a ground-state eigen-function of simple analytical form is found to approximate remarkably well to the case of purely quartic vibrations.
Certain integral representations for Whittaker functions
Authors: Shanker Hari 
Published: November 2008

1. Shastri (1) has shown that if and thenBut (Goldstein (2))hence substituting from (1·2) in (1·1) and changing the order of integration, which we suppose to be permissible, we find that ifthenassuming of course that the integrals converge.
Some statistical properties of random noise
Authors: MacDonald D. K. C. 
Published: November 2008

A considerable volume of knowledge is now available on random fluctuations (noise) as regards the behaviour in amplitude. Familiar names in this field are those of Uhlenbeck and Ornstein(7), Fürth(1) and Rice (4), although very many others have made valuable contributions. A particular class of problem, of considerable practical importance, exists when the frequency spectrum is limited to a relatively narrow range. The resulting noise has then the character of a more or less regular oscillation modulated randomly in amplitude and phase. In this case, if we write the fluctuation in the form(where R(t) and θ(t) are variables changing slowly in comparison with sinω0t), it is clear that the magnitude of the envelope R(t) and the phase θ(t) are now the significant quantities. Rice (4), among others, has made a study of the statistical properties of R, deriving in particular the correlation function R(t) R(t + τ) in terms of the characteristics of the (power) spectrum ω(f). Fürth and the writer (2) have extended this work and carried out a collateral experimental investigation.
A note on podolsky electrodynamics
Authors: Matthews P. T. 
Published: November 2008

Three formalisms have been considered for the ‘extraordinary’ field introduced by Podolsky in his generalized electrodynamics.The c-representation (tildons) for negative energy particles (§ 3), leads to an unstable vacuum in electron hole theory and must be discarded (§ 7).The d-representation suggested by Podolsky is a hole theory for bosons. This leads at once to inconsistencies and it is impossible to introduce a Fock representation (§ 6).The least unsatisfactory is the b-representation (tilde photons) used by PKMG. Tilde photons can be created at high energies but decay immediately by pair creation. The introduction of tilde photons does not interfere with any agreement already established between experiment and ordinary quantum electrodynamics. Evidence might be obtained for the value of the constant a from consideration of the 2S level shift of the hydrogen atom and from the theory of showers where the deviation from the usual theory is greatest (§ 7).However, the formalism involves the introduction of an indefinite metric for the tilde photon field and consequently ‘negative probabilities’ for states in which an odd number of tilde photons are present. Approximate results can be obtained by assuming that ‘negative probabilities’ in the theory are positive probabilities in the real world. This leads to a small but fundamental error and it does not seem possible that a theory in this form can have any deep seated validity (§ 5).The same analysis applies to the extension of the Podolsky theory to the Proca field by Green (5). In order that the energy should be positive definite it is necessary to introduce an indefinite metric for one of the two superposed meson fields. Fundamentally the difficulties of interpretation are the same but in practice they will be more obvious because the coupling constants are greater.
The thermodynamics of magnetization
Authors: Guggenheim E. A. 
Published: November 2008

A paper under the above title (1) by G. H. Livens was published recently in this journal. The main object of this paper appears to be to show that the treatment of the same subject (2) by myself is unsound. I shall not attempt to refute Professor Livens's opinions. His views concerning magnetic energy have already been criticized by others (3) more expert than myself. I merely wish to draw attention to two completely untrue statements of fact in Professor Livens's paper, namely the following:(a) On p. 538 “Guggenheim writes therefore