bluuebunny/crossref_metadata_2025 huggingface dataset:
An easy geometrical representation of the Sextic Covariant of a Binary Quartic
Authors: Milne William P.
Published: January 2009

The following is an easy method of representing geometrically the Sextic Covariant of a Binary Quartic which I have not seen given elsewhere. It was suggested to me by my work on Bi-Circular Quartics. The usual method of representing this Covariant is to regard the Quartic as four points on a conic, when the Sextic is represented by the intersections of the conic and the sides of the Harmonic Triangle of the Quadrangle whose vertices are the points of the given Quartic. The present method has the advantage of regarding the given Binary Quartic as a Tetrad of points on a straight line.
Two General Theorems in the Differential Calculus
Authors: Brash William
Published: January 2009

Theorem I. Let nαp denote

where Then for any change in the independent variable x,

say z = f(x), the coefficient of in is nαp.
On the expansion of in positive integral powers of z, when n is a positive integer
Authors: Edwardes F. E.
Published: January 2009

The radius of convergence of the power series is 2π.

The function is regular within a circle whose centre is the origin of the z plane and radius 2π, and can be expanded in a Taylor's series converging at all points within the circle.
Generalisation of the “Orthopole” and Allied Theorems
Authors: Third J. A.
Published: January 2009

The greater part of this paper consists of generalisations of well-known theorems regarding perpendiculars to the sides of a triangle, or other base-lines, the perpendiculars being replaced by isoclinals.
Notes on Mathematical Induction
Authors: Muirhead R. F.
Published: January 2009

Mathematical induction in its simplest form may be stated thus: Suppose there is a set of propositions p0, p1, p2…which are so related that the truth of pn implies the truth of pn+1 then if p0 is true, it follows that all the other propositions of the set are true. For since p0 is true therefore p2 is true, therefore p2 is true, and so on as far as we please.
A Geometrical Construction for the Rainbow Formula
Authors: Robertson David
Published: January 2009

Internal Reflections in a Sphere. A ray of light PQ (Fig. 1) incident at any point Q on the surface of a transparent sphere is partly reflected and partly refracted along QR1. At R1 it is partly reflected along R1R2, and partly emerges along R1s1. The same thing occurs at R2, R3, etc. on which the successive reflected portions fall. AB is the diameter parallel to the incident light, and OQ the radius to the point of incidence. Let μ denote the index of refraction of the material of the sphere relative to the surrounding medium. Divide OA in C so that OC : OA = 1 :μ
Note on a formula connected with Fourier Series
Authors: Macdonald H. M.
Published: January 2009

An expression for the sum of a series of terms which takes account of the different rates of oscillation of the functions involved is of importance for series such as occur in the problems of diffraction, and a relation of this kind has been given by Poisson. This relation can be written in the form

where Sm denotes the sum of m terms of the series Σun, beginning with the term un.
A Symbolic proof of Euler's Addition Theorem for Elliptic Functions
Authors: Saddler W.
Published: January 2009

§1. Let be a binary quartic; then I propose to show symbolically that the solution of Euler's differential equation

can be written in the form

where

are otherwise arbitrary.
Transverse Vibrations of an Elliptic Plate
Authors: Ghosh Jyotirmaya
Published: January 2009

Since the publication of the memoir of Mathieu on the transverse vibrations of an elliptic membrane, the subject has been discussed by many authors from different points of view. But the corresponding problem of the plate has received but little attention. Mathieu discussed the problem as early as 1869, but the method adopted is different from that followed in the present paper, the main object of which is to apply Whittaker's solutions of Mathieu's Equation to the problem of the elliptic plate. These solutions are really better suited for numerical calculations than the evaluation of infinite determinants.
Symbolical algebra and the quadrics containing a rational curve
Authors: Baker H. F.
Published: January 2009

In regard to the algebra of binary forms and the theory of rational curves there exists a wide literature, with which I am not well acquainted. Very possibly the simple remark made in this note is found elsewhere. But the note is a grateful echo of recent delightful colloquy with persons of good will.
Orthogonal Trajectories in Vectorial Coordinates
Authors: Craig James I.
Published: January 2009

The position of a point in a plane may be determined by its distances (r, ρ) from two fixed points which may be termed foci. These distances are termed vectorial coordinates. The determination is unique if attention is confined to the half-plane bounded by the line of foci. In certain cases where the properties of a curve are defined with respect to two points, representation of the curve by an equation between its vectorial coordinates possesses certain advantages. For example, the equation of the ellipse takes the extremely simple form r + p = 2α.
On Series for calculating Euler's Constant, and the Constant in Stirling's Theorem
Authors: Sanjana K. J.
Published: January 2009

Let γn denote the value of

where n is a definite integer; and let γ denote the limit of

when the integer k is indefinitely increased. It is known that the expansion of γn – γ in ascending powers of 1/n is

where B1, B3, B5… are the numbers of Bernoulli. The series (3) is, however, divergent, as B2r+1 not only increases indefinitely with r, but bears† an infinite ratio to B2r–1 in this case. It is proposed to find by elementary methods the expansion of γn – γ up to the term in nr and to estimate the error (of order l/nr+1) made in omitting further terms of series (3). I shall take the case of r = 9, but the process is quite general.
Historical Note on Wallace's Line
Authors: Archibald R.C.
Published: January 2009

In earlier volumes of the Proceedings of the Edinburgh Mathematical Society (cf. III., 104; IX., 83) it has been shown by researches of Dr. J. S. Mackay that the “discovery of the Wallace line … dates back only to about the year 1799 or 1800.” This result is reproduced in Cantor's Vorlesungen über die Geschichte der Mathematik (III., 542, 2te Aufl.). It was arrived at by considering the two following theorems given by Professor Wallace in the old series of Leybourn's Mathematical Repository:

Theorem A (Vol. I., p. 309 ; Vol. II., p. 54–5). If three straight lines touch a parabola, a circle described through their intersections shall pass through the focus of the parabola.
Note on the Geometries in which Straight Lines are represented by Circles
Authors: Sommerville Duncan M. Y.
Published: January 2009

In a recent paper read before the Society, Professor Carslaw gave an account, from the point of view of elementary geometry, of the well-known and beautiful concrete representation of hyperbolic geometry in which the non-Euclidean straight lines are represented by Euclidean circles which cut a fixed circle orthogonally. He also considered the case in which the fixed circle vanishes to a point, and showed that this corresponds to Euclidean geometry. The remaining case, in which the fixed circle is imaginary and which corresponds to elliptic or spherical geometry, is not open to the same elementary geometrical treatment, and Professor Carslaw therefore omitted any reference to it. As this might be misleading, the present note has been written primarily to supply this gap. It has been thought best, however, to give a short connected account of the whole matter from the foundation, from the point of view of analysis, omitting the detailed consequences which properly find a place in Professor Carslaw's paper.
Note on Gauss' Proof of the Reciprocity of Parallelism
Authors: Sommerville D. M. Y.
Published: January 2009

The proposition that if AA′‖BB′ then BB′‖AA′ appears at first sight so simple that it might be regarded as almost intuitive. This is because we already think of parallelism as a symmetrical relationship between two straight lines, in accordance with Euclid's definition of parallels as “straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.” If we take along with this definition Euclid's fifth postulate, or Playfair's equivalent, it defines a unique line through a given point parallel to a given line; but, without the postulate, it cannot be assumed to define more than a class of lines, and a stricter definition is required.
Some Graphical Methods for Determining Centres of Gravity
Authors: Muirhead R. F.
Published: January 2009

This method is associated with the well-known construction of a triangle equal in area to a given polygon.

In Fig. 1 let ABCDD1C1B1A be the polygonal circuit enclosing the area, and let DD1, be any side not adjacent to A.
On the continued fractions which represent the functions of Hermite and other functions defined by differential equations
Authors: Whittaker E. T.
Published: January 2009

The functions of Hermite, which are the same as the functions associated with the parabolic cylinder in harmonic analysis, may be defined* by the differential equation which they satisfy, namely,

where n denotes any constant.
Nicole's Contribution to the Foundations of the Calculus of Finite Differences
Authors: Tweedie Charles
Published: January 2009

While engaged in a study of the Methodus Differentialis of Jas. Stirling (1730) I have been struck by the fact that Nicole's Papers on the same subject, printed in the Memoires de l'Academie Royale des Sciences (Paris), appear to form a fitting prelude to the work published by Stirling. The dates of Nicole's Papers are 1717, 1723, 1724, 1727, and it is almost certain that Stirling was well acquainted with their contents, for he remarks on page 24 of the Methodus Differentialis:—“Hac de re primus quod sciarn egit D. Taylor in Methodo Incrementorum. Eadem etiam fusius et elegantissime traditur a D. Nicol in Actis Academiae Regiae Parisiensis.”
The Apolar Locus of Two Tetrads of Points on a Conic
Authors: Milne William P.
Published: January 2009

In Vol. XXXV. (Session 1916–17), Part I., of the Proceedings of the Edinburgh Mathematical Society, I discussed in considerable detail the properties of the Apolar Locus of two tetrads of points. I showed there that, subject to certain defined conditions, a unique quartic curve would be obtained, which would be the Apolar Locus of the two given tetrads. I mentioned, however, in §7 of the paper, that in the case when the two tetrads lie on the same conic, the above-mentioned conditions are not independent, and that, in fact, not a unique quartic but a pencil of quartics is obtained.
Quaternion Note on the Theory of Confocals
Authors: Knott C. G.
Published: January 2009

The object of this note is to draw attention to a simple extension of a well-known theorem concerning corresponding points on confocal ellipsoids–an extension which seems to have escaped notice. It has been familiar to me for years as an illustration of the quaternion treatment.
An Approximate Formula for the Length of an Arc of a Suspended Rope
Authors: Horsburgh E. M.
Published: January 2009

The length of an arc of a flexible rope or chain suspended in the catenary y = c cosh x/c is s = c sinh x/c when measured from the vertex, but the practical determination of s is troublesome, owing to the difficulty in finding the parameter c from the transcendental equation when the coordinates of the point of suspension are given. The importance of a formula such as Huygens' approximation to the length of a circular arc s = 2B+⅓(2B−A), where A is the chord of the arc and B that of half the arc, is due to the fact that one can scale directly these lengths by rectilinear measurements without requiring to find the central angle or to make any subsidiary calculations. Formulae of this nature applicable to the parabola, or to curves whose arcs might be replaced by parabolic arcs, would be useful in the design of structural works dealing with ropes or chains. In such cases, as the dip is frequently less than one-eighth of the space, the catenary may be replaced by a parabola.
The Stirling Numbers and Polynomials
Authors: Tweedie Charles
Published: January 2009

If we write the product

in the form

the coefficients have been called by Professor Nielsen (following Thiele) the Stirling Numbers of the First Species, because James Stirling, in his Methodus Differentialis (1730), was the first writer to draw attention to their use, and furnished a small table of their initial values.
A Theorem of Sonine in Bessel Functions, with two Extensions to Spherical Harmonics
Authors: Dougall John
Published: January 2009

In his notable memoir on the Bessel Functions, Sonine proves the elegant result that

m > –½, provided a plane triangle can be drawn with sides a, b, c; otherwise the value of the integral is zero.
On the Stereometric Generation of the De Jonquières Transformation
Authors: Tinto J. F.
Published: January 2009

In the geometry of the plane the logical interrelations of figures may often be rendered clearer by considering the plane to be a part of space of three dimensions. Thus, by taking the plane figure as part of a more extensive configuration in space of three dimensions, the elucidation of its properties, and in particular its relation with other figures, are often facilitated. Similarly, the figures of space of three dimensions can sometimes be treated more advantageously and compendiously by considering them as parts of figures in a space of four dimensions, and so on. As a single instance we may take Segre's elegant and powerful mode of treatment of the quartic surface which possesses a nodal conic. This surface he obtains as a projection in space of four dimensions of the quartic surface which constitutes the base of a pencil of quadratic varieties. In the following paper this mode of treatment has been applied to the interesting variety of the Cremona transformation in the plane known as the De Jonquieres transformation, a transformation which possesses some intrinsic interest in view of the fundamental rôle which it plays in the theory of Cremona Transformations. By the aid of a surface in space of three dimensions, a variety in space of four dimensions, etc., simple constructions are given for the De Jonquières transformation between two planes, between two spaces of three dimensions, etc., respectively.
The Co-symmedian System of Tetrahedra inscribed in a Sphere
Authors: Marr W. L.
Published: January 2009

This paper deals with a system of tetrahedra in a sphere corresponding to the co-symmedian system of triangles in a circle. Such a system of tetrahedra, so far as the writer knows, has not been hitherto discussed. The condition that a tetrahedron may have a symmedian point is given in Wolstenholme's “Problems” (1878).
Approximations to the Length of an Arc
Authors: Sommerville D. M. Y.
Published: January 2009

Dr E. M. Horsburgh has given the approximate expression for the length of an arc of the catenary:

where C is the length of the chord and T the sum of the tangents at its extremities, analogous to Huygens' approximation to the length of a circular arc:

where C′ is the sum of the chords of the two halves of the arc. These approximations are not confined to these particular curves, but hold, within wider or narrower limits, for any continuous curve. In fact, if s is regarded as a small quantity of the first order, as are also C, C′ and T, the difference between s and either of the quantities ⅓(2C + T) and ⅓(4C″ – C) is a small quantity of the fifth order. Other expressions of a similar form can be found involving the chords and tangents of the half-arcs.
Asymptotic Expressions for the Bessel Functions and the Fourier-Bessel Expansions
Authors: MacRobert T. M.
Published: January 2009

Asymptotic Expressions for the Bessel Functions.

From the asymptotic expansion for Ku(z) it follows that, if − π < amp z < π,

This theorem is also true if amp z = ± π; to prove this consider the formula
Addition of a Third of a Period to the Argument of the Elliptic Function
Authors: Taylor D. G.
Published: January 2009

1. If I is an inflexion on a non-singular plane cubic curve, a variable line IPP′ establishes a (1, 1) correspondence between points P, P′ on the curve. This correspondence defines a perspective transformation of the whole plane, with I for pole, and the harmonic polar of I for axis, of perspective; for, when I is projected to infinity on the y-axis, and its harmonic polar taken for x-axis, the resulting equation

indicates a curve symmetrical with respect to the latter.
Determination of the Arbitrary Constants which appear in the Asymptotic Expansions for the Functions of the Elliptic Cylinder
Authors: Marshall William
Published: January 2009

In an article, published some time since, the author of the present paper deduced an asymptotic expression for the functions of the elliptic cylinder, which expression took the following form:

Here P and Q are certain asymptotic series, and C and a arbitrary constants. General expressions for these constants were not determined in the aforementioned article on account of the difficulties there set forth, though it was pointed out that their numerical calculation for any particular problem was simply a matter of arithmetic computation. It is the object of the present paper to deduce general expressions for these constants C and a in terms of the two parameters which appear in the defining equation for U.
Notes on Everett's Interpolation Formula
Authors: Lidstone G. J.
Published: January 2009

Writing of his now well-known Interpolation Formula, Professor Everett said, “The only novelty in the formula is the simplicity of its form.… The best known formulae for interpolation by central differences are difficult to carry in the memory on account of their unsymmetrical aspect, one law being applicable to the odd and another to the even terms. … This disadvantage does not apply to the formula proposed,” viz., that which now goes by Everett's name.
On Mathieu Functions of Higher Order
Authors: Humbert Pierre
Published: January 2009

The definition and properties of Mathieu (or elliptic-cylinder) functions are well known to the members of this Society, owing to the appearance in its Proceedings from time to time of various papers by different authors, wherein these functions are discussed. The object of the present paper is to introduce a new kind of function which can be considered as a generalisation of Mathieu functions, and for which we propose the name of “Mathieu Functions of Higher Order.”
The Equation of Telegraphy
Authors: Gray M. C.
Published: January 2009

The equation of the propagation of electric signals along cables, generally known as the equation of telegraphy, may be written

Particular solutions of this equation, adapted to various purposes have been found by Heaviside, Poincaré, A. G. Webster, T. W. Chaundy, § and others. The object of the present paper is to unify the theory of the equation by exhibiting the relations which these solutions bear to each other, and by obtaining them as particular cases of a general solution. The derivation of new particular solutions by the solution of integral equations is also discussed.
On an Asymptotic Expansion of the Hypergeometric Function
Authors: MacRobert T. M.
Published: January 2009

In a previous paper the author has employed the expansion

where

and

to establish the theorem that, if −π/2<amp γ<π/2, the function Ps/Ts+1 remains finite as γ→∞. This theorem is valid provided that z is not real and ≧ 1.
Expansions in Series of Spherical Harmonics
Authors: MacRobert T. M.
Published: January 2009

A Generalisation of Christoffel's Summation Formula. The Recurrence Formula

is valid for all values of n and m; but, if m is a positive integer, , hence, when n = m, (1) becomes
Power Coordinates and the Bicircular Quartic
Authors: Wilson R.
Published: January 2009

Casey, in an extensive and complete mémoire, has discussed very thoroughly the bicircular quartic. Among the unfinished notes of Dr Clifford the properties of the curve are established by means of a tetracyclic system of coordinates. Such a system of coordinates has been extensively used by Coolidge. The object this paper is to present a valid discussion of the curve in terms a tricyclic system of “power” coordinates.
A Generalization and Simple Proof of Kronecker's Theorem Concerning the Minors of a Compound Determinant
Authors: Metzler W. H.
Published: January 2009

where (Am m) represents a square of m rows and m columns of a's; (Bm r) represents a rectangle of m rows and r columns of b's; (Cr m) represents a rectangle of r rows and m columns of c's;, and (Orr) represents a square of r rows and r columns of zeros.
Some Axi-Symmetric Determinants with Integers for Elements
Authors: Nassau J. J.
Published: January 2009

B. Pascal and others have studied the properties of the table:
Notes on James Gray
Authors: Tweedie Charles
Published: January 2009

Very little information is now to be found regarding James Gray, the author of the famous Scottish Arithmetic, so universally in use in Scotland during the 19th century as to make his name synonymous for Arithmetic, just as Cocker's was England during the 18th century.
Note on Binet's Inverse Factorial Series for μ(x)
Authors: Copson E. T.
Published: January 2009

Binet shewed that the function

can be expanded as an inverse factorial series. This note furnishes a new and much simpler proof of his result, based on a formula which is an analogue of the Binomial Theorem for factorials.

This formula is that, if we denote by [x]n the ratio

then

where denotes the coefficient of xr in the expansion of (1 + x)m.
Geometrical Notes
Authors: Mackay J. S.
Published: January 2009

A straight line KK′ meets the circumference of a circle at two real or two imaginary points K, K′, and H is the middle point of the real or imaginary chord KK′. If A, B, C, D be any four points on the circumference, and the pairs of straight lines AB, DC, AC, BD, AD, CB meet KK′ at the pairs of points E,E′, F,F′, G,G′; then if any one pair of points be equidistant from H, the two other pairs will also be equidistant.
Boole's and other proofs of Fourier's Double-Integral Theorem
Authors: Alexander Peter
Published: January 2009

In my former paper on Fourier's double-integral I remarked that Poisson's form of the integral gave the same incorrect; result as Fourier's form in an example by which I tested it, and seemed subject to the same limitations.
Radical Axes in Spherical Geometry
Authors: Allardice R. E.
Published: January 2009

It is evident that by an extension of the method of deriving from any triangle its polar triangle, it is possible to derive from any figure whatever another figure, the properties of which may be deduced at once from those of the first. This may be done either by imagining a point to move along the original figure and considering the envelope of the great circle of which the moving point is the pole; or by imagining a great circle to envelope the figure and considering the locus of its pole. In both cases two figures will be obtained; but these will be antipodal, and will therefore have like properties. Since the point of intersection of two great circular arcs is the pole of the great circular arc which joins the poles of these two arcs, the two methods of derivation mentioned above will lead to the same derived figure. These methods of transformation of figures are evidently closely analogous to that of reciprocal polars.
On a method for obtaining the differential equation to an Algebraical Curve
Authors: Chrystal
Published: January 2009

1. Consider the conic represented by the general equation

Differentiating three with respect to a we get

where (y) stands for .
Note on the Integration of
Authors: Muir Thomas
Published: January 2009

The integration of differentials of the form seems to me to be susceptible of a more methodical mode of treatment than that commonly employed. In the ordinary way of presenting the matter there is little choice left to the student, when such an integration is required of him, between a haphazard, tentative process, and the consultation of a text-book, in which lists of ‘formulae of reduction’ are given.
Mnemonics for
Authors: Mackay J. S.
Published: January 2009

The following mnemonics, with one exception, consist of verses or sentences such that if the number of the letters in each word be written down in the order in which the words occur, the desired value will be obtained.
On Integral Relations connected with the Confluent Hypergeometric Function
Authors: Gibb D.
Published: January 2009

In the Bulletin of the American Mathematical Society Whittaker defines the confluent hypergeometric function Wk,m(x) by the equation

where the path of integration begins at t = + ∞, and after encircling the point t = Q in the counter-clockwise direction, returns to t = + ∞ again.
Bipolar and Toroidal Harmonics
Authors: Jeffery G. B.
Published: January 2009

Most of the solutions of Laplace's equation in common use in mathematical physics have been expressed in the integral form given by Whittaker, viz
On the Theory of Continued Fractions
Authors: Datta Haripada
Published: January 2009

An analytic function is generally given either directly as a power-series, or at anyrate in some form which can readily be converted into a power-series. The power-series is not an altogether satisfactory method of representing the function, on account of the failure of its convergence outside its circle of convergence; in this respect it is decidedly inferior to the method of representing the function by a continued fraction, as this latter expression in many cases converges over the whole plane, except on certain curves.
The Hessian-Polars of n-dimensional Cubics
Authors: Milne William P.
Published: January 2009

I have not seen the following properties of the Polar Conic and the Polar Conic of the Hessian given in treatises on the Cubic Curve. The results can be extended to space of n dimensions.
On Symmetric Determinants and Pfaffians
Authors: Datta Haripada
Published: January 2009

The name Pfaffian was given by Cayley to the rational function which is the square root of a zero-axial skew determinant of even order
Functional oesophagoscopy: endoscopic evaluation of the oesophageal phase of deglutition
Authors: Belafsky P C , Rees C J
Published: January 2009

Background:

The anatomy and function of the oropharynx and larynx during deglutition can be assessed using the flexible endoscope, but this evaluation does not provide information on the oesophagus. Guided observation of oesophageal swallowing enables extended dysphagia evaluation.

Objective:

To assess the diagnostic utility of guided observation of oesophageal swallowing in the evaluation of dysphagia.

Study design:

Retrospective case series.

Methods:

Procedures for guided observation of oesophageal swallowing were reviewed for oesophageal findings and compared with fluoroscopy and manometry.

Results:

Twenty-one patients underwent guided observation of oesophageal swallowing and concurrent videofluoroscopy and/or manometry. No complications of the former procedure occurred. The results of guided observation of oesophageal swallowing concurred with those of fluoroscopy in 15/21 cases (71 per cent) and with those of manometry in five of six (83 per cent) cases. Guided observation of oesophageal swallowing revealed anatomic pathology contributing to dysphagia in 15/21 (71 per cent) patients. The procedure identified pathology not detected by fluoroscopy and manometry in 13/21 (62 per cent) patients.

Conclusion:

Guided observation of oesophageal swallowing appears to be a safe diagnostic tool with which to evaluate the oesophageal phase of deglutition.
History of instruments used for mastoidectomy
Authors: Mudry A
Published: January 2009

Aim:

To present the historical development of specific instruments used for mastoidectomy and their resulting implications for this surgery.

Method:

Compilation of original written documents, trade catalogues and collections of instruments used in mastoid surgery, with a review of the secondary literature on the subject.

Results:

The first surgical opening of the mastoid was performed by Petit in 1736 with a trepanation system. More than one and a half centuries later, in 1873, Schwartze codified the operation using chisels and gouges. At the end of the nineteenth century, Macewen introduced the electrical dental burr for mastoid surgery, but it remained largely unrecognised. At the beginning of the 1950s, the systematic use of the microscope in ear surgery allowed generalised use of the drill and improvement of the suction-irrigation system.

Conclusion:

Three instrumental periods are recognisable in the history of mastoidectomy: the trepan period, the chisel and gouge period, and the electrical drill period.
Pain versus bleeding risk following tonsillectomy: do patients and doctors agree?
Authors: Low T-H , Harris P , Esterman A , Carney A S
Published: January 2009

Objective:

To investigate the differing opinions of patients and medical practitioners regarding the relative priorities of pain relief versus bleeding prevention following tonsillectomy.

Methods:

Questionnaires were mailed out to adult patients, paediatric patients' parents, general practitioners and ENT surgeons.

Results:

A total of 72/112 (64.3 per cent) questionnaires were returned. Adult patients, paediatric patients' parents, general practitioners and ENT surgeons all ranked bleeding as the most important factor when assessing risks related to tonsillectomy. Most adult patients indicated that they would accept a bleeding risk of 2 per cent; however, parents indicated that they would accept a higher bleeding risk (3 per cent) for their children in exchange for better pain control.

Conclusions:

Adult patients, paediatric patients' parents and doctors were slightly more inclined to ‘trade-off’ an increased post-tonsillectomy bleeding risk in exchange for better post-tonsillectomy pain control, although concerns about post-operative haemorrhage remained the main priority for all groups.
Influence of temperature on the larval development of the edible crab, Cancer pagurus
Authors: Weiss Monika , Thatje Sven , Heilmayer Olaf , Anger Klaus , Brey Thomas , Keller Martina
Published: January 2009

The influence of temperature on larval survival and development was studied in the edible crab, Cancer pagurus, from a population off the island of Helgoland, North Sea. In rearing experiments conducted at six different temperatures (6°, 10°, 14°, 15°, 18° and 24°C), zoeal development was only completed at 14° and 15°C. Instar duration of the Zoea I was negatively correlated with temperature. A model relating larval body mass to temperature and developmental time suggests that successful larval development is possible within a narrow temperature range (14° ± 3°C) only. This temperature optimum coincides with the highest citrate synthase activity found at 14°C. A comparison for intraspecific variability among freshly hatched zoeae from different females (CW 13–17 cm, N = 8) revealed that both body mass and elemental composition varied significantly. Initial larval dry weight ranged from 12.1 to 17.9 μg/individual, the carbon content from 4.6 to 5.8 μg/individual, nitrogen from 1.1 to 1.3 μg/individual, and the C:N ratio from 4.1 to 4.4. A narrow larval temperature tolerance range of C. pagurus as well as the indication of intraspecific variability in female energy allocation into eggs may indicate a potential vulnerability of this species to climate change. Large-scale studies on the ecological and physiological resilience potential of this commercially fished predator are needed.
Labours of Love: Voluntary Working in a Depressed Local Economy
Authors: MacDonald Robert
Published: January 2009

Whilst studies of employment have fuelled arguments about post-Fordism and questions of flexibility, recent debates about welfare have considered social polarization and the growth of an anti-social, anti-work ‘underclass’. In both cases, relatively little attention has been given to the ways in which people in depressed local economies now survive through precarious, marginal and informal work.

This article explores how people deprived of jobs seek to re-create positive working lives for themselves through voluntary work. Drawing upon qualitative interviews with working-class men and women in Teesside, it explores the motivations and meanings of volunteering and the significance that voluntary action has for work and welfare in such communities. State intervention in the voluntary work sphere is assessed and a number of recommendations are made for policy and practice.
Social Policy Digest
Authors: Bennett Fran
Published: January 2009

A study by the Institute for Fiscal Studies (IFS) found that whilst the income of the poorest tenth of society fell by 18 per cent in real terms between 1979 and 1992 (after housing costs), their expenditure rose by 14 per cent. In a separate report on changes in individuals' incomes over time, the IFS found significant movement in and out of the poorest sections of society between 1991 and 1992. The latest edition ofHouseholds Below Average Incomeshowed that real net income rose by an average of 38 per cent (after housing costs) between 1979 and 1992/93, but fell by 17 per cent for the bottom tenth of the population (24:3/95,1.1). The narrowing of the gap in the north–south divide has halted, but a report on the geography of poverty explores many other divisions between and within areas of the UK. The report of the Commission headed by Lord Dahrendorf called for a new investment strategy and benefits structure, as well as measurement of social and environmental conditions as part of an annual audit of ‘wealth’. Tony Blair, the Labour Party leader, promised a fundamental review of the social security system once in power.
Policy Dilemmas in Belfast
Authors: Osborne R. D.
Published: January 2009

Major policy developments in Northern Ireland concerned with socioeconomic differences between Protestants and Catholics have involved a concern with structural issues and the nature of the policy making process. These initiatives have raised considerable debate concerning the extent to which religion-specific policies are appropriate. In this article each of these initiatives is considered in detail. It is suggested that the debates in Northern Ireland could have significance in the light of proposals to develop race-specific policies in Britain.
Competition in the Mixed Economy of Care
Authors: Forder Julien , Knapp Martin , Wistow Gerald
Published: January 2009

The 1990National Health Service and Community Care Actintroduced sweeping changes to health and social welfare services. The reforms to community care were dominated by the introduction of markets for social care. We argue that the new markets cannot be guaranteed to deliver the range of services required to meet community care objectives. When they began to assume their new responsibilities, few key purchasers had a basic understanding of the functioning and imperfections of markets. Consequently, they were poorly equipped to anticipate or ameliorate the sources of market failure that we identify. Like any other relatively ill-informed purchaser, local authorities risk being unable to buy what they want on behalf of their residents and at an appropriate volume, cost and quality. We discuss where and how market imperfections are likely to occur. In this context, we offer an economic framework to help in the shaping and managing of social care markets.
Combining Employment with Childcare: An Escape From Dependence?
Authors: Ward Clare , Dale Angela , Joshi Heather
Published: January 2009

The availability of childcare is an important factor in enabling motherhood to be combined with paid employment. This article uses evidence from the fifth sweep of the National Child Development Study to analyse the use of childcare by a cohort of employed women who were aged 33 in 1991. There is a heavy reliance on informal care by women in partnerships and also by lone mothers. Formal care is most heavily used by women whose youngest child is under five, especially if the woman works full-time. Reported costs of childcare represent nearly a quarter of net weekly earnings for mothers with a child under five. Formal childcare is shown to play an important role in facilitating women's full-time employment. Full-time employment is the route by which women achieve financial independence from their partner. It also increases the likelihood of contributing to an occupational pension which, in turn, has implications for financial independence in later life. However, the majority of women in this cohort do not take the full-time route. For these women, low earnings potential and part-time working make paid childcare uneconomic and reinforces both their role as minor financial contributors within the family and their lack of pension provision in later life.
Goal-setting in urban planning: A case study from Czechoslovakia
Authors: Musil Jiří
Published: January 2009

The discussion on goals and goal-setting procedures in town planning which has recently been going on in the social and planning sciences1 is concerned – with a few exceptions – with the general methodological aspects of the problem. Undoubtedly this approach, stressing a typology of planning and the importance of planning environments and discussing the advantages of different goal-setting methods, has stimulated planning methodology and helped to modify strictly normative models2 of planning, which did not take into account that planning is also a social process.3
Another look at low pay
Authors: Bosanquet N. , Stephens R. J.
Published: January 2009

Age, lack of skill, employment in certain industries, all contribute to low pay – but with what weight? The purpose of this study is to present evidence that age and skill have been underestimated and the industrial effect misconstrued as factors in low pay. We then attempt to spell out the handicaps of the low paid in labour markets, of which high rates of unemployment are the main sign.
Compensation for Disability
Authors: Bolderson Helen
Published: January 2009

Difficulties encountered in the transfer of money to a minority group in society are explored. Should benefits for disabled people seek to mitigate earnings loss, functional incapacity or damage? Should they take the form of contingency benefits, merited payment, or compensatory and reparatory ‘gifts’? What are the reasons for the different approaches adopted in the War Pensions, Industrial Injuries, and Invalidity Benefit schemes?

An historical account of the development of these schemes shows that payments related to attributed characteristics or ‘condition’ avoid the pitfalls of undue stress on status, performance and achievement inherent in alternative, and apparently more integrative, benefits. Payments related to condition accentuate ‘difference’ but if they represent a collective liability for society's vicariously caused diswelfares, they need not be experienced as stigmatizing. It may therefore be possible to conceive of a compensatory / reparatory payment for all disabled people, as of right, independent of insurance status, average life earnings, current wage, and other measured achievements. To avoid ‘physiological and psychological means testing’ the basic payment would be assessed on a disabled person's assumed ‘loss of faculty’ but, in the interest of equity, individual measurements of functional limitation may be necessary for additional cash benefits and services.
Diversity and Esteem in Higher Education
Authors: Eustace Rowland
Published: January 2009

There are many calls for greater variety in the provision of higher education combined with greater transferability between courses and institutions – in short, that we should end the present hierarchy of esteem in which institutions and subjects of study are commonly held.

Is this likely to be done easily? Too little consideration has been given to the size and strength of the social forces that create educational elitism. Some idea of this size and strength may be gained by looking, as a revealing example, at some educational history. Elitism has survived in times when the factors usually thought of as decisive have been strongly adverse to it. We should not hope that its virulence is any less now. New approaches are needed, and a concerted effort to decide what these approaches should be is now urgent.

To have much hope of achieving perceived equality of esteem of diverse types of higher education, an intensive study of the causes of elitism in education, and of measures that would have some chance of reducing it, is needed. A single Royal Commission type of inquiry is unlikely to be enough. A structured set of parallel inquiries might offer more hope.
The Structure of Social Casework and Behavioural Change
Authors: Toren Nina
Published: January 2009

The casework method practised in social work is assessed from a sociological-structural perspective. Social workers are viewed as agents of social control who wield power and authority in order to change their clients' attitudes and behaviour. It is argued that the main weaknesses of casework as a technique for personal change lie in its dyadic structure and isolation from the client's real-life environment. These characteristics impede the operation of the basic processes through which control and influence are generally accepted. It is proposed to substitute small groups of clients for the one-to-one casework setting, to link the treatment situation to real-life experiences, and to emphasize learning processes. It is believed that this restructuring of the worker-client encounter will increase the effectiveness of social work therapeutic intervention.
Workmen's Compensation in the United States: The Effects of Fifty Years of Local Control and Private Enterprise on the Administration of a Social Welfare Programme
Authors: Chambers Donald E.
Published: January 2009

From an examination of the available data it appears that the present Workmen's Compensation system in the United States is providing a deprivation livelihood for the work-injured and their survivors and is failing to meet its objectives as a service delivery system because it results in a gross misallocation of public costs. It is not providing coverage at all to many workers most exposed to industrial injury and is not getting benefits to an important proportion of those entitled to them. At the same time, it is providing dependable but undisclosed profits to private insurance carriers.
Living without the Mental Hospitals
Authors: Hewett Sheila , Ryan Peter , Wing John
Published: January 2009

Changes in the administrative structure of the National Health Service and in policy concerning the role of the psychiatric hospitals in the delivery of mental health care mean that local authorities have a growing responsibility for providing a range of supportive services for people who formerly would have lived for long periods in mental hospitals. Sheltered living environments will be an essential part of these services but there is little systematic information regarding the kind of care required in terms of the needs of the adult mentally ill. A pilot study is reported of the non-hospital residential care experienced by mentally ill adults who were financially assisted by three South London boroughs. The findings are related to a wider study of new long-stay patients in mental hospitals, some of whom could be discharged if alternative services were available. The appropriateness of short-term rehabilitation hostels as opposed to long-term maintenance environments of various kinds is discussed. The study is now being extended to include other forms of care including group homes, sheltered housing schemes and a wider range of local authority hostels than was encountered at the pilot stage.
Public Spending and Social Policy: The United Kingdom 1950–1977
Authors: Gould Frank , Roweth Barbara
Published: January 2009

This article, in which we examine developments in public expenditure on social policy in relation to total public spending in the United Kingdom (UK) in the period after the Second World War, is part of a larger international study on developments in social welfare spending on which we are currently engaged.

In Section 1 we briefly sketch in the theoretical background to the study of public expenditure growth in general and social welfare spending in particular. We shall not in this article attempt to evaluate the validity of the competing hypotheses – this exercise is in hand as part of the international study, and we shall report the findings at a later date. Section 2 examines the growth of public expenditure in the UK at the aggregate level. In Section 3 we analyse public expenditure at the individual programme level and in Section 4 we summarize the conclusions.
The State, Class Ideology and Social Policy
Authors: Taylor-Gooby Peter
Published: January 2009

This article suggests that a central tradition in social administration finds difficulty in accommodating theoretical perspectives which offer a thorough-going critique of the suitability of the state as a vehicle for maximizing welfare. The point is illustrated through consideration of social administration's treatment of marxist work on the problem of how contemporary capitalist welfare states can retain political legitimacy. Two possible solutions to the problem in the work of Marx and subsequent marxists are identified. One stresses the success of the dominant class in persuading the subordinate class of the legitimacy of its power. The other argues that this process is aided by the ideological framework in which it takes place and that this framework of ideas results not only from the activity of the ruling class but also from the experience of everyday life in capitalist society. The former tends to be the version of marxism presented in social administration treatment. It offers a less radical critique because it can be taken to suggest that the main barrier to welfare lies in the individual members of a particular social group who can in principal be defeated in a ‘battle for consciousness’; and not so much in a particular kind of social life, which represents a more profound obstacle.
Public Opinion and the Demand for Social Welfare in Britain
Authors: Whiteley Paul
Published: January 2009

This article discusses the role of public opinion in the social policy making process. It argues that existing accounts of social policy formation are inadequate in their treatment of public opinion, and inconsistent in their estimation of its importance. It then goes on to examine detailed examples of the role of public opinion in policy making; and finally tests two hypotheses concerning the sources of the demand for social welfare spending on the part of the British electorate.
Disability, Retirement and Unemployment of Older Men
Authors: Piachaud D.
Published: January 2009

Among older men in England from 1971 to 1981 the increase in the extent of those defined as disabled was of the same order as the increase in unemployment. Using Census data for the forty-six counties of England, changes in disability, retirement and economic activity are related to changes in unemployment. A substantial proportion of the overall increase in disability and the decline in economic activity is attributable to the general rise in unemployment.