bluuebunny/crossref_metadata_2025_split huggingface dataset:
Surface adsorption and the velocity of chemical action at gas-solid interfaces
Authors: Constable F. Hurn 
Published: November 2008

The relation between the reaction velocity of catalytic dehydrogenation and the rate of passage of alcohol vapour over the catalyst has been found by experiment. At low rates of flow the concentration of the aldehyde and hydrogen in the effluent gas, and therefore over the catalyst, is comparable with that of the reactant. The whole of the surface is thus not covered with the reactant, and the adsorbed reaction products cause marked decrease in the reaction velocity.When the concentration of the reaction products becomes sufficiently small, that is, when the rate of passage of the alcohol vapour exceeds some limit, the velocity is approximately independent of the rate of flow of reactant. With very high speeds the reaction velocity tends to fall again, but this is probably due to the difficulty of keeping the temperature of the catalyst constant.The formula previously deduced connecting the partial pressure of the reactant in a mixture with the fractional reaction velocity has been verified for mixtures of alcohol vapour with water, acetone and benzene; and the composition of the adsorbed gas film with the fractional partial pressure of the gases for mixtures of carbon monoxide with oxygen on platinum.The effect of mixture of vapours on the temperature coefficient of reaction is considered, and equations deduced to show the alteration produced. If the heat of desorption of the reactant is greater than that of the diluent, then the temperature coefficient is diminished, if they are equal there is no alteration, and if less the temperature coefficient is increased. Experiments show that water present in alcohol has little effect on the temperature coefficient of the reaction.
Disintegration by slow Neutrons
Authors: Chadwick J. , Goldhaber M. 
Published: November 2008

All the light elements up to aluminium and some heavier ones have been examined for disintegration by slow neutrons. Large effects have been found in lithium and boron and a small effect in nitrogen, the reactions beingand probably The charged particles emitted in the disintegration of lithium and boron afford a convenient and sensitive indicator for slow neutrons.One of us (M. G.) desires to acknowledge the financial assistance received from the International Student Service, London, and from Magdalene College, Cambridge.
The specific heat of carbon dioxide and the form of the CO2 molecule
Authors: McCrea W. H. 
Published: November 2008

SummaryTwo alternative forms of the CO2 molecule have been suggested by various authors who have discussed the band spectrum data. The specific heat curves based on these models are considered here. It is found that neither is quite satisfactory over the whole range of temperature and we discuss the difficulties for the low temperature and high temperature portions separately. In order to get agreement for low temperatures we find it necessary to introduce a further hypothesis about the molecular model which also seems to explain one or two outstanding difficulties in interpreting the fine structure of the bands. This assumption does not make any difference at higher temperatures where we show the error in one of the curves to be of the order we should expect to be accounted for by a centrifugal stretching of the molecule.
An Approximate Method of Determining the High-Velocity Limits of Continuous β-ray Spectra
Authors: Chalmers J. A. 
Published: November 2008

A method of obtaining approximately the high-velocity limits of continuous β-ray spectra by electroscope measurements is established and used for the β-ray bodies of thorium active deposit.The absence of thorium C γ-rays is confirmed and leads to some interesting results.The work was carried out in the Cavendish Laboratory, Cambridge. Thanks and gratitude are due to Professor Sir Ernest Rutherford, P.R.S., for his interest in the problem; to Dr C. D. Ellis, F.R.S., who suggested the problem, for continual help and advice; to Mr G. A. R. Crowe for help in preparation of the sources; and to the Department of Scientific and Industrial Research for a Grant during the time the work was being carried out.
Two notes on the Riemann Zeta-function
Authors: Little-wood J. E. 
Published: November 2008

Let Λ (n) be the arithmetic function usually so denoted, which is zero unless n is a prime power pm (m ≥ 1), when it is log p. We write as usualandwhere the dash denotes that if x is an integer the last term Λ (x) of the sum is to be taken with a factor ½. We wrute further
A Valve Amplifier for Ionisation Currents
Authors: Wynn-Williams C. E. 
Published: November 2008

A method of using a valve for amplifying ionisation currents 100,000 times is described, which avoids the instabilities usually associated with such apparatus. The necessary conditions to be satisfied, while extremely simple, are based on theoretical conditions which are discussed in full. Used in conjunction with a galvanometer of sensitivity 200 mm. per micro-ampere, the system behaves in a similar manner to a low capacity quadrant electrometer of sensitivity 6350 mm. per volt, shunted by a leak of 360 megohms, the value of the latter being slightly greater for negative currents than for positive. In addition, it has the advantages of portability, compactness, and ease and rapidity of erection and operation, being specially suitable for lecture demonstrations.The method of compensation can also be applied to other valve circuits, resulting in a much steadier zero.
An Asymptotic Expansion for
Authors: Mulholland H. P. 
Published: November 2008

In the theory of the specific heats of gases of diatomic molecules the functionplays a well-known and important part. The rotational specific heat Crot of a diatomic molecule, which is susceptible of representation as a rigid body with two equal principal moments of inertia, without spin about the other principal axis, is given bywhere R is the gram-molecular gas-constant andthe pair of equal moments of inertia being equal to A. Whether such a model is or is not an adequate representation is a matter for determination by a detailed study of the structure of the band spectrum, particularly of the nature of the normal electronic and vibrational state. It is known to be applicable to normal molecules of the halogen hydrides, to CO and other molecules which have a normal state of type 1S including (but for a certain special feature) H2.
Bisecant curves of ruled surfaces
Authors: Welchman W. G. 
Published: November 2008

The bisecant curves of a ruled surface, that is to say the curves on the surface which meet each generator in two points, are fundamental in the consideration of the normal space of the ruled surface. It is well known that if is a bisecant curve of order ν and genus π on a ruled surface of order N and genus P, thenprovided that the curve has no double points which count twice as intersections of a generator of the ruled surface.
Torsion of beams whose cross-section is a regular polygon of n sides
Authors: Seth B. R. 
Published: November 2008

E. Trefftz has discussed the problem of the torsion of a beam whose cross-section is bounded by a polygon with the help of the Schwarz-Christoffel transformation given bywhere a1, a2, …, an are external angles of the polygon in the w-plane, and ξ1, ξ2, …, ξn are the points on the real ξ-axis in the t-plane that correspond to the angular points of the polygon in the w-plane. In the case of regular polygons a further transformation of the upper half of the t-plane into the interior of a circle in the z-plane with the help of the transformationgreatly simplifies the problem, and some definite results can be obtained.
The radioactivity of the fluorine isotope of mass twenty
Authors: Curran S. C. , Strothers J. E. 
Published: November 2008

The transition 20F → 20Ne is shown to occur with the emission of a β-particle of maximum energy 5·0 × 106e. V., followed by a γ-quantum of energy 2·2 × 106e.V.The transition from the excitation level of 20Ne at 2·2 × 106 e.V. sometimes occurs in two stages with the emission of two quanta of smaller energy.
The Vapour-Pressure Equations of Solutions and the Osmotic Pressure of Rubber
Authors: Miller A. R. 
Published: November 2008

Assuming that the solute and solvent molecules in a solution can be regarded as occupying sites on a regular lattice and that the potential energy arises from interactions between molecules which occupy closest neighbour sites, the vapour-pressure equations have been determined for solutions in which each solute molecule contains three groups (or submolecules) and occupies three lattice sites in such a way that successive submolecules occupy closest neighbour sites on the lattice while each solvent molecule occupies only one site. The vapour-pressure equations are compared with those which have already been obtained by Fowler and Guggenheim for the case in which each solute molecule contains two submolecules in order to determine the effect on the form of the vapour-pressure equations of the number of submolecules in each solute molecule. This enables the determination of the vapour-pressure equations when each solute molecule contains n submolecules and occupies n lattice sites in such a way that successive submolecules occupy closest neighbour sites on the lattice. In this latter case the vapour-pressure equations areThese equations are used to determine the osmotic pressure of solutions of long-chain polymers, and it is found that in the region of osmotic interest, the osmotic pressure is given by an equation of the formwhere c g. of solute per 100 c.c. of solution is the concentration. It is shown that this equation can be written approximatelywhich is the quadratic relation which has usually been fitted to osmotic measurements. To this approximation π/c plotted as a function of c gives a straight line of which the intercept on the π/c axis determines the molecular weight of the polymer molecule and the gradient determines the number of submolecules in each polymer molecule.
The determination of intermolecular forces in gases from their viscosity
Authors: Burnett D. 
Published: November 2008

A method of determining the coefficient of viscosity of a gas of spherically symmetrical molecules under ordinary conditions has been given by Chapman. His result is equivalent towheremis the mass of a molecule of the gas,Tis the absolute temperature,kis Boltzmann's constant 1·372. 10−16and ε is a small quantity which later investigations on a gas in which the intermolecular force is inversely proportional to thenth power of the distance have shown to vary from zero whenn= 5 to 0·016 whenn= ∞ (equivalent to molecules which are elastic spheres); it may reasonably be supposed that ε is positive and less than 0·016 in all cases which are likely to be of interest, and it will be neglected in this paper. Alsoπ(r) being the mutual potential energy of two molecules (that is, the repulsive force between them is − ∂π/∂r), andr0the positive zero of the expression in the denominator, or the largest such positive zero if there are several.
Über die monotone Konvergenz der Cesàro-Mittel bei Fourier- und Potenzreihen
Authors: Turán P. 
Published: November 2008

1·1. Es bezeichne für nichtnegative ganze n und kdas n-te Cesàro-Mittel der Ordnung k der Reihe μ0 + μ1 + … Insbesondere ist also die n-te Partialsumme dieser Reihe.
The evaporation of concentrated films of sodium
Authors: Bosworth R. C. L. 
Published: November 2008

A three-filament mechanism is described which will enable multimolecular films to be studied by the method of contact potentials and this method is applied to the study of the evaporation of sodium films of various thickness from one to twenty layers. It is shown that the vapour pressure and heat of evaporation both increase as the thickness increases from one to three layers and thereafter become practically independent of any further increase in the film thickness. The vapour pressure for a thickness of four layers is within experimental error the same as that for bulk sodium.A difficulty due to the effect of the evaporating stream of atoms annulling the space charge around the emitter filament is discussed, and attempts are made to use this effect to measure the rate of evaporation at temperatures from 500° K. to 825°K.
The thermal conductivity of metals
Authors: Makinson R. E. B. 
Published: November 2008

The methods used to measure separately the electronic and lattice heat conductivities κeand κgin a metal are reviewed, and it is pointed out that care is necessary in interpreting the results in view of the underlying assumptions. The equations given by Wilson for κeand for the electrical conductivity σ are used to plot the theoretical values of the electronic Lorentz ratioLe= κe/σTas a function ofT, both for the monovalent metals and for a model metal with 1·8 × 10−2conduction electrons per atom, which is taken to represent bismuth sufficiently accurately for this purpose. Curves for κeand κgas functions ofTare given in both cases, and these, together with a comparison of the observed Lorentz ratio andLe, show that in the monovalent metals κgis unimportant at any temperature, but in bismuth it plays a major part at low temperatures, in agreement with experimental conclusions. Quantitatively the agreement is good for copper and, as far as the calculations go, reasonable for bismuth.Scattering of lattice waves at the boundaries of single crystals (including insulators) at temperatures of a few degrees absolute is shown to be consistent with the experiments of de Haas and Biermasz on KCl and to be responsible for the rise in thermal resistance in this region as suggested by Peierls.The assumption in the theory of electronic heat conduction that the lattice energy distribution function has its thermal equilibrium value is examined in an appendix. The conclusion is that it should be satisfactory, though the proof of this given by Bethe is seen to be inadequate.
Superlattice formation of the type AB in an adsorbed layer
Authors: Chang T. S. 
Published: November 2008

The possibility, pointed out in a previous paper, of superlattice formation in an adsorbed layer when the adsorbed atoms tend to repulse each other is developed in detail. Both Bragg and Williams's approximation and Bethe's approximation are used, but restricted to superlattices of the type AB. In a range of θ, the fraction of surface covered, a superlattice is found to be possible. Bragg and Williams's approximation shows further that the state with the lowest free energy is the one with a superlattice when the latter is possible. Rough kinetic expressions are also given. The equations derived from the principle necessary to preserve equilibrium are found to reduce to those of detailed balancing, and they also agree with the formula obtained statistically. As expected, all the corresponding results obtained from the two methods become the same when the number of nearest neighbours of a site approaches infinity, provided that the product of this number and the interaction potential of two adsorbed atoms occupying two neighbouring sites remains finite.The only significant result is the large value of the slope of isotherms (the rate of change of the pressure with respect to the fraction of adsorption) when there is a nearly complete superlattice.
Some relations between certain methods of summation of infinite series
Authors: Good I. J. 
Published: November 2008

Let f(t) be defined and measurable for t > 0, and suppose that it has non-vanishing moment constantswhere the integrals are Cauchy-Lebesgue integrals, or possibly if f(t) is null for t > t0 but not for t < t0 (a convention to which we adhere throughout).
Negative probability
Authors: Bartlett M. S. 
Published: November 2008

SummaryIt has been shown that orthodox probability theory may consistently be extended to include probability numbers outside the conventional range, and in particular negative probabilities. Random variables are correspondingly generalized to include extraordiary random variables; these have been defined in general, however, only through their characteristic functions.This generalized theory implies redundancy, and its use is a matter of convenience. Eddington(3) has employed it in this sense to introduce a correction to the fluctuation in number of particles within a given volume.Negative probabilities must always be combined with positive ones to give an ordinary probability before a physical interpretation is admissible. This suggests that where negative probabilities have appeared spontaneously in quantum theory it is due to the mathematical segregation of systems or states which physically only exist in combination.
Diamagnetism and superconductivity of a collective electron assembly
Authors: Band William 
Published: November 2008

AbstractExchange energy between electrons moving in a conductor is assumed to be such that the mean contribution per electron is proportional to the product of the total current within a defined range and the speed of the electron in the direction of the total current.The ideal resistance of a conductor can be neutralized by such an exchange energy at sufficiently low temperatures.The surface of the conductor, and internal surfaces of discontinuity if sufficiently marked, are regarded as sites for two-dimensional resonance states in equilibrium with the three-dimensional resonance states in the metal.The superconducting transition occurs when, at the critical temperature, the neutralization of the ideal resistance of the surface by-passes the residual resistance of the body of the metal.At the same critical temperature, equilibrium conditions ensure that exactly the right number of electrons enter the surface states to give the whole metal an ideal diamagnetic susceptibility.These equilibrium conditions are disturbed by a magnetic field, and the transition temperature is shown to depend on the magnetic field in the observed manner.The intermediate state is explained as one in which the number of electrons in the superconducting surface states is constrained by a non-uniform magnetic field to remain at an intermediate value which is inadequate to produce ideal diamagnetism.By regarding either the outer surface or internal surfaces of discontinuity as the only regions becoming perfectly conducting, the details concerning restoration of resistance by a current are well explained, as also are the observed size effects in thin films, and the phenomena of ‘non-ideal’ superconductors among the alloys.Finally, the observed distribution of superconductors in the periodic table receives a satisfactory qualitative explanation.
A ring in graph theory
Authors: Tutte W. T. 
Published: November 2008

We call a point set in a complex K a 0-cell if it contains just one point of K, and a 1-cell if it is an open arc. A set L of 0-cells and 1-cells of K is called a linear graph on K if(i) no two members of L intersect,(ii) the union of all the members of L is K,(iii) each end-point of a 1-cell of L is a 0-cell of Land (iv) the number of 0-cells and 1-cells of L is finite and not 0.
On the integrals of a partial differential equation
Authors: Friedlander F. G. 
Published: November 2008

The ordinary one-dimensional wave equationhas special integrals of the formwhich satisfy the first-order equationsrespectively, and are often called progressive waves, or progressive integrals, of (1·1). The straight linesin an xt-plane are the characteristics of (1·1). It follows from (1·2) that progressive integrals of (1·1) are constant on some particular characteristic, and are characterized by this property.
Three-dimensional stress distributions in hexagonal aeolotropic crystals
Authors: Elliott H. A. , Mott N. F. 
Published: November 2008

The conditions for equilibrium in an elastically stressed hexagonal aeolotropic medium (transversely isotropic) are formulated, and solutions are found in terms of two ‘harmonic’ functions ø1, ø2, which are solutions ofν1, ν2 being the roots of a certain quadratic equation.It is also shown that in the case of axially symmetrical stress systems the solution may be expressed in terms of the third-order differential coefficients of a single stress function Φ.The solutions for an isotropic medium may be deduced as a special case.The problems of nuclei of strain in such a hexagonal solid are solved, and the results for zinc and magnesium contrasted with those for an isotropic solid.
The number of individuals in a cascade process
Authors: Good I. J. 
Published: November 2008

A number of important Markoff processes, with a continuous time parameter, can be represented approximately by a discrete process, interesting in its own right, of the following type. A class of individuals gives rise seasonally (in January say) to a number of new individuals (children), the probabilities of an individual having 0, 1, 2, … children being p0, p1, p2, …. These probabilities are the same for all individuals and are independent. The individuals formed each January are regarded as a new generation, and only this generation is capable of reproducing in the next January. Letso that F(x) is the probability generating function (p.g.f.) of the number of children of an individual. Clearly the series for F(x) is absolutely convergent when |x| < |1.
Classical statistical mechanics of a rectilinear assembly
Authors: Gürsey Feza 
Published: November 2008

It is shown that all the classical thermodynamical properties and the equation of state of a rectilinear assembly of spherical molecules with short-range attractive forces acting only between neighbours can be derived from a single partition function which is an analytic function of the pressure and the temperature. The thermodynamical functions are simply related to the Laplace transform of the function e−E(x)/(kT), where E(x) is the interaction energy between two neighbouring molecules. Although this linear model behaves like a perfect gas at high temperatures and like a crystal near the absolute zero, there are no critical phenomena, owing to the analytic character of the partition function. It is, however, pointed out that at very low temperatures the slope of the isothermal curves can suffer extremely sharp changes which may be interpreted as changes of phase, and this point is illustrated by an example.Finally, I should like to express my sincere gratitude to Prof. H. Jones for his guidance of this work and for his invaluable advice throughout. My thanks are also due to the Turkish Ministry of Education for the award of a scholarship.
A note on a singular integral equation
Authors: Heins Albert E. 
Published: November 2008

In his treatise entitled Introduction to the theory of Fourier integrals, E. C. Titchmarsh derives a Fourier transform of the solution of the integral equationThe transform of the solution given by him does not satisfy the Riemann-Lebesgue lemma, and further suffers from the defect that it has certain exponential properties which prevent the actual calculation of the function φ(ξ), since the inversion integral does not exist for all ξ > 0. We shall correct these defects and show further that the solution of (1) is particularly simple and that it can be expressed as the Legendre function of an order which depends on λ.