bluuebunny/crossref_metadata_2025 huggingface dataset:
Grammatically Judgments and Second Language Acquisition
Authors: Ellis Rod
Published: November 2008

This article takes a critical look at grammaticality judgment tasks in second language acquisition research. It begins by examining the theoretical assumptions that underlie grammaticality judgment tasks, pointing out that previous studies have reported considerable differences between the results obtained from grammaticality judgment tasks and from other, production-oriented tasks. A description of the design features of grammaticality judgment tasks that have been used to date is then provided. There follows an account of a small-scale study designed to investigate the nature of learner judgments. Twenty-one adult advanced Chinese learners of English were asked to judge sentences designed to test their knowledge of dative alternation. The results indicated that the learners rarely used the “not sure” option in the test. Eight of these subjects were then administered a reduced version of the original test as a think-aloud task 1 week later. The results showed that these learners were inconsistent in 22.5% of their judgments. The think-aloud protocols showed that they resorted to a variety of strategies in making judgments. The article concludes by arguing that grammaticality judgment tasks elicit a particular kind of performance that needs to be understood much more thoroughly before it is used as a basis for investigating second language acquisition.
Research Methods in Interlanguage Pragmatics
Authors: Kasper Gabriele , Dahl Merete
Published: November 2008

The article reviews the methods of data collection employed in 39 studies of interlanguage pragmatics, defined narrowly as the investigation of nonnative speakers' comprehension and production of speech acts, and the acquisition of L2-related speech act knowledge. Data collection instruments are distinguished according to the degree to which they constrain informants' responses, and whether they tap speech act perception/comprehension or production. A main focus of discussion is the validity of different types of data, in particular, their adequacy to approximate authentic performance of linguistic action.
Methods in Second Language Classroom-Oriented Research
Authors: Nunan David
Published: November 2008

In this article, the current state of second language classroom-oriented research is subjected to critical review. The article begins by providing a brief overview of aims and issues in classroom-oriented research, before focusing more specifically on methodological issues in research. The review is based on an analysis of 50 empirical investigations of teaching and learning. These studies are analyzed in terms of their rationale, the environment in which they were carried out, the design and method of data collection, and the type of analysis carried out on the data. In the final part of the article, the implications of the study for future classroom research are presented and discussed.
The Acquisition of Second Language Speech
Authors: Leather Jonathan , James Allan
Published: November 2008

From being a relatively neglected area in the study of second language learning, the acquisition of second language speech has emerged over the last decade as an important research field with a wide range of approaches; the traditions of articulatory, acoustic, perceptual, phonetic, phonological, and psycholinguists investigation contribute a rare interdisdplinarity to this area of linguistic inquiry. Current scholarly interest augurs well for future theoretical advances.
The Production of Word-Final Voiced Obstruents in English by L1 Speakers of Japanese and Cantonese
Authors: Edge Beverly A.
Published: November 2008

This study is a partial replication and extension of Eckman's (1981a) study on the production of English word-final voiced obstruents by native speakers of Japanese and Cantonese, in which he reported evidence of an interlanguage rule of schwa paragoge for Japanese speakers and one of terminal devoicing for Cantonese speakers. In the current study, data from subjects performing three tasks varying in the speech style elicited were compared to the broad transcription of English and to data from a comparison group of native speakers of English performing the same tasks. The inclusion of native speaker data allowed the identification of variants in non-native production as either interlanguage phenomena or native-like simplified or assimilated forms. Results showed that devoicing was significant for the Japanese subjects, as well as for the Cantonese subjects. In addition, the Japanese subjects approximated target variants significantly more often than the Cantonese subjects, raising questions about the sources of the variants observed.
Learnability and the Acquistion of Extraction in Relative Clauses andWh-Questions
Authors: Quintero Kate Wolfe
Published: November 2008

Learnability theory is an investigation of the cognitive principles that determine developmental stages and eventual success in language acquistion. The focus of this study is on the learning principles within learnability theory that account for developmental stages in adult second language acquisition. Three learning principles, cumulative development, continuity, and conservatism, predict a complex sequence of development in the acquisition of relative clauses andwh-questions in English. They predict an early no-prep stage, gradual development through two additional stages of greater embeddedness of the extracted noun, stranded before nonstranded prepositional structures, and the likelihood of resumption at early stages. These predictions are confirmed by data from previous studies and are further investigated in this study by means of elicited production data collected from 35 Japanese learners of English and 17 native speakers of English. The data show the expected stages of development and confirm the relevance of learning principles to a comprehensive theory of learnability in second language acquisition (SLA).
The Effect of Graphic Representation of Knowledge Structures on ESL Reading Comprehension
Authors: Tang Gloria
Published: November 2008

Research suggests that English as a second language (ESL) students take upwards of 5 years to acquire a level of proficiency in academic language that is comparable to their English-speaking peers. They are likely to be denied full access to school knowledge unless teachers help to bring about student content knowledge learning and second language acquisition simultaneously.
Grammaticalization in Second Language Acquisition
Authors: Dittmar Norbert
Published: November 2008

Singular

Nominative—Mein guter Freund, my good friend.
Genitive—Meines guten Freundes, of my good friend.
Dative—Meinem guten Freund, to my good friend.
Accusative—Meinen guten Freund, my good friend.

Plural

Nominative—Meine guten Freunde, my good friends.
Genitive—Meiner guten Freunde, of my good friends.
Dative—Meinen guten Freunden, to my good friends.
Accusative—Meine guten Freunde, my good friends.

Now let the candidate for the asylum try to memorize those variations, and see how soon he will be elected. One might better go without friends in Germany than to take all this trouble about them. I have shown what a bother it is to decline a good (male) friend; well this is only a third of the work, for there is a variety of new distortions of the adjective to be learned when the object is feminine, and still another when the object is neuter. Now there are more adjectives in this language than there are black cats in Switzerland, and they must all be as elaborately declined as the example above suggested. Difficult? Troublesome? (Mark Twain, ‘The Awful German Language,’ in Twain, 1879, pp. 271–272)
Why Does the Production of Some Learners Not Grammaticalize?
Authors: Perdue Clive , Klein Wolfgang
Published: November 2008

In this paper we follow two beginning learners of English, Andrea and Santo, over a period of 2 years as they develop means to structure the declarative utterances they produce in various production tasks, and then we look at the following problem: In the early stages of acquisition, both learners develop a common learner variety; during these stages, we see a picture of two learner varieties developing similar regularities determined by the minimal requirements of the tasks we examine. Andrea subsequently develops further morphosyntactic means to achieve greater cohesion in his discourse. But Santo does not. Although we can identify contexts where the grammaticalization of Andrea's production allows him to go beyond the initial constraints of his variety, it is much more difficult to ascertain why Santo, faced with the same constraints in the same contexts, doesnotfollow this path. Some lines of investigation into this problem are then suggested.
Auditory Memory and Perception in Younger and Older Adult Second Language Learners
Authors: Scott Mary Lee
Published: November 2008

This study compared younger and older adult monolingual English speakers and bilingual (English/Spanish) speakers on aspects of language learning aptitude, specifically, measures of auditory perception and memory span, in English and Spanish. Multivariate analyses of variance revealed no age difference in auditory memory span in English; however, both older and younger bilinguals performed better than monolinguals on these tasks. Younger subjects performed better than older subjects on measures of auditory perception in English. Older and younger monolinguals performed similarly on a measure of auditory memory span in Spanish, whereas younger monolinguals demonstrated more accuracy on Spanish perception tasks. The Spanish proficiency of the younger bilinguals far exceeded that of the older bilinguals, and their performance was better on measures of auditory memory and perception in Spanish even when differences in proficiency were statistically controlled. However, a comparison of subgroups of older and younger bilinguals showing a similar level of Spanish proficiency revealed that the performance of the older bilinguals approached fairly closely the performance of the younger subjects on the Spanish auditory memory and perception tasks.
The Effects of Age on the Rate of Learning a Second Language
Authors: Slavoff Georgina R. , Johnson Jacqueline S.
Published: November 2008

The present study evaluates the role of age on the rate of acquiring English as a second language in an immersion setting. Subjects were children with native languages typologically very different from English. The children arrived in the United States between the ages of 7 and 12 years and were tested on their knowledge of English grammatical morphology and syntax at different lengths of stay in the United States, ranging from 6 months to 3 years. Subjects' performance was predicted by the length of their stay in the United States and by gender, with females outperforming males. Age of arrival played no role in predicting subjects' rate of acquisition. Performance was very similar between two age groups examined (7–9– and 10–12-year-old arrivals) throughout the 3 years measured. The present results suggest that, on certain aspects of grammar, different-aged children acquire a second language during the first 3 years of acquisition at similar rates when their native language is very different in typology from the target language.
Dis-integrating Perspectives of Language Acquisition
Authors: Jacobs Bob
Published: November 2008

I wish to warn young men against the invincible attraction of theories which simplify and unify seductively.Ruled by the [reticularist] theory, we who were active in histology then saw networks everywhere[italics added].… This [reticularist theory] was admirably convenient, since it did away with all need for the analytical effort involved in determining in each case the course through the gray matter followed by the nervous impulse.It has rightly been said that the reticular hypothesis, by dint of pretending to explain everything easily and simply, explains absolutely nothing; and, what is more serious, it hinders and almost makes superfluous future inquiries regarding the intimate organization of the centers[italics added]. (Ramóny Cajal, 1989, pp. 303–337)
Repetition in Nonnative Speaker Writing
Authors: Reynolds Dudley W.
Published: November 2008

This paper presents an empirical study of repetition in expository essays written by 24 nonnative speakers (NNS) and 16 native speakers (NS) of English. Repetition is coded according to three categories: the degree of particular types of repetition, the interaction between instances of repetition, and the location of these interactions (Hoey, 1991). Four quantitative measures devised for this study show no significant differences between the two groups. A qualitative comparison of three essays from each group, however, shows that the NSSs do not match their degree of repetition to the development of the argument structure of the text in the same way as the NSs. These examples from NNS texts show that when considering the significance of repetition the content of what is being repeated is as important as the quantity.
The Effect of Discourse Markers on Second Language Lecture Comprehension
Authors: Flowerdew John , Tauroza Steve
Published: November 2008

This paper measures the effect of the presence or absence of discourse markers such as so, right, well, OK, and now on second language lecture comprehension. A control group viewed a video recording of an extract of a naturally occurring lecture, whereas an experimental group viewed the same extract, but with discourse markers deleted. The results clearly indicate that subjects comprehended the lecture better when discourse markers were included than when they were deleted. This finding contrasts with earlier research that suggested discourse markers play no significant role in comprehension. This contrast is interpreted as being due to differences in experimental procedures.
Input in an Institutional Setting
Authors: Bardovi-Harlig Kathleen , Hartford Beverly S.
Published: November 2008

This paper investigates the nature of input available to learners in the institutional setting of the academic advising session. The advisory session, an unequal status encounter that by nature is a private speech event and cannot be observed by other learners, provides a starting point for the investigation of real and perceived availability of input. Evidence for the realization of speech acts as well as appropriate content and form, positive evidence from peers and status unequals, the effect of stereotypes, and limitations of a learner's pragmatic and grammatical competence are factors that may influence the course of development of interlanguage pragmatics in the institutional setting.
A generalized Poisson bracket and an associated natural one-form
Authors: Sudbery A.
Published: November 2008

Starting from an arbitrary algebra in place of the algebra of smooth functions on a differentiable manifold M, we construct an algebra which generalizes the algebra of polynomial functions on T*M. We define a Poisson bracket on this algebra and show that it can be obtained from a natural one-form which generalizes the fundamental one-form on T*M.
On sequential versions of the generalized likelihood ratio test
Authors: Barbour Andrew D.
Published: November 2008

It is shown that the Wilks large sample likelihood ratio statistic λn, for testing between composite hypotheses Θ0 ⊂ Θ1 on the basis of a sample of size n, behaves as n varies like a diffusion process related to an equilibrium Ornstein-Uhlenbeck process, whenever the null hypothesis is true. This fact is used to construct large sample sequential tests based on λn, which are the same whatever the underlying distributions. In particular, the underlying distributions need not belong to an exponential family.
Contractions of rotation groups and their representations
Authors: Dooley A. H. , Rice J. W.
Published: November 2008

It is a classical result in the theory of special functions that Bessel functions are limits in an appropriate sense of Legendre polynomials. For example in (11), § 17.4, the following result is attributed to Heine:

such limiting formulae are also known for certain other special functions (cf. (1), (5)). Apart from their intrinsic interest, these formulae have been used in the theory of special functions to obtain product formulae, etc. for the limit function from those of the approximating sequence.
Conservation laws and null divergences
Authors: Olver Peter J.
Published: November 2008

For a system of partial differential equations, the existence of appropriate conservation laws is often a key ingredient in the investigation of its solutions and their properties. Conservation laws can be used in proving existence of solutions, decay and scattering properties, investigation of singularities, analysis of integrability properties of the system and so on. Representative applications, and more complete bibliographies on conservation laws, can be found in references [7], [8], [12], [19]. The more conservation laws known for a given system, the more tools available for the above investigations. Thus a complete classification of all conservation laws of a given system is of great interest. Not many physical systems have been subjected to such a complete analysis, but two examples can be found in [11] and [14]. The present paper arose from investigations ([15], [16]) into the conservation laws of the equations of elasticity.
Representation of tiled matrix rings as full matrix rings
Authors: Chatters A. W.
Published: November 2008

It can be very difficult to determine whether or not certain rings are really full matrix rings. For example, let p be an odd prime, let H be the ring of quaternions over the integers localized at p, and set

Then T is not presented as a full matrix ring, but there is a subring W of H such that T ≅ M2(W). On the other hand, if we take H to be the ring of quaternions over the integers and form T as above, then it is not known whether T ≅ M2(W) for some ring W. The significance of p being an odd prime is that H/pH is a full 2 x 2 matrix ring, whereas H/2H is commutative. Whether or not a tiled matrix ring such as T above can be re-written as a full matrix ring depends on the sizes of the matrices involved in T and H/pH. To be precise, let H be a local integral domain with unique maximal ideal M and suppose that every one-sided ideal of H is principal. Then H/M ≅ Mk(D) for some positive integer k and division ring D. Given a positive integer n. let T be the tiled matrix ring consisting of all n x n matrices with elements of H on and below the diagonal and elements of M above the diagonal. We shall show in Theorem 2.5 that there is a ring W such that T ≅ Mn(W) if and only if n divides k. An important step in the proof is to show that certain idempotents in T/J(T) can be lifted to idempotents in T, where J(T) is the Jacobson radical of T. This technique for lifting idempotents also makes it possible to show that there are (k + n − 1)!/ k!(n−1)! isomorphism types of finitely generated indecomposable projective right T-modules (Theorem 2·10).
A note on real H*-algebras
Authors: Cabrera M. , Martinez J. , Rodriguez A.
Published: November 2008

Complex (associative) H*-algebras were introduced and studied in detail by Ambrose[1]; it was proved that every complex H*-algebra with zero annihilator is the l2-sum of a suitable family of topologically simple complex H*-algebras and that the H*-algebras (H) of all Hilbert-Schmidt operators on any complex Hilbert space H are the only topologically simple complex H*-algebras. In a recent paper [2] Balachandran and Swaminathan observe that the reduction of the theory of real H*-algebras to the topologically simple case follows easily with minor changes of the complex argument, and they prove a theorem describing topologically simple real H*-algebras. This theorem can be equivalently reformulated as follows.
Asymptotic expansions of generalized Bernoulli polynomials
Authors: Weinmann A.
Published: November 2008

Asymptotic expansions of certain generalized Bernoulli polynomials are obtained, some in terms of elementary functions and others in terms of gamma functions and their derivatives. The latter results can also be written in terms of elementary functions, by using the known asymptotic expansions of the gamma functions, and the leading terms are obtained in this way. The results obtained give the asymptotic form of the coefficients occurring in all the usual central-difference formulae of the calculus of finite differences.
The integration of generalized hypergeometric functions
Authors: Barr G. E.
Published: November 2008

Let the generalized hypergeometric function of one variable be denoted by

where (a)m is the Pochhammer symbol ((1, 3)).
On some results involving Fox's H-function and Jacobi polynomials
Authors: Bajpai S. D.
Published: November 2008

In this paper we have evaluated an integral involving Fox's H-function and Jacobi polynomial and employed its particular cases to establish two expansion formulae for the H-function involving Jacobi polynomials.
Application of the E-operator to evaluate an infinite integral
Authors: Singh F.
Published: November 2008

1. The object of this paper is to evaluate an infinite integral, involving the product of H-functions, generalized hypergeometric functions and confluent hypergeometric functions by means of finite difference operators E. As the generalized hypergeometric function and H-function are of a very general nature, the integral, on specializing the parameters, leads to a generalization of many results some of which are known and others are believed to be new.
Extremum principles for a class of boundary-value problems
Authors: Arthurs A. M.
Published: November 2008

Maximum and minimum principles are developed for boundary-value problems with field equations T*Tφ + f(φ) = 0 in some region V, subject to φ = h(Tφ) on the boundary of V.
The volume of a lattice polyhedron
Authors: Macdonald I. G.
Published: November 2008

Let L be the lattice of all points with integer coordinates in the real affine plane R2 (with respect to some fixed coordinate system). Let X be a finite rectilinear simplicial complex in R2 whose 0-simplexes are points of L. Suppose X is pure and the frontier Ẋ of X is a Jordan curve; then there is a well-known formula for the area of X in terms of the number of points of L which lie in X and Ẋ respectively, namely

where L(X) (resp. L(Ẋ)) is the number of points of L which lie in X (resp. Ẋ), and μ(X) is the area of X, normalized so that a fundamental parallelogram of L has unit area.
Two-dimensional elliptic inclusions
Authors: Bhargava R. D. , Radhakrishna H. C.
Published: November 2008

The simple concept of minimum potential energy of the classical theory of elasticity, first applied to solve inclusion problems (1) by one of the authors (R. D. B.), who considered spherical and circular inclusions, has now been extended to solve elliptic inclusion problems. The complex-variable method of determining the elastic field, first enunciated by A. C. Stevenson in the U.K. and N. I. Muskhelishvili in the U.S.S.R., has been used to determine the elastic field in the infinite material (the matrix) around the inclusion. Strain energies are calculated. The equilibrium size of an elliptic inclusion of elastic (Lamé's) constants λ1 and μ1, differing from those of matrix, for which the constants are λ and μ, has been determined.

An independent check on the calculations has been made by testing the continuity of normal and shearing stresses. The results also agree with the known results for the much simpler case when inclusion and matrix are of the same material.
Rotating fluid masses in general relativity
Authors: Boyer R. H.
Published: November 2008

In what follows we shall derive some properties of the gravitational field of an isolated, axially symmetric, uniformly rotating mass of perfect fluid in a steady state, according to the general theory of relativity. Several exact models describing rotating fluids are known in Newtonian mechanics, the Maclaurin and Jacobi ellipsoids ((6)) being perhaps the most interesting. In general relativity, no such exact solution is known in its entirety, although Kerr ((4)) has exhibited a certain vacuum solution possessing features that one might expect of a space-time exterior to some rotating body. Throughout this paper we shall have Kerr's solution in mind. The question that we shall keep before us is whether a perfect fluid interior can be matched to any given exterior field. Our main results exhibit the class of all possible fluid boundaries, given the exterior field, and some relations between the pressure, density, 4-velocity, and interior metric tensor.
On the stability of two superposed fluids
Authors: Willson A. J.
Published: November 2008

The dispersion equation describing the character of the equilibrium of two viscous incompressible superposed fluids under the action of gravity is considered in detail. Approximations for extreme wave-numbers are obtained and exact numerical results for particular cases are given. The existence of certain secondary modes is also considered.
The Capture of Electrons by α-Particles
Authors: Webster H. C. , Rutherford E.
Published: November 2008

Davis and Barnes have recently reported new and unexpected phenomena concerning the capture of electrons by swift α-particles. A beam of α-particles from a polonium source was passed through a stream of electrons emitted from an oxide-coated filament and accelerated by a known voltage so as to move in directions roughly parallel to those of the α-particles. The α-particles were then deflected by a magnetic field, and finally fell on a zinc sulphide screen, where the scintillations were counted. If any of the α-particles captured electrons while passing through the electron stream, they would fall on a different part of the screen, since the magnetic deflection is proportional to the charge. Any capture could thus easily be detected, and its dependence on the accelerating voltage examined.
Theory of Statistical Estimation
Authors: Fisher R. A.
Published: November 2008

It has been pointed out to me that some of the statistical ideas employed in the following investigation have never received a strictly logical definition and analysis. The idea of a frequency curve, for example, evidently implies an infinite hypothetical population distributed in a definite manner; but equally evidently the idea of an infinite hypothetical population requires a more precise logical specification than is contained in that phrase. The same may be said of the intimately connected idea of random sampling. These ideas have grown up in the minds of practical statisticians and lie at the basis especially of recent work; there can be no question of their pragmatic value. It was no part of my original intention to deal with the logical bases of these ideas, but some comments which Dr Burnside has kindly made have convinced me that it may be desirable to set out for criticism the manner in which I believe the logical foundations of these ideas may be established.
The bursting of soap-bubbles in a uniform electric field
Authors: Wilson C. T. R. , Taylor G. I.
Published: November 2008

The stability of a charged raindrop has been discussed mathematically by Lord Rayleigh. The case of an uncharged drop in a uniform electric field is perhaps of more meteorological importance but a mathematical discussion of the conditions for stability turns out to be very much more difficult in this case, owing to the fact that the drop ceases to be spherical before it bursts. Moreover it does not seem possible to express its geometrical shape by means of any simple mathematical expressions. On the other hand, by using a soap bubble instead of a water drop it was found possible to carry out experiments under well-defined conditions in this case, whereas experiments with Rayleigh's charged drop would be difficult.
The passage of electrons through small apertures
Authors: Lehmanna J. F. , Osgood T. H.
Published: November 2008

The velocities of electrons emerging through an aperture in an anode to which they were accelerated have been investigated.

The velocity distribution of electrons passing through holes ranging from 0·13 mm. to 3·24 mm. in diameter in a thin copper sheet is shown in Fig. 2. In this case the accelerating field between filament and anode was 204 volts.

Corresponding results for a capillary tube 0·40 mm. in diameter and 16 mm. long are shown in Fig. 3, where the curves are plotted for different accelerating potentials. Experiments were also made with shorter lengths, down to 5 mm., and with a tube 1·25 mm. in diameter. All the tubes investigated gave the same distribution of velocities of the electrons in the emergent beam, within the limits of error of the experiments.

In conclusion the authors wish to express their thanks to Sir Ernest Rutherford for his interest and advice during the course of the work.
On the Theory of Excitation by Collision with Heavy Particles
Authors: Mott N. F.
Published: November 2008

1. It has been shown, in a well-known paper by Born and Oppenheimer, that in evaluating the energy levels of a molecule, the nuclei may be treated as fixed, or slowly vibrating, centres of force. IfMbe the average mass of the nuclei, andmthe mass of an electron, the error involved in doing this is of order of magnitude (m/M)½. The possibility therefore of treating the nuclei as fixed depends on their great mass, compared with that of the electron.
A quantum mechanical theory of energy exchanges between inert gas atoms and a solid surface
Authors: Jackson J. M.
Published: November 2008

The interaction between gas atoms and solid surfaces has been studied experimentally for many years. The first detailed study of the nature of this interaction was perhaps due to Knudsen, who in his classical researches introduced the idea of the accommodation coefficients for energy or momentum exchanges between gas atoms and a solid surface, when the gas atoms and the solid are at different temperatures or possess different mass motions. Knudsen and other investigators have given numerical values for these accommodation coefficients for various gases and solid surfaces, which seem to indicate that the accommodation coefficients are never small and are often of the order unity. This means that the gas molecules before reflection accommodate themselves almost completely to equilibrium with the temperature or motion of the wall. Before the recent work of Roberts referred to below, which has inspired this paper, no special precautions had been taken in the preparation of the wall surface, and as we now know the walls used by all previous investigators must have been completely covered with at least a mono-molecular film of gas. Thus the old observations of the accommodation coefficient do not determine it under precise conditions, and find in fact a value many times larger than that found by Roberts for the energy exchanges between the gas and a clean tungsten surface. For helium and metal with a dirty surface the value of the accommodation coefficient is some 6 times as large as the true value for the clean surface. The older values of the coefficients were so large that there were apparently grave difficulties in the way of any simple theory, but this is so no longer.
On some series of functions, (3)
Authors: Paley R. E. A. C. , Zygmund A.
Published: November 2008

We propose here to improve on two of the theorems given earlier, to prove some fresh theorems and to give the proof of Theorem XI stated without proof in the first part of the paper.
The general double integral problem in the calculus of variations
Authors: Gillespie R. P.
Published: November 2008

In a previous paper in these Proceedings the problem of the double integral

was discussed when the function F had the form

where

It is proposed in the present paper to extend the method to the general problem, where F may have any form provided only that it satisfies the necessary condition of being homogeneous of the first degree in A, B, C.
Incidence scrolls
Authors: Welchman W. G.
Published: November 2008

1. The work of this paper was undertaken with a view to finding out what ruled surfaces can be determined by incidences, i.e. generated by the lines which meet a certain set of spaces which I shall call a base. Such ruled surfaces I shall call incidence scrolls. In [3] the lines which meet three lines generate a quadric surface. In [4] it is easy to show that a base consisting of a line and three planes gives the general rational quartic scroll, while the lines which meet five planes in [4] give the general elliptic quintic scroll. One might be tempted to think that at least all the rational normal scrolls could be obtained as incidence scrolls by taking for base a suitable number of spaces containing directrix curves, but unfortunately there is a residual surface except in the case of the rational scrolls of general type and of those with a directrix line.
Note on Ramanujan's arithmetical function τ (n)
Authors: Hardy G. H.
Published: November 2008

In his remarkable memoir ‘On certain arithmetical functions’* Ramanujan considers, among other functions of much interest, the. function τ(n) defined by

This function is important in the theory of the representation of a number as a sum of 24 squares. In fact

where r24 (n) is the number of representations;

where σs(n) is the sum of the 8th powers of the divisors of n, and the sum of those of its odd divisors; and
Planar threefolds in space of four dimensions
Authors: Welchman W. G.
Published: November 2008

1. It is known that, in [3], a ruled surface of order n and genus p has in general a double curve of order ½ (n − 1) (n − 2) − p and genus ½ (n − 5) (n + 2p − 2) + 1, 2(n + 2p − 2) torsal generators, 2(n − 2)(n − 3) − 2(n − 6)p generators which touch the double curve, and triple points.
Surface motion of sputtered particles
Authors: Ditchburn R. W.
Published: November 2008

According to the Frenkel theory of adsorption, the first molecules striking a surface move about on it like a two-dimensional gas before finally being adsorbed. This surface motion has been demonstrated by Estermann and by Cockcroft in the case of vaporised cadmium.
On the polarisation of mercury lines emitted from a discharge tube in a magnetic field
Authors: Skinner H. W. B.
Published: November 2008

1. Polarisation measurements are described on the Hg lines λ 4358, 5461, 5770, 5791 emitted from a low-pressure electron-maintained arc to which a longitudinal field of up to 3000 gauss may be applied.

2. Two types of polarisation effect have been found. The first is typified by the line λ 5461. It is a polarisation of the light with the electric vector perpendicular to the lines of force. Its maximum value is 9% but it decreases to zero (a) with decreasing field strength and (b) with decreasing current in the tube. It is suggested that this effect is due to a self-reversal of λ 5461 owing to the metastability of the 2 3p2 state and that the polarisation may be caused through a slight non-uniformity of the magnetic field.

The second type of effect is found for λ5770 and 5791. The polarisation is in a plane parallel to the discharge, and is found in a zero magnetic field. This effect is further discussed elsewhere. The line λ 4358 is unpolarised under all conditions tried.

3. Neither of these effects implies a polarisation of the total light emitted directly from atoms in the Transverse Zeeman Effect when the atoms are excited under isotropic conditions and the experiments give definite evidence against the existence of such a polarisation effect.
The adsorption of hydrogen on tungsten
Authors: Roberts J. K.
Published: November 2008

A method for studying the adsorption of hydrogen on a clean tungsten surface has been developed which depends on the fact that the accommodation coefficient of neon is different for a bare surface and for a surface with an adsorbed film on it.

It has been shown that on a bare tungsten surface, saturation occurs at a partial pressure of hydrogen of 4.10−4 mm. of mercury and probably much lower, so that the adsorption is of the nature of chemi-sorption.

Important deductions can be drawn concerning the process of activation if any for this chemi-sorption of hydrogen on a bare tungsten surface.

The accommodation coefficient of neon with a tungsten surface covered with a hydrogen film of the type investigated is 0·17 at 295°K, and 0·32 at 79°K.

The experiments described were carried out during my tenure of a Moseley Studentship at the Cavendish Laboratory, and I should like to thank Lord Rutherford for his interest in the work and the Council of the Royal Society for their continued support. I should also like to thank Professor Rideal for his interest in the results.
On the regularity of surfaces, III
Authors: Roth L.
Published: November 2008

1. In two previous papers the regularity of non-singular surfaces in higher space was investigated by geometrical methods based on theorems which are themselves deducible by algebraic-geometrical methods. Among the results obtained, one of the most important was a consequence of the following theorem, due to Severi:
The 6 × 6 Latin squares
Authors: Fisher R. A. , Yates F.
Published: November 2008

The problem of the enumeration of the different arrangements of n letters in an n × n Latin square, that is, in a square in which each letter appears once in every row and once in every column, was first discussed by Euler(1). A complete algebraic solution has been given by MacMahon(3) in two forms, both of which involve the action of differential operators on an expanded operand. If MacMahon's algebraic apparatus be actually put into operation, it will be found that different terms are written down, corresponding to all the different ways in which each row of the square could conceivably be filled up, that those arrangements which conflict with the conditions of the Latin square are ultimately obliterated, and those which conform to these conditions survive the final operation and each contribute unity to the result. The manipulation of the algebraic expressions, therefore, is considerably more laborious than the direct enumeration of the possible squares by a systematic and exhaustive series of trials. It is probably this circumstance which has introduced inaccuracies into the numbers of 5 × 5 and 6 × 6 Latin squares published in the literature.
On the Resistance to the Rotation of a Disc Immersed in a Fluid
Authors: Goldstein S.
Published: November 2008

The motion of a fluid due to the rotation of an immersed plane disc about an axis perpendicular to itself is turbulent if ωa2/ν is greater than about 105, where ω is the angular velocity of the disc, a its radius, and ν the kinematic viscosity of the fluid. The torque opposing the rotation, due to the surface friction of the fluid, was calculated originally by Kármán, both when the motion of the fluid is steady and when it is turbulent.
A Connection between Correlation and Contingency
Authors: Hirschfeld H. O.
Published: November 2008

Let us consider a discontinuous bivariate distribution. That is, let us consider N × Q non-negative values pνq (ν = 1, 2, …, N; q = 1, 2, …, Q), being the theoretical probabilities of the νth value of a variate Xμ (μ = 1, 2, …, N) concurring with the qth value of a second variate Ys (s = 1, 2, …, Q).
Discussion of Probability Relations between Separated Systems
Authors: Schrödinger E.
Published: November 2008

The probability relations which can occur between two separated physical systems are discussed, on the assumption that their state is known by a representative in common. The two families of observables, relating to the first and to the second system respectively, are linked by at least one match between two definite members, one of either family. The word match is short for stating that the values of the two observables in question determine each other uniquely and therefore (since the actual labelling is irrelevant) can be taken to be equal. In general there is but one match, but there can be more. If, in addition to the first match, there is a second one between canonical conjugates of the first mates, then there are infinitely many matches, every function of the first canonical pair matching with the same function of the second canonical pair. Thus there is a complete one-to-one correspondence between those two branches (of the two families of observables) which relate to the two degrees of freedom in question. If there are no others, the one-to-one correspondence persists as time advances, but the observables of the first system (say) change their mates in the way that the latter, i.e. the observables of the second system, undergo a certain continuous contact-transformation.
The Two Centre Problem in Wave Mechanics
Authors: Baber W. G. , Hassé H. R.
Published: November 2008

This problem, in the particular case of the hydrogen molecular ion, is so well known that a detailed reference to the large number of papers dealing with it is unnecessary. The investigations to which chief reference is made will be found at the end of this paper.
The pedal planes of a tetrahedron
Authors: Grace J. H.
Published: November 2008

The locus of a point the feet of the perpendiculars from which on the faces of a tetrahedron are coplanar is known to be a cubic surface having nodes at the corners: the pedal planes, by which I mean planes containing the feet of four perpendiculars, do not seem to have been much discussed. I propose to prove two theorems concerning them and make some remarks on their envelope.
Simplexes and other configurations upon a rational normal curve
Authors: White F. P.
Published: November 2008

The theorem that if two triangles be inscribed in a conic their six sides touch another conic is, of course, to be found in all the text-books; it is apparently due in the first place to Brianchon. The further remark, that if three triangles be inscribed in a conic the three conics obtained from them in pairs have a common tangent, is to be found in Taylor's Ancient and Modern Geometry of Conics; it was made independently by Wakeford.
Notes on Spectrophotometry
Authors: Ditchburn R. W.
Published: November 2008

The source of light used as a background is an important factor in determining the convenience and accuracy of ultra-violet absorption work, etc. If a source of light of constant intensity is available, a direct comparison method can be used and it is only necessary to calibrate the plates. If the source of light is not constant in intensity, it is necessary to divide the light into two beams and use one to check the variations of intensity while the other goes through the absorbing substance or (during calibration) the reducing sector or wedge. This latter method requires much more complicated apparatus and if the variations in the source are at all large it becomes inaccurate. In addition to being constant in intensity a good background for ultra-violet absorption spectra should possess the following qualities:

(1) Most of the energy should be emitted in the form of a continuous spectrum.

(2) It is desirable to be able to use one photograph of the whole region to be investigated. For this purpose it is necessary that the variations of intensity in different parts of the spectrum should be small enough for it to be possible to arrange the exposure so that all parts of the spectrum are within the correct exposure range, i.e. it must not be necessary to over-expose any part in order to get a strong enough intensity at another wave-length.

The hydrogen continuous spectrum possesses both these qualities and is an excellent background for the region on the short wave-length side of 3200 A.U. It may be used for longer wavelengths, but the hydrogen secondary lines are apt to prove trouble-some unless a fairly large dispersion is used.
Slip in a crystal and rupture in a solid due to shear
Authors: Starr A. T.
Published: November 2008

The problem was suggested by Professor G. I. Taylor as being of interest and importance in the phenomena of rupture in a solid, due to the presence of a crack, and the slip in a crystal. In experiments on the distortion of a crystal of aluminium under a tensile stress the conclusion is reached that “…as far as these experiments go, the distortion of a crystal of aluminium under compression is of the same nature as the distortion which occurs when a uniform single-crystal bar is stretched. The distortion is due to slipping parallel to a certain crystal plane and in a certain crystallographic direction, and the choice of which of twelve possible crystallographically similar types of slipping actually occurs depends only on the components of shear stress in the material and not at all on whether the stress normal to the slip plane is a pressure or a tension.”
The Interaction of Excited Helium and Hydrogen Atoms
Authors: Jones H.
Published: November 2008

The work of Heitler and London has shown that the first order perturbation energies of two atoms taken as a function of the separation between the nuclei gives a fairly good description of the behaviour of the atoms with regard to possible molecular formation. For example, the dissociation energy of the hydrogen molecule calculated in this way is of the same order of magnitude as the accepted observed value, being in fact about 25% too small. The theory has been generalised by Heitler, and also by London and others, to the case where each atom contains many electrons, but detailed calculations do not appear to have been made for systems more complex than that of two hydrogen atoms.
The Upper Limits of Energy in the β-ray Spectra of Actinium B and Actinium C″
Authors: Sargent B. W.
Published: November 2008

Absorption curves in paper have been obtained for the β-rays of actinium (B + C) and actinium C′. Some inferences regarding the shape of their energy distribution curves have been drawn, and the ranges of the β-rays of actinium B and actinium C′ fix their maximum β-ray velocities at Hρ 3430 and 6140. The potency of the method is emphasized for elements which cannot be easily investigated directly in a magnetic spectrograph.

The γ-ray ionizations of actinium B and actinium C′ have been compared under the same conditions with the β-ray ionization of actinium C′.

In conclusion, the writer wishes to thank Professor Sir Ernest Rutherford for his kind interest in the work. Thanks are also due to Dr J. Chadwick and Dr C. D. Ellis for many valuable suggestions and discussions.
Note concerning the β particles of very small Energy emitted during Radioactive Transformation
Authors: Feather N.
Published: November 2008

A preliminary investigation is described in which a type of gold leaf source suitable for use with an expansion chamber is developed. Such a source is necessary for the detailed examination of β particles of energy less than about 50,000 electron volts by the Wilson method. Some results obtained with sources of radium D and thorium B + C of this type are presented in outline.

The writer would like here to acknowledge the help and encouragement he derived from many discussions with Professor Sir Ernest Rutherford and with Dr J. Chadwick during the course of the investigation, and further to express his thanks to Mr G. R. Crowe for assistance in the preparation of some of the sources.