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The effect of the magnetic dipole and electric quadrupole upon the depolarization of light scattered by spheroids that are not very small compared to the wavelength is investigated. It is found that the three degrees of depolarization, ρu, ρσ, and ρπ, differ appreciably in their response to changes in the parameter values α (related to spheroid size), p (axial ratio), and m (relative refractive index). These differences should allow one to determine both molecular weight and physical dimensions of nonspherical macromolecular scatterers and the volume and dimensions of compact, nonspherical, colloidal particles conclusively from depolarization measurements within a wide dimensional range not accessible to the classical Rayleigh‐Gans theory of depolarization.

For the linearized problem of a spheroid torsionally oscillating in a viscous fluid a general solution in terms of spheroidal functions is obtained. For small eccentricity the results are shown to agree with those of Buchanan.

A solution to the problem of potential flow about a prolate spheroid placed axially symmetric in a circular duct has been derived. The solution is in the form of a distribution of vortex rings over the surface of the spheroid. The vortex strength is expressed in terms of an infinite series of Legendre polynomials and the analysis yields an infinite set of equations for determining the coefficients of this series. An expression for the velocity distribution on the surface of the spheroid as well as the longitudinal added mass coefficients of the spheroid are derived in terms of the coefficients of the Neumann series expansion of the vortex sheet strength.

The Stevenson extension of the Rayleigh‐Gans theory on the light scattering by spheroids at an angle of observation θ of 90° with respect to the incident beam was supplemented by the inclusion of θ as a further variable. The somewhat lengthy equations were evaluated for various values of the parameters α, p, θ, and m. Because of the inclusion in the Stevenson theory of the quadrupole contribution, the new data should allow one to determine the molecular weight M up to about 100 million (or the corresponding particle weight) and the axial ratio p of spheroidal bodies assuming the use of visible radiation. Detailed theoretical results are given for θ=90°, and a relatively simple practical procedure is outlined for the simultaneous determination of M and p at θ=90°.

Curves relating the reflected acoustic pressures to frequency for a rigid sphere and spheroid and for elastic spheres of aluminum, brass, and tungsten carbide in water are obtained. Experimental measurements using single short acoustic pulseforms are compared with theory. Excellent agreement is obtained for the limited ranges of ka over which the experiments were done. Only the case of monostatic reflection is considered.

Numerical solutions have been found for the vapor density field around a simple ice plate, idealized as an oblate spheroid of axis ratio 0.05, having Reynolds numbers between 0.1 and 20, and failing in a fluid of Schmidt number 0.71. The present solutions are compared with experimental data after Thorpe and Mason for evaporating ice plates, the numerical results of Masliyah and Epstein for oblate spheroids of axis ratio 0.2, and the analytical results of Brenner for thin disks. It is shown that the ventilation coefficient varies linearly with NSc⅓NRc½ at higher Reynolds numbers, while as the Reynolds number approaches zero it approaches its stationary value via the analytical solution of Brenner. Over the range of Reynolds numbers investigated, ventilation coefficients for thin oblate spheroids were found to be lower than those for spheres.

The development of avian erythrocytes involves a spheroid to discoid transformation in shape. The disk shape of the young erythroid cells is dependent on the presence of microtubules in a marginal bundle in the early stages of postmitotic maturation. Disassembly of microtubules with colchicine, vincristine, sulfate or cold temperature produces the spheroidal shape. Erythrocytes which have acquired the flattened ellipsoidal shape do not alter their shape with disassembly of the microtubules. The number of microtubules decreases as cell maturation occurs. The correlation coefficient for the number of microtubular profiles in one end of erythrocytes and the concentration of ribosomes (cell age) is 0.88. Microtubules of immature erythrocytes disappear more rapidly at 0°C than do microtubules of mature cells. It is concluded that microtubules play little or no role in the maintenance of mature red cell shape; however, they play an important role in the development of the flat discoid shape of avian erythrocytes during maturation.

Es wird eine Theorie fur die Stromung einer elastoviskosen Flussigkeit aufgestellt, in der ein axialsymmetrischer Korper Drehschwingungen ausfuhrt. Ziel ist die Behandlung des Scheiben-Elastoviskosimeters. Zu diesem Zweck Losen wir die Randwertaufgabe fur Rotationsellipsoide und leiten daraus durch Grenzubergang die Losung fur die Scheibe her. Es werden die Werte sowohl der Geschwindigkeit im Stromungsfeld als auch des Drehmoments, das die umstromten Korper erleiden, abgeleitet. The theory is developed for the flow of an elastico-viscous fluid when an axially symmetric body executes rotary oscillations in it. Our aim is to discuss the disk elastico-viscometer. For this purpose we solve the boundary value problems for the spheroids and derive the solution for the disk as a limit from that for the oblate spheroid. The values for the velocity field as well as the torque experienced by these bodies are derived.

Friction coefficients for the uniform rotation of prolate and oblate spheroids in a viscous fluid, with the slipping boundary condition, are computed numerically and reported in tabular form.

The angular variation of spheroid scattering is investigated as a function of spheroid volume (or molecular weight), axial ratio, and relative refractive index using equations given recently by the authors. On using visible radiation, the limiting largest dimension of spheroidal bodies is defined by 1500–2000 A. This corresponds to a molecular weight of 106–108, the pertinent order of magnitude depending on the axial ratio of the spheroids. Results are given for the σσ, ππ, and πσ=σπ components of polarized light. Regularities for unpolarized light can easily be computed using previously given relations. The dissymmetries of light scattering are discussed for the same components. Several methods are proposed for the utilization of the results in order to determine simultaneously the volume of rigid compact particles—or the molecular weight of macromolecules—and the physical dimensions parallel and perpendicular to the symmetry axis of prolate or oblate spheroidal bodies.

The image system of singularities of an arbitrary exterior potential field within a triaxial ellipsoid is derived. It is found that the image system consists of a source and doublet distribution over the fundamental ellipsoid. The present contribution is a generalization of previous theories on the image system of an exterior potential field within a sphere and spheroid. A proof of Havelock’s spheroid theorem, which apparently is not available in the literature, is also given.The knowledge of the image system is required, for example, when hydrodynamical forces and moments acting on an ellipsoid immersed in a potential flow are computed by the Lagally theorem.The two examples given consider the image system of singularities of an ellipsoid in a uniform translatory motion and in pure rotation.

In maturing oocytes of the newt Triturus viridescens, the nucleoli undergo a series of morphological changes that are very similar to those described by Callan for the axolotl, Ambystoma mexicanum. The nucleoli first assume the form of spheroids which then become extended into ring or necklace shapes that are DNase-sensitive; in mature oocytes the nucleoli revert to a spheroidal form. Short term in vitro incorporation studies with uridine-3H on both species show that RNA synthesis occurs in a restricted, eccentric portion of the spheroidal nucleoli, thereby producing an asymmetrical pattern of labeling. In the ring forms, however, the localization of the radioactivity suggests that synthesis takes place symmetrically throughout their entire length. The changes in nucleolar morphology apparently reflect the fact that the component DNA has undergone a redistribution from a localized region in the spheroidal nucleoli to an extended circle in the rings; the patterns of uridine-3H incorporation, therefore, parallel the distribution of DNA in both the spheroidal and the ring nucleoli. Ultrastructurally, the nucleoli contain a fibrillar component that corresponds in position to that of the DNA. The typical spheroidal nucleolus consists of a fibrillar core situated eccentrically and surrounded by a hull of granular, ribonucleoprotein material. The ring nucleoli are composed of a central fibrous region that is ensheathed all around its circumference by a layer of similar granular material. This granular substance is thicker at intervals along the length of the rings, representing the "beads" of the necklaces.

The stripwise clamping of a submerged prolate spheroid is derived utilizing spheroidal co-ordinates. For a slender spheroid the results agree with those of the preceding paper. Various limiting cases are investigated and the possibility of negative local damping is discussed.

It has been suggested that the observed low coercive forces of some ferromagnetic powders, as compared with predictions of single-domain-particle theory, may be due to cavities in the particles. Here this possibility is investigated theoretically. Some general formulas are established for a particle of arbitrary shape and for an ellipsoidal particle containing an ellipsoidal cavity; attention is then turned to the case in which both ellipsoids are spheroids, the particle prolate, the cavity either prolate or oblate. Several special cases are studied. In some cases the cavity increases the coercive force, in others it decreases it; for an originally large coercive force, the usual effect is a decrease. It is concluded that the proposed mechanism is capable of accounting, at least in part, for the observed decrease.

The method of Laumbach and Probstein is applied to a point explosion in a spheroid with exponential density distribution. It is shown that the shock wave propagates strongly along the direction of symmetry axis and the envelope of the shock front elongates to the same direction. The rate of elongation of the shock envelope increases with the eccentricity of the spheroid and finally the blowout of the shock wave along the polar axis occurs when the eccentricity exceeds some critical value. It is suggested that such a blowout of the shock may be connected with some galactic outburst having axial symmetry.

The radiation patterns of prolate spheroidal conductors, excited by an electric dipole in its tip, are calculated, for a number of spheroids of varying thickness, the wavelengths being equal to roughly π, π/2, and π/3 times their major axes.

Stresses have been calculated in the cases of concentric composite elastic spheres and spheroids when they are twisted by couples. The results have been obtained in closed forms.

Charts and tables of the demagnetizing factors of prolate and oblate spheroids are readily available; however, demagnetizing factors of ellipsoids of three different axes are incompletely tabulated and laborious to calculate. This article presents charts and tables which make possible easy determination of the demagnetizing factor for any principal axis of an ellipsoid of any shape. Formulas for the demagnetizing factors of the general ellipsoid are included together with supplementary formulas which cover a large number of special cases.

The exact solution of the equation of motion of a spheroid accelerated along its axis of symmetry to an arbitrarily applied force in a viscous fluid of infinite extent is obtained. The solutions are presented in terms of tabulated functions. The unsteady drag predicted by the Stokes-flow solution is adopted in the analysis. Both prolate and oblate spheroids are considered. The results are reduced to those of accelerated sphere case, in which the spheroid becomes a sphere. The prolate spheroid with the ratio of major axis to minor axis equal to 1.96 is found to have the greatest terminal settling velocity due to gravity and to travel longest distance due to an impulsive force among the spheroids of equal volume. The variations of velocity and displacement with time for some spheroids falling from rest are presented in graphs.

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A general solution of the Stokes equations of a viscous fluid with boundary conditions related to a spheroid is considered and the formulae for drag and moment are obtained to a certain order of approximation. The results are applied to the problem of sedimentation of two spheroids in which the spheroids have the same shape and velocity and their axes of symmetry are both in horizontal directions. The drag and torque acting on a spheroid are given in terms of mutual interaction of the spheroids. They are considered to a higher order for the special cases where the centers of the spheroids are both on a vertical line or in a horizontal plane.

The corpus cardiacum of Locusta consists of a syncytium containing nuclei of two sizes. The most obvious cytoplasmic inclusions are spheroid bodies, mostly about 0.6µ in diameter, which are easily seen in the living tissue, especially by phase-contrast microscopy. They do not appear in routine microscopical preparations, but are blackened by the classical ‘Golgi’ techniques. They give positive reactions for phospholipines. The cytoplasm also contains very numerous minute granules, which appear to be mitochondria.

The following paper contains the investigation of the mass-motion of viscous and imperfectly elastic spheroids, as modified by a relative motion of their parts, produced in them by the attraction of external disturbing bodies; it must be regarded as the continuation of my previous paper, where the theory of the bodily tides of such spheroids was given. The problem is one of theoretical dynamics, but the subject is so large and complex, th at I thought it best, in the first instance, to guide the direction of the speculation by considerations of applicability to the case of the earth, as disturbed by the sun and moon.

The hydrodynamical problem of finding the waves or oscillations on a gravitating mass of liquid which when undisturbed is rotating as if rigid with finite angular velocity in the form of an ellipsoid or spheroid, was first successfully attacked by M. Poincaré in 1885. In his important memoir “Sur l’Équilibre d’une Masse fluide animée d’un Mouvement de Rotation,” Poincaré has (§ 13) obtained the differential equations for the oscillations of rotating liquid, and shown that by a transformation of projection, the determination of the oscillations of any particular period is reducible to finding a suitable solution of Laplace’s equation.

An exact, closed-form solution of the problem of the motion of a satellite in the equatorial plane of an oblate body is obtained. It is shown that the classic formula for the motion of the perihelion is a first order approximation to the exact formula.

The Stokes creeping flow, induced by the passage of a uniform current parallel to the axis of a stationary non-conducting ellipsoid of revolution in an incompressible viscous fluid occupying, apart from the ellipsoidal region, the whole space, is investigated. The magnetic field, which is due to the distortion of the uniform current by the ellipsoid, is zero all over the surface of the ellipsoid. The induced flow field is symmetric with respect to the axis, and also with respect to a plane through the centre perpendicular to the axis of the ellipsoid. The case of a non-conducting circular disk, with its plane perpendicular to the direction of the undisturbed current, is deduced from that of a planetary ellipsoid.

An account is given of an investigation in which the low-sulphur S-carboxy-methylkerateine fractions (SCMK-A) from wool, human hair, and ovine horn were dried from, solution at various pH values and the films so formed examined in the electron microscope, both negative-staining and platinum-shadowing techniques being used. Rod-shaped particles, spheroidal aggregates, and filaments were observed. At pH 2.5–3.5, spheroids predominated, and at pH 90 the rod-shaped particles predominated, whereas filament formation was favoured near neutrality. The filaments had diameters of 20–50 A; the rod-shaped particles had diameters of about 20 A and lengths ranging from less than 200 A to about 800 A, the most favoured lengths having a common factor of about 160 A. The spheroids ranged in diameter from about 100 A to about 600 A and were usually flattened. The helix-rich fractions obtained by partial digestion of SCMK-A with Pronase P or chymotrypsin appeared to consist chiefly of rod-shaped particles at pH 6–9. The si...

1. Evidence is put forward in support of the view that the Golgi complement of the vertebrate sympathetic neurone consists of a dispersed system of spherical bodies. These bodies can be studied in living cells and with vital dyes and each consists of a neutral red staining core (the vacuome of Parat) enveloped in a lipoidal sheath. 2. The classical Golgi body is shown to be an artifact produced within the cell. With the osmium techniques the spheroid bodies together with the mitochondria form a framework which serves as a centre for a non-specific deposition of metallic particles. 3. The Golgi spheroids exhibit a secretion cycle with the formation of a granular product. The granules are identified with the ‘neurosecretion’ granules of Scharrer. 4. These granules appear to be transported to the nucleus of the cell and there to be absorbed. This observed interrelationship between nucleus and Golgi product is discussed.

There is at present no absolute standard method of measurement by which the high voltages now in common use may be compared. The paper gives an account of such a method in which the polarization of a metallic ellipsoid of revolution, suspended by an insulating fibre between vertical circular pole-plates, is observed. The dimensions and proportions of the ellipsoid and of the horizontal field were determined with high accuracy, and the magnitude of the electric gradient on the axis of symmetry of the instrument was calculated for given applied voltages. The working formula of the instrument is F=K(n2?n20)frac12;, where F is the field strength, k a constant found from the dimensions, n the number of swings per second of the ellipsoid with the field on and n0 with it off. The influence of the spacing of the plates, of shielding the ellipsoid, of gas pressure and temperature, was examined, and the readings of the instrument were compared with Whitehead and Castellain's sphere-gapdeterminations of voltage. As a combined check on the accuracy of their readings and those of this instrument, a value of the ratio c of the electromagnetic to the electrostatic units of quantity is obtained which agrees with the best previous results. It is concluded that continuous measurements of voltages up to 200kV can be made with the precautions indicated in the paper, to an accuracy of at least 3 parts in 1 000, the constant of the instrument depending upon the value accepted for the ratio c

A datum change between two geodetic systems with points in common may be derived in three stages; slight adjustments of coordinates to make the networks of common points geometrically similar in the two systems; a scale factor to make them geometrically congruent; finally, an orthogonal transformation to swing them into coincidence.

The scattering of a plane electromagnetic wave by a perfectly conducting spheroid with small eccentricity is treated by a method of expanding the scattered field directly in a series of spherical vector wave functions. An expression for the first‐order solution of the backscattered field is obtained for arbitrary angles of incidence of a plane wave. The numerical values of echo areas computed from the first‐order expression are shown for various cases, and rough experimental results are also discussed. During this study some mathematical formulas involving the associated Legendre functions have been derived.

The problem considered here is to determine the couple required to maintain the steady rotation about its axis of symmetry of an oblate spheroid which is placed in a uniform stream of viscous fluid moving parallel to this axis. The conditions of flow are assumed to be such as to permit the use of Oseen's approximation in the equations of motion. An expression in terms of spheroidal wave functions is derived for the transverse component of velocity in the fluid, and from this the expression for the couple is deduced. The disk rotating about the normal through its centre is considered as a special case, and some numerical results are given for certain values of a Reynolds number. A comparison is made, and agreement found, with results obtained by Jeffery in a previous paper which treated the case in which the mainstream was at rest.

Mature ultimobranchial follicles in the Fischer rat thyroid are characterized by being lined by two or more layers of cells (U cells) and by having an abundance of desquamated cells in the lumen. Such follicles, of variable size and shape, were found in almost every lobe in rats at least 30 days old. They were usually in the interior of the lobe in contact with perivascular connective tissue. Ultimobranchial follicles with multiple layers of cells were not observed in the two‐day‐old rat indicating that these follicles are an example of postnatal development. The most common precursor in the rat was a follicle, relatively large compared with the usual thyroid follicle, containing some cells or debris. Other precursor structures included narrow tubes, sheets or spheroids of cells characteristically having little cytoplasm. Intermedlate forms between these precursors and mature ultimobranchial follicles were recognized. Cells were desquamated while nucleated, and, later, the nuclei disappeared. Thus, in some follicles non‐nucleated debris accumulated. Many follicles were composed of mixed populations of cells, both typical thyroid epithelium and U cells. The relative abundance of the two cell types varied markedly as did the proportions of colloid and cell debris. Copyright © 1971 Wiley‐Liss, Inc.

In this paper are embodied our observations on the morphology, origin, and role of the Golgi bodies in the spermatogenesis of the slug, Anadenus altivagus, and the snail, Euaustenia cassida. Living cells have been studied under the phase-contrast microscope and photomicrographed. In the juxta-nuclear Golgi region in primary spermatocytes the Golgi bodies exist in the form of (1) granules and rods of dark contrast, (2) spheres of pale contrast, and (3) spheroids showing a duplex structure, each consisting of a sphere of pale contrast and an incomplete or complete cortex or sheath of dark contrast. The Golgi spheroids have been shown to arise three times in the course of spermatogenesis from the mitochondrial granules by a process of alignment. The acrosome is formed from a cap of tiny acrosomal granules, which are deposited in front of the spermatid nucleus by the Golgi bodies (acroblasts).

Exact solutions to the diffusion equation are obtained which correspond to diffusion controlled growth of elliptical paraboloids (dendrites; forward growth with linear time dependence) and spheroids (growth with square root of time dependence). The elliptical dendrite includes as special cases the dendrite of circular cross-section and the dendrite platelet. The dependence of the velocity V of dendritic growth on (the smaller) tip radius of curvature R, undercooling ΔgJ and axis ratio 1/√(1 + B) of the elliptic cross-section is found to be of the form V ∝ (Δϑ)nR, where the exponent n, a slowly varying function of Δϑ, is (contrarily to past assumptions) noticeably greater than 1 in the range of experimentally accessible undercoolings. The value of n is about 1.2 for the circular cross-section (B = 0), and about 2 for the dendritic platelet (B = ∞). The spheroid solution includes as special cases the known results for the sphere, the circular cylinder and the plate.

This paper is concerned primarily with an investigation of the loxodromic distance between two points on the spheroid. This is derived by a modification of the meridional parts method in terms of the track angle and the difference of latitude reduced by a correction which is a function of the latitudes concerned.Since the method is unsuitable when the track angle is near to 90°, the known formula for the mid-latitude correction is examined and an alternative method suggested for use in this case.The results obtained are compared in a practical example with those found by the usual methods, and finally means are proposed by which the refinement described above can be incorporated into current plotting practice on aeronautical Mercator charts.

In a memoir on the Attraction o f Spheroids, published in the 'Connaissance des Tems’ for 1829, Poisson showed that certain important formulæ were true up to the third order inclusive o f the standard small quantity. The object of this note is to establish the truth o f the formulæ for all orders o f the small quantity. 1. Suppose we require the value of the potential of a homogeneous body at any assigned point. Take a fixed origin inside the body; let r ', θ ', ψ ' denote the polar coordinates of any point of the body; and let r, θ, ψ , be the polar coordinates of the assigned point; and, as usual, put μ ' for cos θ '', and μ for cos θ. The density may be denoted by unity.

This is the first of a series of reports on the scattering of waves by a penetrable prolate spheroid. In this letter, the exact solution of the scattering of acoustic waves by a liquid prolate spheroid is obtained. Results are given in terms of the spheroidal functions. It is found that each expansion coefficient of the scattered or transmitted wave is coupled to all coefficients of the series expansion for the incident wave, except when the spheroid degenerates to a sphere. Detailed numerical computations for the radiation patterns of the scattered wave are carried out for a sphecific example. It is found that, in general, the radiation patterns for the scattered waves are more directional and possess more side lobes as the prolate spheroid becomes more elongated.

The Kelvin modes of oscillation of a selfgravitating, homogeneous fluid spheroid in hydrostatic equilibrium with a poloidal magnetic field inside and a dipole type field outside, are studied, using a variational principle. On the assumption that the eccentricitye of the spheroid is small, the frequencies of oscillation are calculated to the first order ine2.