The Royal Society

The effect of Coriolis perturbations on the perpendicular infra-red bands of symmetric top molecules is studied in the first approximation. The sum of the Coriolis coefficients for the vibrations in any symmetry class is shown to assume an extremely simple form, and its value is given for the general case. A straightforward method is described for the calculation of first-order Coriolis coefficients, and rules are derived whereby the rotational spacing of an overtone or combination band may be calculated from the Coriolis coefficients of the component vibrations.

The rifts of the 14 basaltic shield volcanoes that extend from Kauai to Hawaii are composed of thousands of dykes that were fed laterally by periodic leakages from central volcanic con­duits. Individual dykes are believed to be thin, steeply dipping blades, several kilometres from top to bottom, that extend horizontally outward for as much as 120 km. The dykes are contained largely within the volcanic edifices, and, because of such shallow emplacement, the direction of dyke propagation is interpreted to be strongly influenced by the gravitational stresses within these edifices. Simple isolated shields, such as Kauai and West Molokai, had nearly symmetrical stress fields, influenced only slightly by regional stresses, and the dykes injected into these volcanoes had little or no tendency to cluster into well-defined rifts. Other volcanoes, such as Koolau and Kilauea, pierced the thick, sloping apron of pre-existing neigh­bour volcanoes. The dykes that propagated from these centres were strongly influenced by the gravitational stress fields of the sloping aprons in which they grew. Accordingly, they clustered into well-defined rifts oriented roughly perpendicular to the downslope direction of these aprons. With only minor exceptions, 8 of the 14 volcanoes forming the southeast part of the Hawaiian chain conformed to this pattern of growth; the influence of regional Pacific structure on rift orientation is suspected in only 6 volcanoes that grew as simple, iso­lated shields, away from the influence of gravitational stresses of any neighbour volcano.

The disintegration of drops in strong electric fields is believed to play an important part in the formation of thunderstorms, at least in those parts of them where no ice crystals are present. Zeleny showed experimentally that disintegration begins as a hydrodynamical instability, but his ideas about the mechanics of the situation rest on the implicit assumption that instability occurs when the internal pressure is the same as that outside the drop. It is shown that this assumption is false and that instability of an elongated drop would not occur unless a pressure difference existed. When this error is corrected it is found that a drop, elongated by an electric field, becomes unstable when its length is 1.9 times its equatorial diameter, and the calculated critical electric field agrees with laboratory experiments to within 1 %. When the drop becomes unstable the ends develop obtuse-angled conical points from which axial jets are projected but the stability calculations give no indication of the mechanics of this process. It is shown theoretically that a conical interface between two fluids can exist in equilibrium in an electric field, but only when the cone has a semi-vertical angle 49.3°. Apparatus was constructed for producing the necessary field, and photographs show that conical oil/water interfaces and soap films can be produced at the calculated voltage and that their semi-vertical angles are very close to 49.3°. The photographs give an indication of how the axial jets are produced but no complete analytical description of the process is attempted.

Simultaneous measurements have been, made of the friction and adhesion of steel sliding on indium in air. The results show that both the normal and tangential stresses play a part in the deformation of the metallic junctions formed at the interface. When the surfaces are first placed in contact, a minute tangential force is required to initiate relative motion between the slider and the indium surface, since the junctions are already plastic under the applied load. As relative motion proceeds, the region of contact grows with a corresponding increase in the tangential force and the adhesive force. An upper steady state is reached where the tangential force increases more rapidly than the rate of growth of the region of contact and sliding on a macroscopic scale occurs. The detailed behaviour of the junctions during the early stages of the sliding process may be expressed quantitatively in terms of von Mises's criterion for plastic deformation under combined normal and tangential stresses, and there is good agreement between the theoretical relation and the experimental observations. The results emphasize the reality of the cold welding process which occurs at the points of intimate contact when metal surfaces are placed together. The metallic junctions so formed are responsible both for the friction and the adhesion observed. Lubricant films diminish the amount of metallic contact and so lead to a reduction in the friction and adhesion.

An equation for the flux of electrolyte through a water-swollen cation-exchange resin membrane separating two solutions of the same electrolyte at different concentrations is derived on the basis of several assumptions regarding the physical nature of a swollen resinous exchanger. The complete flux equation contains three terms, one determined by the concentration difference across the membrane, another determined by the variation of the activity coefficient of the electrolyte with concentration in the membrane and a third concerned with the rate of osmotic or hydrostatic flow through the membrane. If ions in the resin are transported entirely in an internal aqueous phase, the mobilities required for the flux equation can be related to mobilities in aqueous solution and to the volume fraction of resin in the swollen membrane. The treatment is readily extended to anion exchangers.

Einstein's equations for empty space are solved for the class of metrics which admit a family of hypersurface-orthogonal, non-shearing, diverging null curves. Some of these metrics may be considered as representing a simple kind of spherical, outgoing radiation. (Among them are solutions admitting no Killing field whatsoever.) Examples of solutions to the Maxwell-Einstein equations with a similar geometry are also given.

In this paper a theoretical analysis is made of the electrokinetic phenomenon known as the ‘electroviscous effect’. A general formula is given for the effective viscosity of a suspension of solid, spherical, charged non-conducting particles in an electrolyte. The increase of the effective viscosity due to the surface charge and the ionic double layer surrounding the particles is determined by a modification of Einstein’s method for the calculation of the viscosity of solid suspensions. The effective viscosity may be expressed in the form η = η ₀ {1+2.5 (v/V) (1+Ʃ ^∞ _{r -1} a _r Q ^r )}, where η ₀ is the viscosity of the electrolyte, v the volume of suspension in volume V of solution and Qe is the charge on each particle. It is shown that a ₁ = 0 and a ₂ is determined explicitly. It is found that the electroviscous contribution to η, for a given charge Q , tends to increase as the thickness of the double layer increases. When the thickness of the double layer is small compared with the radius of the particle the effect vanishes. A comparison with previous theoretical work is made, and it is shown that much improved agreement with experiment is obtained.

The results of an earlier paper are extended. The elastic field outside an inclusion or inhomogeneity is treated in greater detail. For a general inclusion the harmonic potential of a certain surface distribution may be used in place of the biharmonic potential used previously. The elastic field outside an ellipsoidal inclusion or inhomogeneity may be expressed entirely in terms of the harmonic potential of a solid ellipsoid. The solution gives incidentally the velocity field about an ellipsoid which is deforming homogeneously in a viscous fluid. An expression given previously for the strain energy of an ellipsoidal region which has undergone a shear transformation is generalized to the case where the region has elastic constants different from those of its surroundings. The Appendix outlines a general method of calculating biharmonic potentials.

A simple molecular field theory is developed to explain at least qualitatively the behaviour of weakly ferromagnetic and strongly paramagnetic alloys near their critical concentration c F . The free energy of a weakly ferromagnetic alloy can be expanded in powers of magnetization ζ and a modified Landau theory is used to calculate the concentration dependence of the magnetization, specific heat and the susceptibility near c F . It is believed that such a theory can work better in this case than does the usual Landau theory as fluctuations in ζ are relatively small for low temperatures. A change in low temperature resistivity around c _F is also expected as a result of ciritcal scattering of conduction electrons. This change was first calculated by Rice (1967) for strongly paramagnetic alloys giving a large T ² term. However, this calculation is not applicable for c very close to c _F . It is shown that for c → c _F the paramagnetic resistivity remains finite and has a maximum for c ═ c _F , ρ ^Para _c ═ c F ∝ T ^5/3 . It is also found that the ferromagnetic resistivity ρ ^ferro has a similar dependence on concentration and temperature as ρ ^Para and ρ ^ferro c ═ c _F ═ ρ ^Para c ═ c _F , i.e. the resisitivity is symmetrical around c _F .

A unified treatment is given of the Eckhaus mechanism of stability or instability of two-dimensional flows, which are periodic in one spatial dimension, and the Benjamin—Feir instability mechanism of the two-dimensional Stokes water wave. The method of the amplitude equation is used, following the lead of Newell in a related context. This method easily allows the analysis of the so-called side-band perturbations, which are a crucial feature of the Eckhaus and Benjamin—Feir resonance mechanisms. In particular, it is shown that Eckhaus’s result, that a periodic flow is stable only within a particular band of wavenumbers narrower than the span of the neutral curve of linearized theory, is only valid when the eigenvalues and other parameters are real. A corrected and extended form of the result is given for the general case of complex eigenvalues and coefficients. It is noted, however, that Eckhaus’s result is valid for the important examples of Taylor vortices and Bénard cells.