bluuebunny/crossref_metadata_2025 huggingface dataset:
Instructional Strategies and SLA in Early French Immersion
Authors: Harley Birgit
Published: November 2008

Examining the role of instruction in second language acquisition (SLA) entails not only a specification of what aspects of SLA stand to be affected but also a clear conception of what is meant by instruction. In this paper the potential of various instructional strategies for promoting SLA among child second language (L2) learners is considered in relation to empirical findings in early French immersion programs. Several principles are proposed concerning the what, when, and how of code-focused L2 instruction in a communicatively oriented school-based acquisition context. These proposals need to be put to the test in further experimental research.
Erratum
Authors: Lantolf James P.
Published: November 2008

I would like to apologize to Robin Scarcella and Rebecca Oxford for an erroneous statement I made in my review of their book, The Tapestry of Language Learning. In the review I accused the authors of not referencing Vygotsky's seminal work, Thought and Language. Upon rereading the review, I suddenly realized that the authors do indeed cite the first volume of Vygotsky's collected works which includes his Thought and Language.
Negative Feedback in Child NS-NNS Conversation
Authors: Oliver Rhonda
Published: November 2008

This paper reports on a study that examines the pattern of interaction in child native speaker (NS)–nonnative speaker (NNS) conversation to determine if the NSs provide negative feedback to their NNS conversational partners. It appears that just as children are able to modify their input for their less linguistically proficient conversational partners in first language acquisition (Snow, 1977), so too are children able to modify their interactions for NNS peers in the second language acquisition process and, in doing so, provide negative feedback. Two forms of NS modification were identified in this study as providing reactive and implicit negative feedback to the NNS. These were (a) negotiation strategies, including repetition, clarification requests, and comprehension checks, and (b) recasts. The results indicated that NSs respond differentially to the grammaticality and ambiguity of their NNS peers' conversational contributions. Furthermore, NS responses (negotiate, recast, or ignore) appeared to be triggered by the type and complexity of NNS errors, although it was more likely overall that negative feedback would be used rather than the error ignored. Additionally, evidence suggested that negative feedback was incorporated by the NNSs into their interlanguage systems. This indicates that not only does negative evidence exist for child second language learners in these types of conversations, but that it is also usable and used by them in the language acquisition process.
Using Time-Series Research Designs to Investigate the Effects of Instruction on SLA
Authors: Mellow J. Dean , Reeder Kenneth , Forster Elizabeth
Published: November 2008

This paper argues that the study of second language acquisition theory and pedagogy can be enhanced through the use of time-series research designs. As quasi-experiments, time-series designs have features that improve internal validity. In addition, because these designs only require a small number of subjects, they are very practical, encouraging a greater number of empirical investigations of the many claims within the field and permitting the use of authentic measures that have high construct validity. The longitudinal nature of the designs also enhances construct validity, potentially yielding new insights into the effects of instruction on SLA. The designs utilized in two time-series studies (Kennedy, E., 1988, The Oral Interaction of Native Speakers and Non-Native Speakers in a Multicultural Preschool: A Comparison between Freeplay and Contrived NS/NSS Dyads, unpublished master's thesis, University of British Columbia, Vancouver; Mellow, J. D., 1996, April, A Longitudinal Study of the Effects of Instruction on the Development of Article Use by Adult Japanese ESL Learners, unpublished manuscript, University of British Columbia, Vancouver) are reviewed in order to illustrate the design features, the questions that may be investigated, and the issues that are raised in interpreting data.
The effects of L1 orthography on L2 word recognition: A study of American and Chinese learners of Japanese
Authors: Chikamatsu Nobuko
Published: November 2008

This paper examines the effects of a first language (L1 ) orthographic system on second language (L2) word recognition strategies. Lexical judgment tests using Japanese kana (a syllabic script consisting of hiragana and katakana) were given to native English and native Chinese learners of Japanese. The visual familiarity and length in test words were controlled to examine the involvement of phonological or visual coding in word recognition strategies. The responses of the English and Chinese subjects were compared on the basis of observed reaction time. The results indicated that (a) Chinese subjects relied more on the visual information in L2 Japanese kana words than did English subjects and (b) English subjects utilized the phonological information in Japanese kana words more than did Chinese subjects. Accordingly, these findings demonstrate that native speakers of English and Chinese utilize different word recognition strategies due to L1 orthographic characteristics, and such L1 word recognition strategies are transferred into L2 Japanese kana word recognition.
An oscillographic study of the production of X-rays by a Coolidge tube
Authors: Crowther J. A.
Published: November 2008

Radiologists have often had cause to note certain apparent anomalies in the behaviour of their apparatus. It is quite well known that different X-ray tubes, excited by different kinds of high tension apparatus, yield X-radiation of markedly varying quality and quantity even under conditions which, as measured by spark gap and milliammeter (the usual measuring instruments of the radiologist), are apparently identical. These anomalies seemed to offer an interesting field for investigation, and one which might not be without value on the practical side.
Jordan algebras spanned by Hermitian elements of a Banach algebra
Authors: Bonsall F. F.
Published: November 2008

The Vidav–Palmer theorem [(11), (5), (2) (p. 65)] characterizes C*-algebras among Banach algebras in terms of the algebra and norm structure alone, without reference to an involution, in the following way. Let B denote a complex unital Banach algebra, and let Her (B) denote the set of Hermitian elements of B, that is the elements of B with real numerical ranges. In this notation, the Vidav–Palmer theorem tells us that if

then B is isometrically isomorphic to a C*-algebra of operators on a Hilbert space, with the Hermitian elements corresponding to the self-adjoint operators in the C*-algebra.
Canonical extensions for embeddings of topological spheres of any codimension
Authors: Brakes W. R.
Published: November 2008

Given any embedding f:Sr × Bn−r → Sn, f ∣ Sr × 0 can be extended to a homeomorphism of Sn, except when r = n − 2 and f is actually knotted (10). Is there any sense in which this extension can be chosen to vary continuously with respect to f? If r = n − 1, there certainly is: this is simply the canonical Schoenflies theorem, proved in varying (but equivalent) forms in (6), (5) and (1). One of the principal results of this paper provides an affirmative answer to this question when r < n − 1. In the usual fashion of such canonical extension theorems, we look for a local version; that is attempt to find a neighbourhood of the inclusion in E(Sr × Bn−r, Sn) on which a map F can be defined with each F(f) a homeomorphism of Sn which extends f and F (inclusion) = identity. Now if the neighbourhood is sufficiently small, any element of it can be viewed as an embedding Sr × Bn−r → Sr × Rn−r, still close to the inclusion, by removing a standard Sn−r−1 from the image space. There are known methods for extending such embeddings. It would not be hard to adapt Kister's methods (8) for extending embeddings of Bk in Rk canonically to homeomorphisms (approximately the method that is sketched for the r = n − 1 case in (5)). Alternatively the existence of a canonical extension in this situation follows explicitly from the more general Theorem 5 of (1). Unfortunately both methods extend the embedding in a ‘radial’ fashion, with the result that there is little control over the extension towards infinity, and the final homeomorphism cannot necessarily be further extended over the missing Sn−r−1 to yield a homeomorphism of Sn. In fact this failure is due to the extension map F, derived in either of these ways, being continuous with respect to the compact-open topology on the image space, H(Sr × Rn−r). The extension map to be constructed here is continuous with respect to the uniform topology on the image space, and so the homeomorphisms F(f) of Sr × Rn−r are bounded and can thus be extended over all of Sn by setting F(f) ∣ Sn−r−1 equal to the identity.
Magnetization curves of ferromagnetic single crystals
Authors: Lawton H.
Published: November 2008

Recent papers by Néel (8) and Lawton and Stewart (7) have provided an explanation of the process of magnetization in a single crystal, using the well-known ideas of the domain theory but bringing out the important role played by the demagnetizing field. These authors applied their ideas to two shapes of single crystals of iron, long rods and oblate spheroids, but in the latter case the only crystal orientation worked out in detail was that in which the equatorial plane was (100). The case of oblate spheroids of iron and iron-silicon where the equatorial plane is a (110) plane of the crystal, and the magnetic field is applied in this plane, are considered in detail in this paper. Calculations are made for In, the component of magnetization perpendicular to the applied field He, and comparison made with experimental measurements. This particular problem was considered by Bozorth and Williams (4) who calculated the torque per unit volume (i.e. the product InHe) experienced by the crystal in a magnetic field. Their calculations are, however, incomplete, because their picture of the magnetization process is not a valid one in moderate fields. Moreover, the demagnetizing field was taken into account only in assessing the size of the field H acting within the crystal, but not its direction.
Wave propagation in elastic rods with multiple wave speeds
Authors: Bachman R. C. , Cohen H.
Published: November 2008

This paper deals with the propagation and decay of nth-order displacement waves in linear hyperelastic rods having multiple wave speeds. The vector decay equation is integrated to find the explicit behaviour of all waves which can propagate in the rod. Examples are treated using a special form of the constitutive relations and results are given for rods of various geometries and wave multiplicities.
The cohomology of finite H-spaces as U(M) algebras III
Authors: Kane Richard
Published: November 2008

In the previous papers in this series (see (5) and (6)) we used Brown-Peterson theory to obtain necessary conditions for the mod p cohomology of finite H-spaces to be U(M) algebras. In this paper we will use connective K-theory to strengthen the main results of (6). We should mention that we will be assuming a general knowledge of the previous two papers from this series. The definitions and notation from these papers will be used freely. (In particular, the reader is directed to § 2 of (5) for the definition of a U(M) algebra.)
Stochastic integrals in an arbitrary probability gauge space
Authors: Barnett C. , Streater R. F. , Wilde I. F.
Published: November 2008

In § 7 of [1] we described how a stochastic integral of non-commuting process cesan be constructed. This was achieved via a Doob-Meyer decomposition for the square of a self-adjoint L2-martingale. We introduced a ‘condition D'’ derived from the lsquo;class D’ of stochastic process theory, and showed that if the square of a self-adjoint L2-martingale satisfies this condition then it has a decomposition of the Doob-Meyer type. The purpose of this paper is to extend the results of § 7 of [1] and to introduce another construction of the stochastic integral that does not employ condition D.
A product theorem for ideals over orders
Authors: Singer Michael
Published: November 2008

Fröhlich(1) has obtained certain invariants for modules over commutative separable orders over dedekind domains, whose values are ideals in the dedekind domain. In two particular applications he has shown that these invariants supply a criterion for a module over a given order to be projective ((1), Theorem 4), and another one for a fractional ideal to be invertible ((1), Theorem 5).
Topological aspects of the projective unitary group
Authors: Simms D. J.
Published: November 2008

1. Introduction. The group U(H) of unitary transformations of a complex Hilbert space H, endowed with its strong operator topology, is of interest in the study of unitary representations of a topological group. The unitary transformations of H induce a group U(Ĥ) of transformations of the associated projective space Ĥ. The projective unitary group U(Ĥ) with its strong operator topology is used in the study of projective (ray) representations. U(Ĥ) is, as a group, the quotient of U(H) by the subgroup S1 of scalar multiples of the identity. In this paper we prove that the strong operator toplogy of U(Ĥ) is in fact the quotient of the strong operator topology on U(H). This is related to the fact that U(H) is a principal bundle over U(Ĥ) with fibre S.
Spaces of cuts
Authors: Zabeeh Joan Gordon
Published: November 2008

Introduction. We will study here for normal T1 spaces the space of cuts—defined and analysed by Hurewicz (3) for separable metrizable spaces.
The principal bundle action in the Eilenberg-Moore spectral sequence
Authors: Barcus W. D.
Published: November 2008

In (2) the author determined a formula for computing, by means of the Eilenberg-Moore spectral sequence, the action of the group in a principal G-bundle, under the hypothesis that H*(G) be universally transgressively generated. This rather severe restriction was due to the method of proof, which used the theory of Guy Hirsch. Since Hirsch's work can be derived as a special case of Brown's twisted tensor products (3), one might hope to obtain the formula for the group action in the general case from the latter theory, and this we shall do (Theorem 1·2 below).
A nonstandard proof of the Riesz representation theorem for weakly compact operators on C(Ω)
Authors: Sun Yeneng
Published: November 2008

An easy way to construct the representing vector measures of weakly compact operators on C(Ω) is given by using the Loeb measure technique. This construction is not based on the Riesz representation theorem for linear functionals; thus we have a uniform way to treat the scalar and vector cases. Also the star finite representations of regular vector measures follow from the proof.
On the multiplicative structure of sections of vector bundles on an algebraic curve
Authors: Ballico E.
Published: November 2008

Here we study (in a more general setting) the following problem. Let C be a smooth projective curve, E and F vector bundles on C and V ⊆ H0 (C, E) (resp. W ⊆ H0 (C, F)) vector spaces generically spanning E (resp. F); find lower bounds for the dimension of the image of the multiplication map V ⊗ W → H0 (C, E ⊗ F) generalizing the case rank(E) = rank(F) = 1.
Concerning automorphisms in finitely generated Abelian groups
Authors: Liebeck H.
Published: November 2008

Of particular importance in the structure theory of finitely generated groups are those groups G having the property ℳd that for any two sets of generators g1, …, gd; h1, …, hd of G there is an automorphism θ of G such that (i = 1, …, d). Gaschütz(1) proved that all groups G having† ℳd also possess a further manifestation of symmetry, the property that if M and N are finite normal subgroups of G, any isomorphism between G/M and G/N can be induced by an automorphism of G. The case in which G is a finite p-group had previously been considered by Taunt (6) and Liebeck(2), who proved that for such groups the above property on the quotient groups of G is equivalent to ℳd.
On inequalities of the Tchebychev type
Authors: Kingman J. F. C.
Published: November 2008

1. A type of problem which frequently occurs in probability theory and statistics can be formulated in the following way. We are given real-valued functionsf(x),gi(x) (i= 1, 2, …,k) on a space(typically finite-dimensional Euclidean space). Then the problem is to set bounds for Ef(X), whereXis a random variable taking values in, about which all we know is the values of Egi(X). For example, we might wish to set bounds for P(X>a), whereXis a real random variable with some of its moments given.
Photographic plates for the detection of mass rays
Authors: Aston F. W.
Published: November 2008

The sensitivity of photographic plates to mass rays bears practically no relation whatever to their sensitivity to light. A short account is given of tests on the relative merits of different brands of plates since the first experiments on positive ray analysis. The process of improving the qualities of plates by schumannising is discusseci and details are given of the process found likely to give the best results. Success cannot be guaranteed even with the most careful manipulation, but if achieved yields plates of outstanding value for use in such methods of analysis as the mass-spectrograph.
A remark on metrically convergent series in F-spaces
Authors: Charsky H. M.
Published: November 2008

Let X be an F-space, not necessarily locally convex, with a quasi-norm ‖x‖ (see (7), p. 31). The series

of elements of X is commutatively convergent if and only if converges for every permutation {Yn}nεω of {Xn}nεω.
The general solution of the Low equation for KΛ-scattering
Authors: Lardner R. W.
Published: November 2008

A derivation is given of the general solution of the static baryon Low equation for KΛ-scattering. This model has previously been used by Low to indicate possible ambiguities in the terms elementary and bound-state as applied to particles. The solution derived here can be used to establish this result from a general viewpoint which may possibly be applicable to more realistic models.
The effect of heat transfer on boundary-layer growth
Authors: Brown S. N.
Published: November 2008

The effect of heat transfer on boundary-layer growth is considered for the problem of a main stream of small Mach number which is instantaneously released past a heated cylinder, or alternatively the cylinder is accelerated impulsively into a stream at rest. In particular the effect of different values of the given wall temperature on the interval to separation and the thickness of the boundary layer is investigated. It is found that the former is decreased and the latter increased by the presence of heat transfer.
The order-types of central series
Authors: Hartley B.
Published: November 2008

Let

be a series of type Ω of the group G. By this we mean that Ω is an ordered set (we shall always understand ‘ordered’ to mean ‘totally ordered’) and Λσ and Vσ are subgroups of G satisfying

(i) Vσ ◃ Λσ for all σεΩ,

(ii) Λσ ≤ Vτ if σ < τ

(iii) , where G−1 denotes the set of elements ≠ 1 of G and Λσ−Vσ the set of elements of Λσ not belonging to Vσ,

(iv) Vσ ≠ Λσ for all σ ε Ω.
The Problem of Relativity in reference to several bodies
Authors: Hargreaves R.
Published: November 2008

§ 1. If the kinetic potential for the relative motion of two masses is written with an added constant as

a close connexion with the relativity quadratic appears. The latter is in fact

where

a modification of the primary form

which shows an unaltered determinant. The condition in respect to the determinant, suggested, I believe, by Schwarzschild, is one which to me appears to give the most significant form to the results. From the dynamical standpoint we may regard it as imposing a counterpoise in the inertia coefficients to the modification introduced by the potential; or from a geometrical point of view we may regard it as minimizing the departure from the normal use of coordinates. An illuminating example of the loss of meaning that accompanies transformation in which this condition is disregarded is furnished by the isotropic form which is sometimes given to Einstein's quadratic.
The (2, 1) Correspondence
Authors: Vaidyanathaswamy R.
Published: November 2008

This communication is a sequel to a former paper on “The General (m, n) Correspondence” read before this Society in March, 1926*. It contained the general exposition (§ 1) and the theory of complete and closed sets (§ 2). For convenience these reference numbers will be here adopted, so that the present work, which opens with § 3, will be understood as a direct application of the previous sections.
On the Attenuation of Wireless Signals in Short Distance Overland Transmission
Authors: Ratcliffe J. A. , Barnett M. A. F.
Published: November 2008

1. It is pointed out that the signal strength of a wireless wave at a distant point depends on:

(a) the electrical constants of the ground,

(b) the curvature of the earth,

(c) the existence of an “atmospheric” ray coming downwards from the Heaviside layer.

2. We can eliminate the effect of (b) and (c), and so obtain direct evidence about the electrical constants of the ground, by making measurements near the transmitter.

3. Measurements on wave lengths of 300 m. and upwards give information about the resistivity of the ground, and on shorter wave lengths (15 m.) give the dielectric constant of the ground.

4. Attenuation measurements have been made over short distances for wave lengths of 1600 m. and 360 m.

5. The results are compared with those calculated from Sommerfeld's theory and show close correlation for distances beyond 10 wave lengths, but show deviations from the theory for shorter distances.

They give as values for the resistivity of the ground

p = 1·8 × 1013 E.M.U.

for the Daventry signals, and

p = 0·6 × 1013 E.M.U.

for the London signals.
In memory of the Rev. William Cecil, M.A., sometime Fellow of Magdalene College and Fellow of the Cambridge Philosophical Society
Authors: Yule G. Udny
Published: November 2008

Engineering is not, as some are mistakenly apt to imagine, a comparatively recent introduction into Cambridge curricula. Professor William Farish, B.D. of Magdalene, Jacksonian Professor and our first President, contributed the first paper in Vol. I of our Transactions, “On Isometrical Perspective,” a method of which he appears to be the inventor. The reason for the invention he explains. He was evidently teaching engineering—or applied mechanics—so he wanted numerous models of machines and “would have found it difficult to procure a warehouse large enough to contain them.” So he obtained a number of interchangeable parts: loose brass wheels all gearing together, pulleys, axles, bars and frames from which different models could be built up, in fact he invented the forerunner of Meccano and all its competitors. His assistants needed drawings showing them how to assemble the parts for these different models, and he devised this very simple and readily comprehensible method for making such drawings.
Note on some linear Diophantine inequalities
Authors: Oppenheim A.
Published: November 2008

1. Mordell has recently proved that if A, B, C, D, P, Q are any real constants such that Δ = AD − BC ≠ 0, and if ΔBC ≠ 0, then the inequalities

are satisfied by integer values of x and y.
On the Orthogonal Groups in Four Dimensions
Authors: Robinson G. de B.
Published: November 2008

Configurations of points in higher space have been known and studied for some time. In what follows we shall classify those configurations of points lying on the hyper-sphere in [4] which may be said to possess the group property. In this classification we shall seek to enumerate only those configurations which are essentially different from this point of view, in order to bring out any geometrical differences which might throw light on the fundamental problems of the theory of linear groups.
A Mathematical Theory of Natural and Artificial Selection. Part VII. Selection intensity as a function of mortality rate
Authors: Haldane J. B. S.
Published: November 2008

The assumption is often made that when competition is extremely intense at any stage in a life cycle, natural selection is bound to be intense also. This assumption will be examined quantitatively and it will be shown that the intensity of selection may diminish and become negative at high rates of elimination, while at its best its increase is extremely slow.
Note on the Lorentz group
Authors: Brill J.
Published: November 2008

The Lorentz group is denned by the equations

where the coefficients are subject to the conditions

It is an intransitive group possessing the single invariant
On Pedal Quadrics in Non-Euclidean Hyperspace
Authors: Gabbatt J. P.
Published: November 2008

1. The following are well-known theorems of elementary geometry: Given any euclidean plane triangle, A0 A1 A2, and any pair of points, X, Y, isogonally conjugate q. A0 A1 A2; then the orthogonal projections of X, Y on the sides of A0 A1 A2 lie on a circle, the pedal circle of the point-pair. If either of the points X,- Y describe a (straight) line, m, then the other describes a conic circumscribing A0 A1 A2, and the pedal circle remains orthogonal to a fixed circle, J; thus the pedal circles in question are members of an ∞2 linear system of circles of which the circle J and the line at infinity constitute the Jacobian. In particular, if the line m meet Aj Ak at Lt (i, j, k = 0, 1, 2), then the circles on Ai Li as diameter, which are the pedal circles of the point-pairs Ai, Li, are coaxial; the remaining circles of the coaxial system being the director circles of the conics, inscribed in the triangle A0 A1 A2, which touch the line m. If Mi denote the orthogonal projection on m of Ai, and Ni the orthogonal projection on Aj Ak of Mi, then the three lines Mi Ni meet at a point (Neuberg's theorem), viz. the centre of the circle J. Analogues for three-dimensional space of most of these theorems are also known ‖.
Cremona Transformations in Four Dimensions
Authors: Archbold J. W.
Published: November 2008

In view of the interest now taken in Cremona Transformations in more than three dimensions, some account seems desirable of such transformations in four dimensions. Many of the ideas in two and three dimensions are capable of immediate extension. In this paper attention is directed to the new possibilities in regard to the Principal and Fundamental Systems. The paper is written on the lines and with the notation of Miss Hudson's book.
The propagation of radio frequency currents along a wire of finite length
Authors: White F. W. G.
Published: November 2008

In the above paper it is pointed out that before we may use the usual wave equation for the propagation of current along a straight wire in free space it is necessary that (a) the inductance L and capacity C per unit length of the wire are independent of the current distribution and (b) that the product LC = 1/c2. This has been shown to be the case.

The inductance and capacity of an element of a conductor are defined generally in the way suggested by Moullin and it is shown that the radiation resistance term, which is a function of the current distribution, is small compared with the corresponding terms involving inductance and capacity. The usual wave equation is derived from Maxwell's equations for the case of a tubular conductor in which the current is a function of the distance z along the conductor only. If the curl of the current is not equal to zero this will not represent the true state of affairs.

It is pointed out in the earlier part of the paper that a complete solution of the problem, taking into account the radiation resistance, and the skin effect, involves the solution of an integral equation which is given.

The field about a tubular current, with a current distribution J0 sin kz along it, is examined. It is found that, for a long wire, the electric force is perpendicular to the surface at every point since we neglect the contribution from the ends. The magnetic force is in circles about the axis as would be expected.

A small component parallel to the current, and in phase with it, is introduced by the charges upon the ends of the tubular conductor, and this component determines the radiation resistance. From this it follows that the radiation resistance could be increased by placing a capacity on the ends—thus increasing the charges there.
On the combinatory scheme of analysis
Authors: Young L. C.
Published: November 2008

The following considerations form the basis of the work on generalised integrals with which I have been engaged for some years. Their intimate connection with Alexander's new notation for combinatory topology encourages me to publish them separately.
The weak lines in the natural β-ray spectrum of radium C
Authors: Ellis C. D. , Elliott H. H.
Published: November 2008

The β-ray spectrum of radium C is remarkable for the large number of faint lines of about equal intensity which occur aboveHρ 4900. These lines were first measured by Rutherford and Robinson and many of them were found again by Ellis in a reinvestigation of this spectrum. It was then stated that no attempt was made to check the existence of each faint line and that Rutherford and Robinson's measurements of the faint lines were taken over directly, with certain necessary adjustments to the absolute energies. Subsequently the intensities of the β-ray lines in this spectrum were measured by Ellis and Wooster and by Ellis and Aston and the faint lines were again treated in much the same way.
Some enumerative results for curves
Authors: Welchman W. G.
Published: November 2008

1. The problem of finding the number of space cubic curves which pass through p given points and have 6 – p given lines as chords has been solved by several different methods. The similar problem, in space of four dimensions, of the number of rational quartic curves which pass through p given points and have 7 – p given trisecant planes has been solved for p > 1 by F. P. White and for p = 1 by J. A. Todd. In a recent paper I discussed a similar problem for elliptic quartic curves. My present object is to apply the method of that paper to the problems mentioned above and to obtain two other sets of numbers which I believe to be new. They are (1) the number of rational normal quartic curves which have three assigned chords, pass through p assigned points, and have 3 – p assigned trisecant planes; (2) the number of curves of intersection of three quadrics in [4] which have a suitable number of assigned points and chords. The evaluation of Schubert symbols which occur in the work is done by means of a formula due to Giambelli‖. This formula is stated in a more simple form in a note at the end of this paper (7).
Modified ionic states in crystals
Authors: Snow C. P. , Rawlins F. I. G.
Published: November 2008

After a review of the magnetic and spectroscopic properties of compounds of the rare earth and of transitional elements of the first group, the types of bands in spectra of the latter are considered in detail. Reasons are advanced for the view that these are of “molecular” origin in ferric salts, but that the spectra of some transitional compounds contain lines which cannot be regarded in this way. Such lines are shown to be ionic, or quasi-ionic, and accord well with the suggestion of inter-combination transitions such as 4F—2G.

The theoretical intensity conditions, as a function of multiplet intervals, are in agreement with the observed appearance of intercombination transitions in Cr, and possibly also in Mn and Co. Similar considerations apply to the rare-earth spectra. As an example we have shown that the strong absorption in Pr and Nd compounds, and the much weaker lines found in Sa and Eu, are in perfect agreement with the theoretical prediction of intercombinations.
A mathematical theory of natural and artificial selection. Part IX. Rapid selection
Authors: Haldane J. B. S.
Published: November 2008

Equations (3) and (4) describe the changes undergone by a Mendelian population mating at random, and under intense selection.
The energy exchanges between molecules
Authors: Henry P. S. H.
Published: November 2008

The marked disagreement between the specific heats at high temperatures of the diatomic gases as found by sound velocity measurements, and those calculated from theoretical considerations, has for long been a source of perplexity to statistical mechanists; a perplexity all the greater in view of the simple nature of the theoretical calculations which appeared to form as direct a test of Boltzmann's hypothesis and the theory of band spectra as was possible to large scale measurements. One way out of the difficulty is to attribute the differences to the experimental difficulties inherent in the sound velocity method of measurement at high temperatures(1), but it cannot be denied that there is a certain measure of agreement between the separate velocity determinations. It consequently becomes necessary to examine the theory.
On surfaces of sectional genus four
Authors: Roth L.
Published: November 2008

1. The classification of surfaces whose sections are hyperelliptic has been given by Castelnuovo and that of surfaces with sectional genus π = 3 by Castelnuovo† and Scorza. For higher values of π the work is naturally more complicated and the possible types far more numerous, but the problem is simplified if we restrict ourselves to the investigation of surfaces without singularities, generally lying in space Sr (r > 3). In the present paper we obtain all such surfaces having sectional genus four.
The reflection of electrons from standing light waves
Authors: Kapitza P. L. , Dirac P. A. M.
Published: November 2008

It is well known that a beam of light falling on a reflecting mirror forms standing waves. This effect has been very beautifully made use of in Lippmann's colour photography process. The standing light waves, in this case, produce a periodic effect in the emulsion of the photographic plate which, when developed, scatters light and produces a similar colour effect. Instead of using a beam of light, it would seem possible to scatter electrons from the emulsion and obtain a reflection of electrons similar to that of a space grating. But it seemed to us that it would be of much greater interest to consider an experiment in which electrons are reflected from the standing waves of light. The direct scattering of free electronic waves by light has strictly never been observed, and it was thought possible that by this method, owing to the interference of the electrons and to the fact that the scattered electrons are focussed to one spot, the magnification of the phenomenon would be sufficient to make it observable. From the theory developed below, it will be seen that the experiment is just on the verge of possibility, and would be very difficult to carry out. The main interest of the experiment would come from the possibility of observing stimulated scattered radiation which up to the present has never been verified experimentally.
On the prior probability in the theory of sampling
Authors: Jeffreys Harold
Published: November 2008

1. If a class consists of n members of which r have the property φ, and we wish to estimate r by the process of sampling, the distribution of probability among values of r, given the composition of the sample, necessarily depends to some extent on our previous knowledge. This is expressed by saying that the prior probability of a particular value of r is f(r). According to Laplace's theory f(r) is constant. It is obvious that there are cases where the previous knowledge is such as to ensure that f(r) is not constant; but the question remains whether such cases should be considered the exception or the rule.
The reflexion of light at a surface covered by a monomolecular film
Authors: Strachan C.
Published: November 2008

The effect of a monomolecular film on the reflexion of light from a plane surface is considered. The film is treated as a two-dimensional assembly of scattering centres, and the possibility of molecular orientation is allowed for. Experimental results, when available, should indicate whether the scattering properties of groups of molecules in the “two-dimensional” state differ from those of molecules in bulk.
Reality distinctions for the rational twisted quartic
Authors: Telling H. G.
Published: November 2008

The problem of discriminating between the different real forms of the rational twisted quartic was first attempted by Adler in 1882. His catalogue is incomplete and some of his results are inaccurate, as has been pointed out by Richmond †. The work was however superseded by a paper in 1891 by Rohn‡ who considered the curve in relation to its allied Steiner quartic surface; his results may be compared with those given in the final section of this paper. Substantially the same results were obtained by Vietoris§ who mapped the curve on a conic by a somewhat different method from that used by Adler.
The algebraic surfaces contained by a cubic primal in four dimensions
Authors: Archbold J. W.
Published: November 2008

1. In this note we investigate, from a new point of view, some properties of cubic primals in [4]. These are enunciated by Fano as follows.
The scattering of electrons by nitrogen molecules
Authors: Massey H. S. W. , Bullard E. C.
Published: November 2008

This paper gives experimental results for the scattering of 4 and 2 volt electrons in nitrogen, which are compared with Stier's theoretical curves. An approximate theory of the scattering of electrons in nitrogen is given which is applicable when the wave length of the electron is small compared to the internuclear distance. The results are compared with experiment.
Extension of a set of theorems in circle geometry
Authors: Grace J. H.
Published: November 2008

The fascinating chain of theorems due to Clifford and recently extended by Mr F. P. White originates in the elementary fact that the circumscribing circles of the triangles formed by four lines meet in a point. From a like simple germ, namely the fact that the centres of the above-mentioned circles lie on a circle, an infinite chain of theorems was first evolved by Pesci and may be enunciated as follows:

(i) The centres of the circumcircles of the triangles formed by four lines lie on a circle; thus from four lines we derive a point, namely the centre of the latter circle.

(ii) Five lines give five sets of four and the five derived points lie on a circle; thus from five lines we derive a point, namely the centre of the latter circle.

(iii) Six lines give six sets of five and the six derived points lie on a circle.
On chains of two-two relations and the theory of elliptic functions
Authors: Baker H. F.
Published: November 2008

1. The relation

in which we suppose each of a, b, c, a2 − c2 to be different from zero, leads, from a value θ, to two values of φ, which we may denote by θ1 and θ−1. Each of these, put in place of θ, leads, beside the value θ of φ, to another value of φ, say, respectively, θ2 and θ−2. If θ2 or θ−2 be put for θ, the same relation leads to two values of φ, say, θ1 and θ3 or θ−1 and θ−3, respectively. And so on. It may happen that θn is the same as θ, in which case also θ−n is the same as θ; this we may express by saying that the relation is closed, or that there is closure, after n links. It is the object of the present note to express in reduced form, in terms of a, b, c, the condition that this may be so. Evidently, if n = pq, the condition of closure after n links is satisfied when the condition for closure after p links (or also after q links) is satisfied. But there is a condition for closure after n links which is not satisfied for any less number of links; this is the condition which we call the reduced or proper condition for closure after n links, and it is this which we seek to express.
The General (m, n) Correspondence
Authors: Vaidyanathaswamy R.
Published: November 2008

The present work is the outcome of a study of the special type of (3, 2) correspondence on a circle, namely that between a point and the extremities of its pedal line. This led to considering correspondences in general, and to the formulation of concepts which are believed to be new, for example the Canonical Forms, § 1 (2), and Multipliers, § 1 (3). The case of the (n, 1) correspondence has already been given by the author.
The Period of Decay of Radium B and Radium C
Authors: Bracelin P.
Published: November 2008

Measurements of the saturation currents produced between two parallel plates by a source of radium C of carefully tested purity have been performed by an accurate galvanometer method. From the results a transformation constant

has been assigned to radium C corresponding to a half-value period of 19·72±·04 minutes.

Similar measurements with radium active deposit have enabled a value to be estimated for the period of radium B between 26·7 and 26·8 minutes, which is the limit of accuracy of the experimental data.
The Cauchy property of the generalised Perron intergrals
Authors: Grimshaw M. E.
Published: November 2008

1. Saks calls an integral complete if it satisfies two conditions, of which one, the condition (C), is as follows.

If f(x) is defined in (a, b) and is integrable in each interval (a + ε, b − η), where a < a + ε < b − η < b, and

exists, then f(x) is integrable in (a, b) and the integral over (a, b) is equal to the above limit.
An extension of a fundamental theorem in the theory of surfaces
Authors: Pedoe D.
Published: November 2008

1. In a paper by Castelnuovo and Enriques the following fundamental theorem is proved:.

“An algebraic surface containing a linear system of curves of freedom r ≥ 0, genus π > 0, and grade n > 2π − 2 is necessarily scrollar.”
Some experimental investigations of the polarisation of downcoming wireless waves
Authors: Witty Roy
Published: November 2008

An account is given of experiments to determine the polarisation of downcoming waves of long wavelength, using the method devised by Ratcliffe and White. The results show that on the whole the polarisation is left-handed, although there is a tendency for right-handed polarisation in the region of 1500 metres.
On the Resolution of Cremona Transformations and particularly those of Genus One in Space of Three Dimensions
Authors: Babbage D. W.
Published: November 2008

In the first section of this paper we illustrate the use that can be made of higher space in dealing with the problem of resolving a given Cremona transformation into the product of simpler Cremona transformations. In the second section we restrict ourselves to a particular large but finite class of Cremona transformations of [3], those of genus one, and show that these can all be built up from the four following simple types:

(1) The bilinear transformation T3,3, determined by three equations bilinear in the coordinates of the two corresponding spaces; in the most general case of this both the direct and the reverse homaloidal systems consist of cubic surfaces passing through a non-degenerate sextic of genus three;

(2) Three transformations Tn, n (n = 2, 3, 4) in which the homaloidal surfaces may in each case be obtained by taking in [4] a primal V of order n which has two (n− l)ple points, and projecting on to a given [3] from one of these points the sections of V by primes through the other; for n = 2 we have the familiar quadroquadric transformation determined by quadrics through a conic and a point.
Phenomena Attending the Splashing of Water in an Electric Field
Authors: Gott J. P.
Published: November 2008

Owing to a chance observation some interesting phenomena were observed during the splashing of water in an electric field. If a water drop falls into water, there is a characteristic splash of which the details were investigated photographically by Professor A. M. Worthington in the latter years of the last century. The final account of this work was given in two papers (1) and also in a book entitled A Study of Splashes (2). The splash cannot be examined with the unaided eye because the various stages of the splash follow one another too quickly. For the moment it may be said that an important stage of the splash consists of the rising up of a cylindrical column of water to a considerable height. The radius of the column is comparable with the radius of the drop.
Some Experiments on the Slowing Down of Neutrons by Collisions with Hydrogen Nuclei
Authors: Westcott C. H. , Bjerge T.
Published: November 2008

The discovery of Fermi and his collaborators, that neutrons are much more readily captured by various atoms, e.g. silver, when their kinetic energies, originally of the order of 106 e.v., have been reduced by collisions with hydrogen nuclei, has been confirmed.

The process of slowing down of the neutrons has been studied in some detail, and the nuclear cross-section for collisions with hydrogen nuclei has been determined for the primary neutrons and for the slow neutrons which are readily captured by silver atoms.

The nature of the “gas” of slow neutrons was also discussed, but it was not found possible to reach a definite conclusion as to the energy of the neutrons concerned.
On Certain Integral Functions of Order 1 and Mean Type
Authors: Cartwright M. L.
Published: November 2008

1. The object of this note is to show the relation between certain results obtained by Wiener and Paley*, and by L'evinson from the theory of Fourier transforms, and a theorem which I proved in a recent paper. We require a general theorem on the function of Phragmèn and Lindelöf:
On the Structure of Abstract Algebras
Authors: Birkhoff Garrett
Published: November 2008

The following paper is a study of abstract algebras qua abstract algebras. As no vocabulary suitable for this purpose is current, I have been forced to use a number of new terms, and extend the meaning of some accepted ones.
On Canonical Threefolds
Authors: Roth L.
Published: November 2008

In a paper which is to be published shortly formulae have been obtained for the virtual characters of the system of surfaces cut out on a primal of S4, having ordinary singularities, by adjoint primals of any order; an account of the principal results has been given elsewhere. As a first application of these formulae we propose in the present paper to investigate the canonical systems belonging to various threefolds and thence to construct the canonical models which correspond to them.
An Illustration of the Space Representation of Circles
Authors: Grace J. H.
Published: November 2008

The circles in a plane can be represented by the points of space of three dimensions in such a way that the points (point circles) of the plane correspond to the points of a quadric Q in space and two orthogonal circles in the plane correspond to two points conjugate with respect to Q. An ∞2 system σ of circles in the plane corresponds to a surface S in space and the reciprocal Sσ′ of circles in the plane closely and reciprocally related to the system σ. So far as I know only trivial examples of such systems σ and σ′ have hitherto been noticed and my object is to direct attention to an illustration drawn from the modern geometry of the triangle which is less simple and perhaps more interesting.
The specific heat of water vapour and the theory of the dissociation of water vapour at high temperatures
Authors: McCrea W. H.
Published: November 2008

The following is an attempt to account theoretically for the observed specific heat of water vapour. The usual theory of the vibrational specific heat together with the theory of the dissociation of the H2O molecule at high temperatures is found to account satisfactorily for the observed facts. It is shown, also, that at temperatures near 100° C. there is an effect due to polymerisation.
On the Phragmén-Lindelöf Principle
Authors: Srivastava P. L.
Published: November 2008

In this short note my chief object is to prove the following theorem:

If

(1) f(z) is a regular function of z(= ρeiψ) in the angle |ψ| ≤ α, where ;

(2) f(z)= 0(eαρ), where K is a positive constant, throughout this angle;

(3) f(z) is not identically zero;

then

(4)

is a continuous function of ψ for |ψ| < α.