bluuebunny/crossref_metadata_2025_split huggingface dataset:
An attempt to detect an Electric Moment in a Light Quantum
Authors: Clark R. J. , Watson W. H. 
Published: November 2008

If a light quantum has an electric moment, we should expect its axis to coincide with the direction of the electric vector, and therefore to be perpendicular to the plane of polarisation. Now an electric doublet of moment μ on entering a uniform electric field E with its doubletaxis parallel or antiparallel to the field will have its energy changed by an amount ∓ μE. For a light quantum this is equivalent to a change in wave-lengthwhen in the field. The method adopted to detect this change was to set up a grating with a strong electric field normal to its surface, and then have a plane polarised parallel beam of light fall on the ruled surface with the electric vector parallel to the direction of the field. The spectra formed near the normal to the grating were then examined both in the presence and absence of the field.
An Involution in the Complex Variable
Authors: Grace J. H. 
Published: November 2008

Suppose that ƒ1, ƒ2, ƒ3 are three quadratics in the complex variable z with complex coefficients, sayand consider the equationthe α's being real quantities. It determines two values ζ, ζ′ of z and thus two points P, P′ in the complex plane. Clearly when P is given the ratios α1: α2: α3 are in general determinate and accordingly P′ also. This is the involutory transformation I propose to discuss.
The Deformation of Soap Bubbles in Electric Fields
Authors: Macky W. A. 
Published: November 2008

Experiments on the deformation of soap bubbles in an electric field show that until the bubble begins rapid vibrations there is no difference between positive and negative bubbles.The positive bubble always bursts very shortly after beginning to vibrate even when resting upon a large supply of soap solution.The negative bubble, however, when resting on ample soap solution, continues vibrating until a much higher field is reached and usually does not burst until some protuberance on the positive plate allows a spark to pass, which may then strike and destroy the bubble.The values of the field for which a particular bubble begins rapid vibrations, so that in continuous light it appears to be conical, are found to be the same within experimental error for both positive and negative bubbles. The fields for bubbles of different sizes are found to vary inversely as the square root of the radius.Photographs are given illustrating the shape of bubbles in various fields.These experiments were carried out at the suggestion of Professor C. T. R. Wilson, and I am greatly indebted to him for his continued advice and interest throughout their progress.
On sets of fractional dimensions
Authors: Best E. 
Published: November 2008

1. Any number x can be expressed uniquely in the formwhere the xr's are positive integers and where xr < r. In the present paper we consider the set of numbers Eb for which the xr's are bounded, so that 0 ≤ xr < b say, where b also is an integer. We prove that this set has dimension functionh(t) = b−u,where t = euu−u−½(b − 1)(2π)−½, in the sense of Hausdorff.
The Gliding of a Plate on a Stream of Finite Depth. Part II
Authors: Green A. E. 
Published: November 2008

7. We have discussed the gliding of a plate of finite length on a stream of finite depth. Numerical calculations have been made for the case when the angle of incidence of the plate to the stream was 30°, the results for any other angle being similar.It was found that, for a given depth of stream and a given height of the trailing edge above the bed of the stream, the value of the lift increases with the length of the plate, until finally, when the plate is infinitely long, the lift assumes a maximum value. Further, for a given depth of stream, the total normal lift on the plate is independent of its height above the bed of the stream, when the length of the plate is small, except when the trailing edge of the plate is above the surface of the stream. Finally, when the depth of the stream is very large and the plate is near the middle of the stream, then our solution approximates to the classical Rayleigh flow past a plate in an infinite fluid.
On the Radiation Emitted by a Multipole and its Angular Momentum
Authors: Heitler W. 
Published: November 2008

1. By expanding the radiation field in a series of spherical waves the complete expressions for the field emitted by an electric and magnetic 2l-pole are obtained (§§ 1, 2).2. It is shown that the wave emitted by a (electric or magnetic) 2l-pole has an angular momentum about the z-axis Mz = mU/ν (U = total energy), where m, according to the orientation of the 2l-pole in space, can assume the values −l, −l + 1, …, + l (§ 3). The angular momentum is contained in that region of the field in which the product EH decreases as r−3.3. By quantizing the waves it is shown that the angular momentum of a light quantum emitted by a 2l-pole behaves like the angular momentum of an electron in a central field of force without spin (commutation relations, etc.) (§ 4). The angular momentum of a single light quantum is an integral multiple of ħ.
Note on the velocity distribution in the wake behind a flat plate placed along the stream
Authors: Rosenhead L. , Simpson J. H. 
Published: November 2008

1. The velocity distribution in fluid of small viscosity, or at large Reynolds number, in the laminar boundary layer associated with a thin flat plate along the main direction of flow, has been worked out by Blasius on the basis of the Prandtl theory. These original investigations covered the region from the forward edge of the plate to the downstream edge. In a recent paper Goldstein investigated the velocity distribution in the wake immediately behind the downstream edge over a region within about 0·5lfrom it,lbeing the length of the plate. LaterTollmien obtained a first approximation to the flow at a great distance down-stream. Goldstein § extended Tollmien's solution by finding a second approximation and by joining it up with his previous work on the flow very near the plate.
Wave functions for negative ions of sodium and potassium
Authors: Hartree D. R. , Hartree W. 
Published: November 2008

Solutions of Fock's equation for the self-consistent field with exchange have been carried out for the negative ions Na−, K−. The results indicate that these negative ions can certainly exist; and calculations of the energy values, and estimates of the errors of these values, indicate that these ions are probably stable and not liable to autoionization.The wave functions for these negative ions are required in calculating atomic cross-sections for the capture of electrons by the neutral atoms.
Current effects in cylindrical superconductors
Authors: Misener A. D. 
Published: November 2008

Experiments are described which show the effect of current on the transition of cylindrical superconductors to the normal state produced by increasing an external magnetic field. The transition curves were determined with an accuracy of 0·1%. Both longitudinal and transverse fields were used.The following results were found.(a) Transverse field(i) The field strength at which the first traces of resistance appeared was independent of current strength for reasonably small currents (up to about 100 mA. for 0·010 cm. wire).(ii) With increase of current the transition curve at first changed shape, becoming more and more nearly linear, and then was displaced parallel to itself toward smaller values of the applied field by an amount in accordance with Silsbee's hypothesis.(iii) The change in shape of the transition curve was accurately reproducible and was identical for specimens of the same material and diameter.(iv) The results for specimens of different diameter could be accurately correlated if the measured values of the resistance were plotted against the current divided by the specimen diameter raised to the power (l + R/Rn), i.e. I/(diam.)(1+R/Rn), where R/Rn is the ratio of the measured resistance to the resistance just above the transition point.(b) Longitudinal field(i) With increase of current, however slight, the transition curve was displaced parallel to itself, toward smaller values of the applied field, without showing any change in shape.(ii) The displacement of critical field for a given change of current was completely independent of the diameter of the specimen.(iii) The observed shift to smaller fields was much greater than could be accounted for by the additional field produced by the current at the surface of the wire.(iv) If we denote the (extrapolated) value of the critical field for zero current by (Hc) and the difference between this and the observed value for a current (I) by (ΔHc) then I and Hc are connected by the empirical relationwhere A and n are constants depending on the nature of the superconducting metal.when Hc is expressed in gauss and I in milliamperes.
On Frullani Integrals
Authors: Iyengar K. S. K. 
Published: November 2008

The object of this note is to obtain necessary and sufficient conditions for the existence ofon the assumption that ø is integrable in any finite positive interval not including zero (0 < α ≤ x ≤ β < ∞). On reference to the literature on the topic, I find no exhaustive analysis of this problem anywhere.
Sur les familles indenombrables de suites de nombres naturels et les problemes concernant la proprieteC
Authors: Rothberger Fritz 
Published: November 2008

Nous ne considérerons, en général, que les sous-ensembles de l'intervalle [0, 1] et nous désignerons paretrespectivement l'ensemble des nombres rationnels et l'ensemble des nombres irrationnels de cet intervalle.Nous allons employer pour les fractions continues la notationÉtant donnée une suite de nombres naturels {zn}, nous dirons que le nombrecorrespondà la suite {zn} et vice versa, et nous écrironnsz=v({zn}). Pareillement, nous dirons qu'un ensemblecorrespond à une famille Φ de suites de nombres naturels si l'on aE=v(Φ).
Deuteron bombardment of gold
Authors: Krishnan R. S. 
Published: November 2008

The paper describes the results obtained from a study of the bombardment of gold with deuterons of energy up to 9·1 M.e.V. The reactions found to take place in gold are the formation of 2·7 day Au198 by a (d-p) process and of 32 hr. Hg198* in a metastable state by a (d-n) process. The β-ray and γ-ray energies associated with each radioactivity have been measured by absorption methods. Excitation functions for the two reactions have been determined and the results have been compared with those to be expected on theoretical grounds.The author takes this opportunity of expressing his gratitude to the past and present members of the Cavendish Cyclotron Laboratory for assistance in running the cyclotron. He wishes to thank the Royal Commission for the Exhibition of 1851 for the award of a Science Scholarship.
The Parseval formulae for monotonic functions. I
Authors: Edmonds Sheila M. 
Published: November 2008

The Parseval formulae for Fourier cosine and sine transforms,are of course most widely known in connexion with the classical theorems of Plancherel on functions of the class L2 (whose transforms are defined by mean convergence), and with their generalizations. We cannot expect to obtain anything as elegant as the ‘L2’ results when we consider (1) for functions of other kinds. Nevertheless, since the most obvious way of defining Fourier transforms is by means of Lebesgue or Cauchy integrals, we naturally wish to know how far the formulae (1) hold good for transforms obtained in this way. The two most familiar classes of functions having such transforms are:(i) functions f(t) integrable in the Lebesgue sense in (0, ∞), whose transforms Fe(x) and Fs(x) are defined by the Lebesgue integrals respectively; and(ii) functions f(t) which decrease in (0, ∞), tend to zero as t → ∞, and are integrable over any finite interval (0, T); in this case the transforms are defined by the Cauchy integrals .
On a new analytical representation of curves in space
Authors: Pedoe D. 
Published: November 2008

It was in a paper bearing this title that Cayley(1) first considered the problem of representing a curve in projective space of three dimensions by means of the complex of lines which meet the curve. He took the conic given by the equationsand found that the linewith dual Grassmann coordinates (…,pij,…), whereintersects the conic if, and only if,where F(u0, u1) is homogeneous and of degree 2 in both sets of indeterminates u0 and u1 and G(…,pij,…) is a form of degree 2 in the pij. Both F(u0, u1) and G(…,pij,…) are easily determined in this case.
The half-life of thorium C′
Authors: Hill J. M. 
Published: November 2008

1. The half-life of Th C′ was determined by a new method of coincidence technique.2. Previous investigators have recognized difficulties in regard to this investigation. These were: (a) random delays in the counters; (b) coincidences due to other disintegrations; (c) possibility of difference in delays in recording α- and β-particles. In this investigation the difficulties arising from these effects have been overcome.3. From this type of experiment it is possible to determine the order in which the particles are emitted.4. It would appear that the time of breakdown of a counter depends slightly upon the magnitude of the initialionization.5. The value for the half-life of Th C′ was found to be 3.0 ± 0.15 × 10−7 sec.
The Bose-Einstein statistics of particles, with special reference to the case of low temperatures
Authors: Dingle R. B. 
Published: November 2008

In this paper, it has been shown that the usual demonstrations of the phenomenon of Bose-Einstein condensation are invalid. Exact formal solutions have been derived for the partition functions and the mean occupation numbers in classical and Bose statistics, and the theory of fluctuations in the case of Bose statistics has been given.In a second paper, convenient approximations will be derived for the mean occupation numbers in Bose statistics, and it will be shown that for temperatures well above the critical temperature of the supposed Bose-Einstein condensation the well-known resultfor the mean occupation numbers is valid, whilst for temperatures rather lower than this critical value it will be shown that particles will condense into the lowest available state. The critical temperatureT0is given bywhere the summation is over all energy levels except the lowest.
Collisions through liquid layers
Authors: Eirich F. R. , Tabor D. 
Published: November 2008

The initial collision (see pp. 571–2). The instantaneous velocity change of the hammer (from V0 to V) when it first strikes the liquid film should be calculated from energy and not momentum considerations, since the hammer has momentum in the vertical direction whilst the liquid is expressed in a horizontal direction and its total momentum is, by symmetry, zero at every instant. The kinetic energy dE of an annulus of liquid of radius r will be ½mc2, where m = 2πrhρdr, and c, the radial velocity of flow, is ½rV/h, since the liquid starts moving in plug flow. Integrating from r = 0 to r = R, we find that the total kinetic energy E imparted to the liquid film is . Assuming that extraneous energy losses, including any energy imparted to the anvil, are negligible, we may equate this to the energy loss of the hammer . HenceTo a first approximation this yieldsThe term at the right-hand side of the denominator is one-half that given in the original derivation (equation (20)), so that the instantaneous decrease in the velocity of the hammer is even less marked. For the given case where M = 400g., R = 1 cm., ρ = 1.6 and h = 5 × 10−2 cm., the velocity decrease is less than 2%.Vol. 44 (1948), pp. 566–80.
Elastic deformations of infinite strips
Authors: Hopkins H. G. 
Published: November 2008

ABSTRACTIn this paper, Fourier integrals are used to solve some elastic problems of generalized plane stress and small transverse displacements in infinitely long, rectangular, isotropic plates stressed only at their edges. The Airy stress function and the transverse displacement satisfy the two-dimensional bi-harmonic equation, and the basic mathematical problem is to solve this equation subject to different sets of boundary conditions. Little attention has been given hitherto to problems in which some of the boundary conditions depend directly upon displacements. Here the general problem is solved when one long edge is fixed, and stresses or displacements are arbitrarily prescribed at the other, with no stresses and displacements at infinity. The problem of a concentrated edge force is discussed in detail and numerical values of the stresses at the fixed edge are given.
The Parseval formulae for monotonic functions. II
Authors: Edmonds Sheila M. 
Published: November 2008

It is clear from § 1 that we shall have quite a large number of theorems to consider, as we may distribute the conditions of monotony and existence in a good many different ways. It is therefore convenient to collect together the various results for series and for transforms in tabular form, for reference and comparison; this is done at the end of this section.The transform table is very simple. The theorems contained in it have been discussed at length in M.F.(I); they may be summarized by saying that (1) holds in all the cases considered, except perhaps in the consine case of section [B] where the truth is not known. The series results are apparently more complicated as well as more numerous, since there are extra conditions to be imposed in [A, 1], [B, 1], [C′, 1] and [C, 2]. However, these are certainly satisfied if we suppose f and g to be positive whenever they are given to be monotonic (a condition which automatically holds in the transform theorems, since in these the monotonic functions tend to zero at infinity). If we confine our attention to this case, the series results are what we should expect from the transform ones, except that the difficulty in section [B] for transforms is not reproduced for series in [B, 1] or [B′, 1]; it is reproduced in [B, 2].
High-speed flow of a gas past an approximately elliptic cylinder
Authors: Levey H. C. 
Published: November 2008

AbstractIn this paper, a family of exact solutions of the problem of two-dimensional flow of a compressible perfect fluid about a cylinder is found, the solutions being generalized from those for the flow of an incompressible fluid about an elliptic cylinder of arbitrary eccentricity and angle of attack. The circulation is taken to be zero and the speed of the fluid at infinity subsonic. This analysis is an application of the general theory given by T. M. Cherry (1, 2); it was done to exhibit the details of the analysis for a flow other than that corresponding to the low-speed flow past a circular cylinder.
A boundedness theorem for non-linear differential equations of the second order
Authors: Reuter G. E. H. 
Published: November 2008

1. This paper deals with the differential equation(dots denoting derivatives with respect to t), where for large x the ‘restoring force’ term g(x) has the sign of x and the ‘damping factor’ kf(x) is positive on the average. It will be shown that every solution of (1) ultimately (for sufficiently large t) satisfieswith B independent of k. The conditions on f(x), g(x) and p(t) (stated in §§ 2, 3) are rather milder than those assumed by Cartwright and Littlewood (1, 2) and Newman (3) in proving similar results.
On the propagation of disturbances from moving sources
Authors: Walters A. G. 
Published: November 2008

AbstractThe concept of the Green's vibrational function given in an earlier paper by the author is used to obtain a general expression for the disturbance from a point source. The potential due to transient sources of sound moving with subsonic and supersonic velocities is derived from this. It is found that the Doppler effect for a supersonic source differs from that for a subsonic source. In the former case it is found that two frequencies are heard simultaneously from a source emitting a note of one frequency.The theory is applied to determine some solutions of the two dimensional equation of supersonic, irrotational compressible flow, corresponding to the flow around an aerofoil taking into consideration the entropy changes at the shock wave.
Wave reflexion near a wall
Authors: Robinson A. 
Published: November 2008

AbstractThe field of flow due to a shock wave or expansion wave undergoes a considerable modification in the neighbourhood of a rigid wall. It has been suggested that the resulting propagation of the disturbance upstream is largely due to the fact that the main flow in the boundary layer is subsonic. Simple models were produced by Howarth, and Tsien and Finston, to test this suggestion, assuming the co-existence of layers of uniform supersonic and subsonic main-stream velocities. The analysis developed in the present paper is designed to cope with any arbitrary continuous velocity profile which varies from zero at the wall to a constant supersonic velocity in the main stream. Numerical examples are calculated, and it is concluded that a simple inviscid theory is incapable of giving an adequate theoretical account of the phenomenon. The analysis includes a detailed discussion of the process of continuous wave reflexion in a supersonic shear layer.
On the decrease of velocity with depth in an irrotational water wave
Authors: Longuet-Higgins M. S. 
Published: November 2008

ABSTRACTThe following theorems are proved for irrotational surface waves of finite amplitude in a uniform, incompressible fluid:(a) In any space-periodic motion (progressive or otherwise) in uniform depth, the mean square of the velocity is a decreasing function of the mean depth z below the surface. Hence the fluctuations in the mean pressure increase with z.(b) In any space-periodic motion in infinite depth, the particle motion tends to zero exponentially as z tends to infinity. The pressure fluctuations at great depths are therefore simultaneous, but they do not in general tend to zero.(c) In a progressive periodic wave in uniform depth the mass-transport velocity is a decreasing function of the mean depth of a particle below the free surface, and the tangent to the velocity profile is vertical at the bottom. This result conflicts with observations in wave tanks, and shows that the waves cannot be wholly irrotational.(d) Analogous results are proved for the solitary wave.
On approximate solutions of linear differential equations
Authors: Jeffreys Harold 
Published: November 2008

ABSTRACTAsymptotic approximations of Green's type to solutions of differential equations are studied, with special reference to the uniformity of the approximation given by the first term. In extension to the complex variable this is found to require substantial restrictions on the region considered. An anomaly previously noticed is traced to non-uniformity of approximation. The case where the coefficient χ0 has a simple zero and χ1 is not zero is treated by a simple method.