bluuebunny/crossref_metadata_2025 huggingface dataset:
A Narrative Perspective on The Development of The Tense/Aspect System in Second Language Acquisition
Authors: Bardovi-Harlig Kathleen
Published: November 2008

A number of studies on the acquisition of tense and aspect by learners of a second language point to the hypothesis that narrative structure influences the distribution of tense/aspect forms in interlanguage. However, the studies have reported conflicting profiles of tense/aspect use. This study suggests that much of the variation that has been previously reported stems from the level of proficiency of the learners. This crosssectional study examines 37 written and oral narrative pairs produced in a film retell task by adult learners of English as a second language. The analysis approaches the texts from two perspectives, from the perspective of acquisition, taking narrative structure (specifically grounding) as an environment for acquisition of tense/aspect, and from the perspective of the narrative itself, characterizing the foreground and background by the tense/aspect forms used. The study finds a developmental pattern in the distribution of tense/aspect morphology with respect to narrative structure. These results permit the assimilation of earlier findings into a developmental sequence in the acquisition of the tense/aspect system.
Markedness Universals and the Acquisition of Voicing Contrasts by Korean Speakers of English
Authors: Major Roy C. , Faudree Michael C.
Published: November 2008

This study of five native speakers of Korean investigates the role of universals in their acquisition of English obstruent voicing contrasts. The data were gathered from a passage and a word list containing voiced and voiceless obstruents in initial, medial, and final word positions. Results reflected principles of markedness universals of L1 acquisition and adult natural languages, suggesting that interlanguage systems behave according to universals of natural languages.
The growth of meteorological disturbances
Authors: Bondi H.
Published: November 2008

1. Introduction. A considerable amount of attention has been paid to the problem of determining the conditions which decide whether a liquid heated from below is stable or unstable. The motion consequent upon the disturbance of an unstable ideal gas does not, however, seem to have been treated so far, and this problem forms the subject of the present paper. Heat conduction and viscosity are at first neglected, and we are therefore dealing with the small motions of a gas slightly disturbed from a position of equilibrium under the influence of gravity. The condition for the stability of such a gas is well known, namely, the temperature gradient must be less than the adiabatic gradient. Furthermore, it is known that there is a sharp distinction between slow large-scale (meteorological) and rapidly varying small-scale (acoustical) phenomena. The present paper confirms these points and derives the time scale of meteorological phenomena. Heat conduction and viscosity are then shown to set a lower limit to the dimensions of such disturbances, while the effect of the earth's rotation is shown to be negligible.
On B() and Br() locally convex spaces
Authors: Sulley L. J.
Published: November 2008

1. Introduction. In his papers (2), (3) and (4), and in his book (5), Husain studied the locally convex, Hausdorff, linear topological spaces (hereafter abbreviated to l.c. spaces) which he called B() spaces and Br() spaces and which satisfy weakened forms of the B completeness and Br completeness conditions of Ptak (8). L.c. spaces satisfying another weakening of the Br completeness condition were studied by Persson in (7) and were called by him, weakly t-polar. We consider some examples in connexion with these spaces.
The isotropic scattering of radiation from a point source in a finite spheroidal atmosphere
Authors: Smith M. G.
Published: November 2008

The integral equation for the three-dimensional Fourier transform of the source function, derived in a previous paper, is applied to scattering in a spheroidal atmosphere. This problem is not amenable to solution by any of the general methods that have been successful for problems of finite atmospheres of a more regular shape.

It is shown that if the dimensions of the spheroid are large the solution can he obtained by iteration as an expansion in powers of 1/R0, where R0 is a typical length. The leading term is shown to be that for the infinite atmosphere, which result would be anticipated on intuitive grounds.
Unipotent normal subgroups of skew linear groups
Authors: Wehrfritz B. A. F.
Published: November 2008

A recurrent problem over many years in the study of linear groups has been the determination of the central height of a unipotent normal subgroup of some matrix group of specified type. In the theory of matrix groups over division rings, unipotent elements frequently present special difficulties and these have usually been by-passed by the addition of some suitable hypothesis. In this paper we make a start on the removal of these extraneous hypotheses. Our motivation for doing this now conies from [9], where by 3·7 of that paper the additional assumptions have finally reduced us to degree one, a situation where unipotent elements present few problems!
The spectrum of the Cesàro operator on c0(c0)
Authors: Okutoyi J. , Thorpe B.
Published: November 2008

1. In a recent paper [6], the spectrum of the Cesàro operator C on c0 (the space of null sequences of complex numbers with the sup norm) was obtained by finding the eigenvalues of the adjoint operator on and showing that the operator (C–λI)−1 lies in B(c0) for all λ outside the closure of this set of eigenvalues. In this paper we apply a similar method to find the spectrum of the two-dimensional Cesàro operator on a space of double sequences c0(c0) (defined in §2). We shall introduce a simplification to the proof in [6] by observing that (C – λI)−1, when it exists, is a Hausdorff summability method (see page 288 of [11] for the single variable case on the space of convergent sequences c), and the crux of our proof is to show that the moment constant associated with the method (C – λI)−1 is regular for the space c0(c0) and the set of λ under consideration. It turns out that c0(c0) ≅ c0c0 (see page 237 of [7]) and that the two-dimensional Cesàro operator on c0(c0) is the tensor product C ⊗ C of the Cesàro operator C on c0. Thus our result gives a direct proof that the spectrum σ(C ⊗ C) equals σ(C)σ(C), which is a special case of the result of Schechter in [8].
Complexity and varieties for infinitely generated modules, II
Authors: Benson D. J. , Carlson Jon F. , Rickard J.
Published: November 2008

It has now been almost twenty years since Alperin introduced the idea of the complexity of a finitely generatedkG-module, whenGis a finite group andkis a field of characteristicp> 0. In proving one of the first major results in the area [1], Alperin and Evens demonstrated the connection of the study of complexity for modules to the group cohomology. That connection eventually led to the categorization of modules according to their associated varieties in the maximal ideal spectrum of the cohomology ringH*(G, k). In all of the work that has followed, two principles have proved to be extremely important. The first is that the associated variety of a module is directly related to the structure of the module through the rank variety which is defined by the matrix representation of the module. The second major result is the tensor product theorem which says that the variety associated to a tensor productM⊗kNis the intersection of the varieties associated to the modulesMandN. In this paper we generalize these results to infinitely generatedkG-modules.
Elementary Theory of the Critical Field of a Dielectric
Authors: Cernuschi Felix
Published: November 2008

It is well known that the eigen-functions corresponding to the free electrons in a one-dimensional lattice are of the form

where C (x) is a periodic function with period c (the lattice constant), and Kis a continuous variable.
Integral transforms based upon fractional integration
Authors: Fox Charles
Published: November 2008

The theory of Fourier transforms

can be developed from the functional equation K(s) K(1 – s) = 1, where K(s) is the Mellin transform of the kernel k(x).

In this paper I show that reciprocities can be obtained which are analogous to the Fourier transforms above but which develop from the much more general functional equation

The reciprocities are obtained by using fractional integration. In addition to the reciprocities we have analogues of the Parseval theorem and of the discontinuous integrals usually associated with Fourier transforms.

In order to simplify the analysis I confine myself to the case n = 1 and to L2 space.
Diffraction by a spherical cap
Authors: Thomas D. P.
Published: November 2008

1. It was first observed by Rayleigh(17) in 1897 that low-frequency approximations to the solutions of the steady-state wave equation could be obtained from the solutions of the corresponding static problems. Rayleigh determined only the first term in the expansion of the solution in powers of the product of the wave number and a typical dimension. Many recent investigations have been concerned with deriving a systematic method of calculating the higher-order terms in the above expansion. Most of the problems which have been solved in this manner have been concerned with scattering by a disk or by a strip: the first systematic approach to these problems was that of Bouwkamp ((3), p. 71).
The statistical distribution of the curvature of a random Gaussian surface
Authors: Longuet-Higgins M. S.
Published: November 2008

The distribution of the total (or ‘second’) curvature of a stationary random Gaussian surface is derived on the assumption that the squares of the surface slopes are negligible. The distribution is found to depend on only two parameters, derivable from the fourth moments of the energy spectrum of the surface. Each distribution function satisfies a linear differential equation of the third order, and the distribution is asymmetrical with positive skewness, in general. A special case of zero skewness occurs when the surface consists of two intersecting systems of long-crested waves.
A note on normal operators
Authors: Bernau S. J. , Smithies F.
Published: November 2008

We recall that a bounded linear operator T in a Hilbert space or finite-dimensional unitary space is said to be normal if T commutes with its adjoint operator T*, i.e. TT* = T*T. Most of the proofs given in the literature for the spectral theorem for normal operators, even in the finite-dimensional case, appeal to the corresponding results for Hermitian or unitary operators.
Statistical mechanics of a one-dimensional Coulomb system with a uniform charge background
Authors: Baxter R. J.
Published: November 2008

This paper obtains an exact description of the statistical mechanics of a one-dimensional system of charged particles moving in a uniform neutralizing background of positive charge. These results are compared with the behaviour of a one-dimensional system of equal numbers of positive and negative charged particles. Although the thermodynamics of the two systems do differ, the discrepancy is small enough to indicate that the assumption of a uniform background of positive charge, common in statistical mechanical treatments of a plasma in equilibrium, may provide a good approximation to a real system of discrete charges.
The temperature distribution in a transformer or other laminated core of rectangular cross section in which heat is generated at a uniform rate
Authors: Cockcroft J. D.
Published: November 2008

The problem of the temperature distribution in transformer or other laminated cores in which heat is generated at a uniform rate, does not appear to have been treated by exact mathematical methods. A good deal of work of a semi-empirical nature has been done by Vidmar, Kuchler and others, the object of which has been to enable designers of transformers to obtain an estimate of the maximum temperature likely to prevail in the core.
Some series and integrals involving associated Legendre functions (II)
Authors: Bailey W. N.
Published: November 2008

1. In a paper published recently in these Proceedings, I have proved the formulae

where R(m)>0;

where R(m) > −½; and

where R(m) >− 1. In each case n is unrestricted.
A note on analytic functions in the unit circle
Authors: Paley R. E. A. C. , Zygmund A.
Published: November 2008

1. Let

be a function regular for |z| < 1. We say that u belongs to the class Lp (p > 0) if

It has been proved by M. Riesz that, for p > 1, if u(r, θ) belongs to Lp, so does v (r, θ). Littlewood and later Hardy and Littlewood have shown that for 0 < p < 1 the theorem is no longer true: there exists an f(z) such that u(r, θ) belongs to every L1−ε and v(r, θ) belongs to no Lε(0 < ε < 1). The proof was based on the theorem (due to F. Riesz) that if, for an ε > 0, we have

then f(reiθ) exists for almost every θ.
The upper limit of energy in the β-ray spectrum of thorium C″
Authors: Terroux F. R. , Alexander N. S.
Published: November 2008

The upper portion of the β-ray spectrum of thorium C″ has been investigated by measuring the tracks produced in a Wilson chamber. No trace of a “tail“ is found, no tracks ofHρ greater than 10,800 being observed in some 600 to 800 disintegrations. The end-point is placed at 9400Hρ, somewhat higher than the value obtained by other workers.
Asymptotic dipole expansions for small horizontal angles
Authors: Murray F. H.
Published: November 2008

An approximate calculation of the electromagnetic field of a vertical dipole at the surface of a conducting earth, for small angles of the radius vector with the horizontal, was given by Sommerfield; the case of large angles with the horizontal has been studied by a number of writers. It is proposed here to develop formulae for the vertical dipole by a method which takes into account the singularities of the integrand of a certain integral more accurately than is done by Sommerfield; the analysis is developed especially for small horizontal angles and small numerical distances.
The significance of the sign of a mutual inductance
Authors: Nimmo R. R. , Poole H. D.
Published: November 2008

It is pointed out that there is some confusion concerning the meaning of the sign of a mutual inductance. The question is examined from first principles and it is shown that since the sign of a mutual inductance depends upon conventions as to sign of current directions, these, as well as the sign of the mutual inductance, must be given in order to specify what is really required—the relation between the directions of winding of the primary and secondary coils. It is also shown that in many cases it is possible to replace mutual inductance by a quantity which is numerically equal to the mutual inductance but which is independent of current directions. The two methods applied to a Wheatstone network yield consistent results.
An extension of Morley's chain of theorems on circles
Authors: Richmond H. W.
Published: November 2008

1. In a recent paper in these Proceedings by Mr H. Lob, and iu an earlier paper by Mr F. P. White, it has been shown how the well-known chains of theorems in plane geometry discovered by Morley and Clifford may be proved by projection from higher space. A curve of order n in space of n dimensions and certain derived loci are projected from one, or two, or three, …, or n − 2, out of n + 1 chosen points of the curve upon a plane which contains two further points of the curve. The n + 1 lines of the plane which form the starting-point of each chain of results as originally proved (and which are obtained in various ways in the course of the projections) are actually the lines in which the plane of projection is met by the primes containing n out of the n + 1 points. Now, with the standard equations of such a curve in [n], viz.
The generalised product moment distribution in a normal system
Authors: Wishart J. , Bartlett M. S.
Published: November 2008

1. In a previous paper (1) the authors used the theory of the moment generating function to deduce the known random sampling distributions of the estimated variance and co-variance in a system of variables following the normal law of frequency. In this paper we shall go much further. By means of the same general method the simultaneous distribution of the ½p (p + 1) second order moment statistics in a normal system of p mutually correlated variables will be deduced. It will be shown to be completely independent of that of the p sample means, and incidentally the method of proof to be developed will be found, in the special cases p = 1 and 2, to be an improvement on that given in the earlier paper, being independent of previous results reached by other authors.
On Herschel's Condition and the Optical Cosine Law
Authors: Steward G. C.
Published: November 2008

§ 1. Sir John Herschel gave the condition which must be satisfied in order that a symmetrical optical system, free from spherical aberration for two conjugate axial points, may also be free from spherical aberration for two neighbouring and conjugate points upon the axis of the system; but Herschel's condition applies only to first order aberration, i.e. to aberration depending upon the cube of the inclination of the ray to the axis. Abbe shewed, later, that this condition could be included in a wider result, viz. that the spherical aberration, supposed zero, is stationary for axial variations provided that the incident and emergent rays for two conjugate axial points, associated with modified magnification m, satisfy the relation

where θ and θ′ are their initial and final inclinations to the axis; and by ‘modified’ magnification is meant the ratio of the reduced sizes of the image and object.
The densities of the regular polytopes, Part 3
Authors: Coxeter H. S. M.
Published: November 2008

This third and last part of the paper is concerned with the interpretation of the Schläfli symbol {k1, k2, …, km−1} when the k's are unrestricted. It is shown that, whenever the k's are integers (greater than 2), the symbol represents a polytope in a generalized space having time-like as well as space-like dimensions.
The Tensile Deformation of Large Aluminium Crystals at Crystal Boundaries
Authors: Aston R. L.
Published: November 2008

The tensile deformation of single crystals of aluminium was examined by Taylor and Elam, using test-pieces composed of one crystal only. Miss Elam kindly supplied the author with a test-piece containing three large crystals, and an investigation of the effect of the constraint at the crystal boundary was carried out upon it as described below.
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.
On the projection of irregular linearly measurable plane sets of points
Authors: Gillis J.
Published: November 2008

1. Elsewhere I have expressed the opinion that a linearly measurable plane set of points, of upper density ½, has zero projection (i.e. projection of measure zero) on almost all directions. Though unable to prove this I have there managed to obtain a partial result. I would not attempt to guess to what extent this is true of a general irregular linearly measurable plane set; these sets are not amenable to the methods used in the case of those of upper density ½, the latter having a remarkable and simple structure. It is a quite trivial matter to construct an irregular set, of upper density 1, with positive projection on some one direction; and from it we can deduce another such set with positive projections on a denumerable every-where-dense set of directions. But, working on a suggestion due to Mr Besicovitch, I have obtained an irregular linearly measurable plane set, of upper density 1, with positive projection on a set P of directions, where the members of P in any sector have cardinal t, though P has measure zero. It may be that the set of points has positive projection on directions other than those of P, but there are no obvious indications of any such directions.
Torsion of beams of ⊥- and ∟- cross-sections
Authors: Seth B. R.
Published: November 2008

The problem of the torsion of beams of ⊥- and L-cross-sections has received attention from very few authors despite its important technical applications. The first mathematical solution in this connection was obtained by F. Kötter in 1908 for an L-section both of whose arms are infinite. He attacked the problem by the use of the known solution of the rectangle and by application of the scheme of conformal transformation. Kötter's method, however, does not lend itself readily to the solution of the problem involving more than one re-entrant angle. The first solution for the torsion of a beam whose cross-section is a rectilinear polygon of n sides was published in 1921 by E. Trefftz who also applied his method to an infinite L-section. Recently I. S. Sokolnikoff has suggested a more general method depending upon the fundamental theorem of potential theory that a harmonic function is uniquely determined by the values assigned along the boundary of the region within which the harmonic function is sought, the boundary condition and the region being subject to certain well-known assumptions of continuity, connectivity, etc. As an illustration of his method he has given an approximate solution for a ⊥-section whose flange and web are both infinite.
On isolated singularities of surfaces which do not affect the conditions of adjunction (Part I.)
Authors: Du Val Patrick
Published: November 2008

By an isolated singularity of an algebraic surface in [r] (i.e. space of r dimensions) I shall mean one which not merely is not upon any branch of a multiple curve of the surface, but has also the property that when the surface is projected into [3] from a general space [r − 4] the singular point remains in isolation, i.e. no branch of the double curve created by the projection will of necessity pass through it.
A Note on the Vorticity-Transport Theory of Turbulent Motion
Authors: Goldstein S.
Published: November 2008

1. G. I. Taylor has lately* pointed out how his vorticity-transport theory of turbulent motion may be extended to three dimensions. Of the typical term expressing the effect of turbulence on the mean motion he remarks: “In general it is so complicated that it is of little practical use, but in certain special cases considerable simplifications may occur.” In the special cases which he himself discussed the mean velocity was in the direction of the axis of x, and its magnitude was a function of y only, (x, y, z) being rectangular Cartesian coordinates.
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 being

and 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

Two 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.
On the Distribution of the Error of an Interpolated Value, and on the Construction of Tables
Authors: Fisher R. A. , Wishart J.
Published: November 2008

Before the introduction of interpolation formulae, beyond linear interpolation by proportional parts, the presentation of the numerical values of mathematical functions was much restricted, for the labour of computation and the cost of printing, to say nothing of the inconvenience of handling a bulky volume, had to be increased quite disproportionately with every increase in accuracy. A four-figure logarithm table occupies two small pages, Chambers's seven-figure table takes 150 pages, while Vega's ten figure table requires 300 pages twelve inches long.
The Absorption and Reduction in Velocity of β-rays on their passage through matter
Authors: Madgwick E.
Published: November 2008

The early experiments of Lenard(1), Leithauser(2), and Becker(3) on cathode rays led to the exponential law of absorption; those of Rutherford(4), Schmidt(5) and Hahn and Meitner(6) on β-rays indicated that the rays from some radioactive bodies were absorbed exponentially and that those from others were not. It was considered by Hahn and Meitner that the exponential law of absorption was an indication of the homogeneity of the rays. It was found also that the exponential law was not disturbed by the thickness of radiating material and this led to the conclusion that the rays are not appreciably reduced in velocity on their passage through matter. The theories of McClelland(7) and Schmidt(8) attributed the absorption to the stoppage of particles in mid-career.
The Quantum Theory of electronic scattering by Helium
Authors: Mott N. F.
Published: November 2008

The problem of the collision between an electron and an atom was first considered on the Quantum theory by Born, who has worked out in detail the case of atomic hydrogen, and has obtained formulae giving the variation of scattering with angle both for elastic and inelastic collisions. Born's solution is only approximate. The purpose of this note is to discuss the physical nature of the approximations used by him, and also to extend his results to Helium, for which experimental evidence is now available. It is found that the theoretical curve agrees with the experimental as well as the approximations used would lead one to expect. We shall confine ourselves to elastic collisions.
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 usual

and

where 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
Some electrical properties of liquid sulphur
Authors: Black D. H.
Published: November 2008

1. The conductivity of liquid sulphur is found to vary with the temperature in a similar manner to that in which the viscosity varies.

2. The conduction is electrolytic in character.

3. There is a definite E.M.F. of polarisation.
The number of β-particles from Radium E
Authors: Emeléus K. G.
Published: November 2008

Using an electrical counter, the number of α- and β-particles from a source of Radium D, Radium E and Radium F in equilibrium has been measured: it has been found that after correction for reflection at the source, their numbers were about equal. According to previous work on their absorption, the β-particles from Radium D would not be recorded under the conditions of these experiments. On this assumption the observed β-radiation was due to disintegration of Radium E, and since this was in equilibrium with Radium F, it follows that about one β-particle is emitted per disintegrating atom of Radium E.
The Atomic Number of a Radioactive Element at the moment of emission of the γ-rays
Authors: Ellis C. D. , Wooster W. A.
Published: November 2008

It is well known that the β-ray type of disintegration is usually accompanied by the emission of γ-rays, and it is a matter of great importance to decide which of these two phenomena occurs first, that is, whether the γ-rays are emitted before the nucleus disintegrates or afterwards. It is not practicable to attempt a direct solution of this problem, but since the emission of the disintegration electron results in a change of the nuclear charge of + 1 it would be sufficient to determine the atomic number of the radioactive body at the moment of emission of the γ-rays. For instance, an atom of the β-ray body radium B has an atomic number 82, but after disintegration when it becomes radium C it has an atomic number 83, so that if the γ-rays were known to be emitted from a body of atomic number 82 it would mean that they were emitted before the disintegration, whereas if the atomic number 83 were found it would show that they were emitted afterwards.
Some Particular Line-systems of Higher Space
Authors: Todd J. A.
Published: November 2008

The tetrahedral complex of lines in space of three dimensions may be defined as the aggregate of lines which meet four given planes in a range of points which is related to some fixed range. In the present paper we consider the more general system of lines, in space of r dimensions ([r]), which meet a certain number k of given primes (or [r−1]) in a range of points which is related to some given range. The paper is divided into three parts. In the first part, after considering successively the cases r = 2, 3, 4, we proceed by an induction argument to the general case. The section following treats the matter from an algebraical point of view, and in it we obtain in a concise form expressions for the locus (when such exists) generated by the lines. In the final section the systems of lines are shown to arise naturally as projections of known configurations in higher space.
A Geometrical Study of the Hyper-Octohedral Group
Authors: Robinson G. de B.
Published: November 2008

The present paper is a companion to one which appeared in these Proceedings some months ago. Since that time the characteristics of the Hyper-Octohedral group of order 2n.n! have been calculated by Dr Alfred Young, who has kindly allowed me to make use of his results.
On the descriptive form of Taylor's theorem
Authors: Pollard S.
Published: November 2008

The particular form of Taylor's theorem considered states that: If ƒ(x)is n times differentiable at a thenwhere.
On Quantum Algebra
Authors: Dirac P. A. M.
Published: November 2008

For the purposes of atomic physics it has been found convenient to introduce the idea of quantities that do not in general satisfy the commutative law of multiplication, but satisfy all the other laws of ordinary algebra. These quantities are called q-numbers, and the numbers of ordinary mathematics c-numbers, while the word number alone is used to denote either a q-number or a c-number. Both q-numbers and c-numbers can occur together in the same piece of analysis, and even in the same equation, as numbers of the two kinds can be added together or multiplied. A c-number may, in fact, be regarded as a special case of the more general q-number. In the particular case when two numbers x; and y satisfy xy = yx, we shall say that x commutes with y. A c-number is assumed to commute with every number.
Note on the sum of an oscillating series
Authors: Verblunsky S
Published: November 2008

Consider the series

and let

The series

is not necessarily convergent. Suppose that its Poisson sum exists. This we denote by

The expression

when existent will be said to be the sum (, p) of the series (1).
Wave Propagation in Strings with Continuous and Concentrated Loads
Authors: Jeffreys Harold
Published: November 2008

The motion of a light string loaded with equal masses at regular intervals has been discussed by operational methods. It is found that the system, though possessing only a. finite number of degrees of freedom, shows most of the characteristic features of dispersion. The operator e−σx/c that occurs in the discussion of uniform continuous strings is found to arise as the limit of an operator defined wholly in terms of definite integration, and its interpretation involves a theorem analogous to Taylor's theorem, but apparently more general. There is no phenomenon analogous to the conduction of heat. Any irregularity in the distribution of mass, however, produces strong internal reflexion of the shortest waves, and may provide a mechanism for conduction.
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.
Operational Solution of Some Problems in Viscous Fluid Motion
Authors: Crossley A. F.
Published: November 2008

Most of the results of this paper have been given before by Professor T. H. Havelock, who obtained them by the solution of a difficult integral equation. The method used here is, however, much easier to handle than that given by Professor Havelock.
An Asymptotic Expansion for
Authors: Mulholland H. P.
Published: November 2008

In the theory of the specific heats of gases of diatomic molecules the function

plays 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 by

where R is the gram-molecular gas-constant and

the 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.
On the Connexion of a Certain Identity with the Extension of Conical Order to n Dimensions
Authors: Robb Alfred A.
Published: November 2008

1. In his book, A Theory of Time and Space, the writer showed that, contrary to the generally accepted view, the ideas of Congruence can be built up from purely ordinal considerations, provided that we do not confine ourselves to linear order, but admit what, for convenience, he has called Conical Order. This Conical Order is built up from the purely abstract asymmetrical relations of before and after and does not pre-suppose the existence of the cones which are used to illustrate it.
A Phase Diagram for Unimolecular Films
Authors: Lyons C. G. , Rideal Eric K.
Published: November 2008

According to the views which we expressed recently (Proc. Roy. Soc. 1929, 124 A, 322) the solid condensed, liquid condensed, expanded and vaporous types of unimolecular films on the surface of aqueous solutions are the two-dimensional analogues of the solid, liquid crystal or smectic, liquid and vapour states of bulk matter. The previously-unsuspected observation that the films show triple point phenomena supports these conclusions.
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, then

provided 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 by

where 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 transformation

greatly simplifies the problem, and some definite results can be obtained.
The surfaces whose prime-sections contain a
Authors: Bronowski J.
Published: November 2008

The surfaces whose prime-sections are hyperelliptic curves of genus p have been classified by G. Castelnuovo. If p > 1, they are the surfaces which contain a (rational) pencil of conics, which traces the on the prime-sections. Thus, if we exclude ruled surfaces, they are rational surfaces. The supernormal surfaces are of order 4p + 4 and lie in space [3p + 5]. The minimum directrix curve to the pencil of conics—that is, the curve of minimum order which meets each conic in one point—may be of any order k, where 0 ≤ k ≤ p + 1. The prime-sections of these surfaces are conveniently represented on the normal rational ruled surfaces, either by quadric sections, or by quadric sections residual to a generator, according as k is even or odd.
The distribution of quadratic forms in a normal system, with applications to the analysis of covariance
Authors: Cochran W. G.
Published: November 2008

Many of the most frequently used applications of the theory of statistics, such for example as the methods of analysis of variance and covariance, the general test of multiple regression and the test of a regression coefficient, depend essentially on the joint distribution of several quadratic forms in a univariate normal system. The object of this paper is to prove the main-relevant results about this distribution. As an application of these results, the theory involved in the method of analysis of covariance will be investigated.
On the extension of the Pflastersatz (Part II)
Authors: Kaufmann B.
Published: November 2008

In the first part of this paper I announced some new Pflaster theorems for arbitrary r-dimensional closed sets lying in the Euclidean space Rn. In § III I proved them for the special case of an r-dimensional closed set F linked (rel a neighbourhood U) with an (n – r – 1)-dimensional spherical cycle. I shall now prove these theorems in the general case of a quite arbitrary closed set F.
The β- and γ-radiation of RaC″
Authors: Devons S. , Neary G. J.
Published: November 2008

Absorption experiments have been carried out on the β- and γ-rays of RaC”. The range of the β-rays in aluminium corresponds to an energy limit of (1·95 ± 0·15) × 106 e.v.; the absorption coefficient of the γ-rays in copper corresponds to a fairly homogeneous radiation of quantum energy equal to (5 ± 1) × 106 e.v. The energy of disintegration is, within the limits of error, in agreement with the value 6·1 × 106 e.v. to be expected from the known energies of the other disintegrations in the RaC branches.
On the stability of crystal lattices. II
Authors: Misra Rama Dhar
Published: November 2008

On the assumption that the potential energy of the three cubic lattices of the Bravais type consists of two terms, an attractive one proportional tor−mand a repulsive one proportional tor−n,n>m,stability conditions are expressed in the form that two functions of the numbernshould be monotonically increasing. These functions have been calculated numerically forn= 4 to 15, and are represented as curves with the abscissan. The result is that the face-centred lattice is completely stable, that the body-centred lattice is unstable for large exponents in the law of force, and that the simple lattice is always unstable,—in complete agreement with the results of Part I.
The scattering of X-radiation by liquid helium II
Authors: Reekie James
Published: November 2008

The unusual physical properties of liquid He ii have led to considerable speculation concerning its internal structure. Since the entropy difference between the liquid and solid states tends to zero as the temperature approaches absolute zero, it appears that in the neighbourhood of zero temperature the liquid must have some kind of ordered structure, and London's theoretical investigations(1) indicated that the best agreement could be obtained with the observed energy and molecular volume by supposing the liquid to have a diamond lattice. On the basis of this work Fröhlich(2) then suggested that in the ordered state He ii possessed a diamond lattice, and that the disordering process consisted in an interchange of the atoms between this lattice and the vacant points of the body-centred cubic lattice from which the diamond lattice may be considered as derived.
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 are

These 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 form

where c g. of solute per 100 c.c. of solution is the concentration. It is shown that this equation can be written approximately

which 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 thermodynamics of crystal lattices
Authors: Born Max , Bradburn Mary
Published: November 2008

In previous papers by Misra(1) and by Born and Misra(2) lattice sums of the type required in discussing the stability of a cubic crystal of the Bravais type in which the forces are central have been calculated. In the investigation of the thermodynamic properties of crystals a more general type of lattice sum occurs, which involves the phases of the waves. In the present paper a method of calculating these sums is developed and tables are computed.
Double Row of Vortices with Arbitrary Stagger
Authors: Rosenhead L.
Published: November 2008

The investigations of von Karman dealing with the unsymmetrical double row of vortices in an infinite sea of liquid are well known. He found that the unsymmetrical double row is stable when, and only when, cosh2πa/b = 2, where 2a is the distance between the two rows and 2b is the distance between consecutive vortices on the same row. A detailed account of the stability of the Karman street and of the symmetrical double row has been given by Lamb, and it has been shown that the symmetrical double row is unstable for all values of the ratio a/b. The object of this paper is to investigate the stability of a double row of vortices of arbitrary stagger. We define a double row of stagger 2l to be the system formed by positive vortices at the points (2nb + l, a) and negative vortices at (2mb − l, − a), where m and n assume all integral values from − ∞ to + ∞. The vortices are thus neither exactly “in step” nor exactly “out of step.” When l = 0 the system reduces to the symmetrical double row and when the system is the unsymmetrical double row.