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In a recent paper (Nishida, 1971b), the response of the magnetosphere as indicated by the AE index to southward-turnings of the interplanetary magnetic field was investigated. The southwardturnings were classified according to magnitude and duration. It is demonstrated that at least in some of the examples shown in the paper, the AE indexes, against which the southward-turnings were compared, were incomplete, requiring modification of son of the conclusions in Nishida (1971b). A reply by Nishida is included. (WDM)

A graph paper is described which is useful in the study of the behavior of the moment of inertia for high spin states of deformed even-even nuclei.

Summary In a previous paper by one of the authors it was shown that spherical drops or bubbles surrounded by a more viscous fluid might have a terminal velocity as great as one and a half times that of a solid sphere of equal size and mass. The present paper shows experimentally and theoretically that the surface-tension of the surface of the drop or bubble decreases the terminal velocity. For any radii appreciably less than a certain critical value the drop or bubble behaves almost like a rigid sphere. After a fairly rapid transition, for all radii appreciably larger than the critical the effect of surface-tension is small. Experiments on the terminal velocity for air in water-glass, air in syrup, mercury in syrup, and water in castor-oil, all give critical radii of the order predicted; but the different media show appreciably mutual disagreement, the cause of which is not vet certain.

In the above-mentioned paper Mr. Ward communicates theoretical and experimental investigations which, as far as they are correct, are in their essential parts already published, and indeed somewhat more completely in three papers by Gouy and ourselves, the latter investigations having been suggested by Professor Kundt. Experiments on the rotation of the plane of polarisation of light by means of interrupted currents, like those of Bichat and Blondlot, are here excluded. Since the above-mentioned papers have not been noticed by Mr. Ward, and are hence probably not well known, it may be of interest to reproduce here their essential contents.

An early paper (1932) by Majorana, that has received but scant attention, is reexamined in light of later developments. This pioneering paper constructs a relativistically invariant theory of arbitrary spin particles, develops and utilizes infinite dimensional representations of the homogeneous Lorentz group, and provides a mass spectrum for elementary particles. The relevance of Majorana's approach and results to later and current research is explained.

In a previous paper I investigated the problem of the formation of waves on deep water by wind, and found that the available data were consistent with the hypothesis that the growth of the waves is due principally to a systematic difference between the pressures of the air on the front and rear slopes. Lamb had already discussed the maintenance of waves against viscosity by an approximate method, but without obtaining numerical results. Being under the incorrect impression that Lamb’s approximation would not hold for the short waves I was chiefly considering, I proceeded on more elaborate lines. It now appears, however, that Lamb’s method is not only applicable to the problem of waves on deep water, but is readily extended to cover the case when the water is comparatively shallow, and to allow for surface tension. The fundamental approximations are first, the usual one that squares of the displacements from the steady state can be neglected, and second, that viscosity modifies the motion of the water to only a small extent. The motion of the water can then, to a first approximation, be considered as irrotational. With the previous notation, let ζ be the elevation of the free surface x, y, z the position co-ordinates, t the time, U the undisturbed velocity of the water, h the depth, and φ the velocity potential. Also let σ, p, q , and ϑ denote respectively ∂/∂ t , ∂/∂ x , ∂/∂ y , and ∂/∂ z , and write p 2 + q 2 = - r 2 .

An analysis of the impact process in a particular type of high-speed printer was undertaken to determine the effect of hammer length on the contact time. The hammer is modeled as a one dimensional wave propagation medium and the paper-ribbon combination as a dissipative, nonlinear medium with hysteresis. The integrated macroscopic viscoelastic parameters for a particular impact geometry and hammer momentum were determined from a combination of the analytical model and the experiments run on an instrumented printer robot. Permanent deformation of the paper-ribbon caused by character penetration was also determined in this manner. The simulated model was then used to predict the change in dynamic behavior of such a system due to variations of the hammer length. The hammer length is shown to have only a tertiary effect on contact time in such a dissipative deformable nonlinear system. This result demonstrates that the widely discussed use of hammer length as a design parameter to control contact time in impact printing is invalid for such a dissipative system.

This paper gives a brief description of the HyA large amplitude horizontal Planar Motion Mechanism system. The mechanical layout and force measurement arrangements are described, and motion generation capabilities are specified.

Summary The propagation of waves of Rayleigh type in a uniform semi-infinite elastic medium with two uniform surface layers is discussed. The waves are dispersive, and the wave velocity equation is obtained as a determinant of the tenth order. By making infinite the thickness of the surface sheet one can derive the velocity equation for waves in an internal stratum. By making the thickness of either sheet zero one can retrieve the known equation for the velocity of Rayleigh waves in a medium with a single surface layer. If the wave-length is very small the determinant reduces to the product of three determinants which, equated in turn to zero, are the velocity equations of very short Rayleigh waves at the free surface and of very short waves of Rayleigh type at the two interfaces. The results of a numerical solution of the wave equation and the application to the surface waves of earthquakes will be communicated in a later paper.

A method of deducing Young's modulus of isotropic materials from flexural resonant frequencies which was suggested in a recent paper by D. Hardie and R. N. Parkins may lead to errors of up to 10%. The use of tabulated correction factors is shown to be a more satisfactory method of treating the experimental results, leading to values accurate to better than ½%.

(Abstract.)In the preceding part of this paper I considered the consequences of a special assumption as to the nature of the molecular force between two particles, the particles themselves being still treated as hard spheres. My object was to obtain, by means of rigorous calculation, in as simple a form as possible, a general notion of the effects due to the molecular forces. My present object is to apply this general notion to the formation and interpretation of the Virial Equation.

This paper considers the problem of determining the inviscid, subsonic compressible (or incompressible) blade-to-blade flow field through a turbomachine blade row, and presents two computer solutions, known as the ‘matrix’ and ‘streamline curvature’ methods, for solving this elliptic problem. In the former method the equations of motion are formulated in terms of a stream function and the numerical solution is based on finite difference approximations; in the latter, the equations of motion are solved in conjunction with the equation of continuity by an iterative process starting from a guess for the streamline pattern. Solutions for several blade profiles, giving flow patterns and blade surface velocity distributions, are included.

In a previous paper PAYTON [1] (hereafter referred to as WF for wave front) considered the shape of the two dimensional wave front induced in a finitely strained elastic body by an impulsive point body force. This problem was characterized by three parameters ct, fl and ~ which were dependent upon the initial strain and the constitutive relations for the material in question. For certain regions of the (~t, fl, ~) space it was shown that the wave front normal curve possessed inflection points and that the associated wave front curve carried cuspoidal triangles. In WF the wave front shape was classified by the number (and location) of normal curve inflection points. It was remarked (through a note added in proof) that the classification of cases n. 5, n. 8 and n. 13, where n = 1, 2, 3 and 4, was incomplete. In cases 1.8 and 4.8 (where ct =fl) and in cases 2.8 and 3.8 (where ctf l=l) this incompleteness was removed but the remaining eight cases were left open. It is now possible to complete this classification through a unified approach.

1. In the first part of this paper (Proc. Roy. Soc. Edin., vol. xxvi., 1905.-6, p. 130), a method was suggested by means of which it might be found possible to discriminate amongst certain oscillatory dynamical systems according as they did, or did not, follow the law of equipartition of energy in their respective vibratory freedoms.

Chaplygin investigated the problems of gas efflux at subsonic velocity from an infinite vessel when the walls make an angle qπ between each other [1]. In [2] the special case of Chaplygin's problem is reviewed when q = 2, and the author maintains that in this particular case it is not possible to use Chaplygin's results. In is shown in the present paper that Chaplygin's method and his results are in fact applicable in this case.

This paper presents a brief review of the ballistic motion of pistons, and includes a survey of rapid expansion machines used for the study of thermodynamic properties of gases. The datum solution is given to the problem of the piston being propelled by a perfect gas expanding isentropically through a simple wave. The problem concerning the motion of a piston in a tube with gas on each side of the piston is discussed and the solution is presented. It is shown that this problem can be discussed in terms of four dimensionless parameters, and the results of calculations are presented graphically in terms of the parameters developed.

The flow of liquids in porous media such as paper can be described by the parabolic diffusion equation divD gradw=∂w/∂t when the only driving forces are capillary in nature. This equation can be extended to include other forces, such as gravitational, by writing the diffusion equation in terms of a free energy or potential gradient.

A few remarks arising out of the perusal of this paper may perhaps not be considered as out of place on the present occasion. They are not meant as in any way impugning the author’s views of the laws determining the fracture and disruption of glacier masses, or their application to glacier-phenomena in general, but in relation to the somewhat mysterious process of regelation itself, and to those generally recognized and most remarkable facts of the gradual conversion of snow into more or less transparent ice, and the reunion of blocks and fissured or broken fragments, under the joint influence of renewed pressure and of that process (whatever its nature), into continuous masses. If regelation be really a process of crystallization, it seems exceedingly difficult to imagine how the molecules forming the cementing layer between two juxtaposed surfaces can at once arrange themselves conformably to the accidentally differing axial arrangements of those of the two surfaces cemented.

The general equations for reflection and refraction of plane waves at a plane interface between two semi-infinite elastic solids were given by Zoeppritz (1919). The papers discusses these equations. (Author)

A method is described for the solution of the electromagnetic field inside resonant cavities and waveguides of arbitrary shape, whether homogeneously or inhomogeneously filled. The method, suitably programmed for use with a digital computer, is based on the direct discretization of the Maxwell equations in integral form. Since the method works with the components of the electromagnetic field, the numerical solution directly gives the distributions of the field in the structure, in addition to the resonant frequencies of cavities or the propagation constants of waveguides. Some numerical applications of the method are given.

The dynamic response of an infinite, elastic plate to a steadily moving transverse force is studied under the so-called improved plate theory. Analytic solutions for the subsonic and the intersonic cases are obtained using the method of integral transforms. The usual difficulty of the nonuniqueness of the steady-state solutions is circumvented by formulating the problems as initial value problems and then seeking the large time limits of the solutions of such initial value problems. The subsonic and intersonic solutions obtained here are similar to that obtained previously for the supersonic case. However, in contrast with the supersonic solution, which contains two families of Mach lines, the subsonic solution contains no Mach lines and the intersonic solution contains only one family of Mach lines.

The actuator disc method, in which each blade row of a turbo-machine is represented by a plane, axisymmetric discontinuity in the flow field, is used to produce an approximate solution of the problem of compressible, irrotational flow through an axial compressor or turbine. The flow equations are linearized and a solution for a single, isolated disc is found. The effects of mutual interference between neighbouring discs are studied for two adjacent discs. A method for extending the solution to any number of discs is outlined. Examples showing applications of the method are given and experimental measurements made near the inlet guide vanes of an axial compressor agree well with the theoretical predictions. A new exact solution for two adjacent actuator discs is also given.

In current analyses of the contact conditions in angular-contact ball bearings it is assumed that sliding occurs in all regions where tangential surface tractions are operative. Other work in similar rolling-contact situations has, however, demonstrated that some of this slip requirement may be accommodated by the elastic surface deformations. This type of analysis leads to areas of sliding and sticking coexisting within the contact areas. These concepts are here applied to angular-contact thrust ball bearings and lead to some interesting deviations from the results obtained using the complete slip analysis. In particular, these concepts of microslip enable the determination of the spin/roll ratio at each race contact. Detailed calculations for conical ball thrust bearings illustrate the main discrepancy of the full slip analysis in over-estimating the frictional-energy losses, such discrepancies being most marked with decreasing contact angle, increasing pitch/ball radii, and increasing coefficient of sliding friction.

The swirling flow inside certain types of internal combustion engine depends in a complex way on a large number of variables. The steady flow of air through a cylinder, which reproduces the main features of an induction swirl engine cylinder, has been investigated. The pressure drop across the inlet ports, the port inclination, and the port opening were varied independently while other variables were held constant. For each condition, tangential velocities were measured and axial velocity directions observed over cross-sections of the cylinder. The results have been compared with a simplified hypothesis of R. S. Benson and with theories of the Ranque–Hilsch vortex tube.

The discharge of compressed air from a cylinder has been studied experimentally. The effect of initial pressure and of orifice geometry on the expansion in the cylinder and on the transient flow through the orifice has been examined in detail. During expansion, radial and axial temperature gradients are established which result in departures from isentropic behaviour. The state can be reproduced analytically only by using a variable polytropic index whose values are dependent on the history of the expansion. From dimensional considerations the effects of fluid dynamical variables and of heat transfer on the transient flow have been isolated.

The distribution of pressure and velocity within the rotor of a radial flow gas turbine is computed using a two-dimensional streamline curvature method. Solutions are obtained on the meridional plane and also on three blade-to-blade surfaces at the hub, mid-blade position, and at the shroud. The torque, as calculated from the blade-to-blade flows, agrees with the measured torque over a speed range of approximately 2:1 with sufficient accuracy to support the usefulness of the flow structure as indicated by two-dimensional calculation methods applied to radial turbomachines.

Up to the commencement of 1876 direct experiments on the difference of potentials of solids in contact with liquids had been made by Volta, Sir Humphry Davy, MM. Buff, Becquerel, Péclet, Pfaff, Sir William Thomson, Hankel, and Gerland, and of liquids in contact with liquids by Kohlrausch; but although extremely interesting they were all incomplete, for the following reasons:— 1. The earlier experiments were not carried out with apparatus susceptible of giving accurate results. 2. Owing to the incompleteness of the apparatus, assumptions had to be made not justified by the experiments. 3. No direct experiments had been performed to determine the difference of potential of two liquids in contact, with the exception of a few by Kohlrausch, using a method which appeared to us quite inadmissible as regards accuracy of result.

A method of calculation is described which allows the effects in time of temperature and pressure on bearing clearances to be investigated. The method is based on the fundamental hydrodynamic equation, the Fourier heat conduction equation, and the thermo-elastic equations, and combines these in a suitable manner. The iterative-numerical treatment of the calculations allows characteristic quantities, such as the revolutions per minute, to be altered during the course of the calculation. In order to simplify the calculations, an infinitely long bearing with lemon-shaped clearance and a centrally running shaft is assumed. This does not imply any limitation to the general applicability of the method, but merely serves as a means of reducing the effort required for the calculation work.

The transformation for E and H between equivalent Euclidean reference systems with constant relative acceleration is obtained, and the necessary modification of the classical equation of motion of the electron is deduced.

From analysis of data for the flow of steam-water mixtures in tubes at pressures between 3 MN/m2 [435 lb/in2 (abs.)] and 17·5 MN/m2 [2540 lb/in2 (abs.)] equations for friction pressure gradient are developed. These equations allow for the influence of the ‘mass velocity effect’, not previously allowed for in accepted correlations. The equations are in a form making them applicable at the critical point, and are compared with the data of Miropolskii, Isbin, and Berkowitz for steam-water flow.

The classical description of the critical point leads to infinities in such properties as the compressibility and the heat capacity at constant pressure, Cp, as the critical point is approached along a path in the homogeneous fluid. However, this description does not require a singularity in the heat capacity at constant volume, Cv, and supposes that the Helmholtz free-energy, A, is everywhere an analytic function of volume, V, and temperature, T. It is now clear that this description is inadequate, that Cv is infinite at the critical point and that A is a non-analytic function of V and T. The classical description must, therefore, be abandoned and it is shown that we have, in its place, a set of inequalities between the degrees of the singularities in such thermodynamic functions as Cv, compressibility, coefficient of thermal expansion along the orthobaric curve, and the curvature of the vapour pressure line. These inequalities provide powerful tests of even the best modern measurements and enable us to give a fairly complete thermodynamic description of the singularities of the critical region. The transport properties are not so well understood. It is probable that the shear viscosity is non-singular whilst the thermal conductivity is known to be highly singular. This last singularity is probably related to the infinity in Cv. The dimensionless functions—Rayleigh number, Prandtl number, and Grashof number—all become infinite at the critical point.