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The paper gives a general review of an investigation on some problems on motion in the relativity theory. We begin by discussing the motion of a single particle in a weak gravitational field and obtain both the linear and angular equations of motion; this is followed by brief accounts of the problem of two bodies and that of a rotating rod. In each case considered the equations of motion arise as conditions of integrability of the relativity equations for empty space. Only one of these problems has previously been treated by this method, this being the case of two bodies not connected by a material tension. However, this investigation, which was carried out by Einstein, Infeld and Hoffmann, introduces difficult ideas relating to the use of certain spatial surface integrals; in the present paper we avoid the use of these integrals. An essential feature of the work is that we take a first-order solution for the particular problem considered and substitute this solution in the quadratic terms ofGμvand then build up a second-order solution. This method can be employed when we discuss the interior of matter; and, as an example, we conclude the paper by investigating the case of a rotating mass of liquid of constant density.

SummaryFresh, unstained and unfixed samples of sperm from many fertile bulls studied under the electron microscope have shown that the anterior portion of the sperm head is always enveloped by a pr...

The construction of an electron diffraction apparatus is described, adapted to both reflection and transmission studies of crystalline materials and built in the laboratory at a moderate cost. This apparatus involves several novel features of construction and utilizes an electrode magnet for obtaining a homogeneous beam of electrons. The application of the instrument to chemical problems is illustrated by the results of a study of the effect of heat and of various gaseous atmospheres upon the structure of gold leaf. Microscopic, x‐ray and electron diffraction evidence indicate that at a temperature of about 400° the gold in a leaf flows into aggregates or larger crystal grains. This coagulation explains the contraction of the leaf as observed visually, the opacity of many patches in the heated leaf as observed microscopically, and the appearance of spots in the diffraction patterns. A ``many ring'' pattern observed when the leaf is heated in air or oxygen is attributed to the formation of an oxide which is rather unstable at about 400°. This observation clarifies some discrepant data in the literature.

Highly complex stimulated Raman scattering (SRS) spectra of hydrogen were produced by using narrow linewidth 1.058‐μ giant‐pulsed laser excitation. Results are presented which include the first reported observation of combination Raman lines whose frequencies are given by mvQ(1) + pvS(1) − vL where vQ(1), vS(1) and vL are the vibrational (4155 cm−1), rotational (587 cm−1) and laser frequency, respectively, m = 6, 7, or 9 and p = 0 or ±1. Numerous Raman lines described by the formula v = vL + mvQ(1) + nvS(0) + pvS(1), (m, n, p = 0, ±1, ±2,…), where vS(1) = 354 cm−1, were also observed.

SynopsisIn a recent paper J. L. Synge (1952) has shown that the theories of Einstein and Whitehead predict practically the same phenomena in the solar field. He finds that the rotation of perihelion, the deflexion of light rays and the red-shift in the sun's spectrum are the same in both theories. In this paper the motion of the centre of mass of a double star is investigated. It is found that Whitehead's theory predicts a secular acceleration in the direction of the major axis of the orbit towards periastron of the larger mass. The possibility of a binary star having such an acceleration has already been considered by Levi-Civita (1937), and he has given an example in which it may become detectable in less than a century. On the other hand, it has been shown by Eddington and Clark (1938) that there is no secular acceleration according to Einstein's theory.

A mass of perfect fluid rotating about an axis is considered. The material stress-system is taken to be one of isotropic pressure. General expressions for the pressure and form of the free surface are assumed. It is shown that the equations of motion cannot be satisfied unless the rotation produces an electromagnetic field which gives rise to additional terms in the total energy-tensor.

In previous papers (1941, 1947) the author has shown that the loss of gravitational energy of a rotating system such as a rod may be established by considering the non-periodic terms of order I 2 ω 5 / r 3 in the equation G μ v = 0 for the external field, I being the moment of inertia in the case of a rod. The present investigation begins by calculating the terms of order l 2 ω 6 / r 2 in the expressions for G μ v . It is found that the equation G μ v = 0 has no solution. Values of the g μ v can be determined, however, for which the material energy-tensor has the form of the Faraday-Maxwell stress-tensor due to certain periodic electromagnetic fields. In this way a link is established between periodic gravitational and electromagnetic fields, but the electromagnetic field is not uniquely determined by the analysis. Next a rotating sphere is considered. The calculation is carried out as far as terms of order m 3 ω 2 / r 7 in the G μ v . Again it is found impossible to find a solution of the equation G μ v = 0, but the ‘material’ energy-tensor can be identified with an electromagnetic energy-tensor. In both the cases of the periodic system and of the sphere potentials are found for which the energy-tensor represents a field of the form proposed by Blackett (1947), but the investigation does not rule out the possibility that other alternative solutions may exist. The solution in the case of a ‘Blackett field’ requires a current-charge vector inside the material with a non-zero charge, but the precise values of either the charge or current densities are determined. The solution, in fact, covers the case of a rotating charge as well as of a rotating ‘neutral' body. Presumably, further physical considerations must be taken into account to solve the problem completely. As the rotation of the earth produces no visible electric field, the resultant charge must be small.

1. In a recent investigation of the problem of two bodies in general relativity theory, Prof. Levi-Civita (1937 b ) has reached the conclusion that the centre of gravity has a secular acceleration in the direction of the major axis of the orbit towards the periastron of the larger mass. He gives an example of a binary star in which this acceleration may become detectable in much less than a century, perhaps even in a few years. Since the periastron slowly revolves, Levi-Civita’s result implies that the binary star as a whole spontaneously describes a circle of very large radius. There seems to be no obvious ground for regarding this as impossible; it is conceivable that an unsymmetrical system may radiate momentum by gravitational waves and so experience a recoil. But the behaviour is so peculiar as to inspire doubt; and we determined to re-examine the problem with a view either to detecting an error or to obtaining further light on the nature of the phenomenon.

The approximate value of the world invariant at a point in a plane containing a rotating cohesive system such as a rod is calculated for a point at great distances from the system. It is found that the invariant has a stationary value when the rod is seen to be pointing towards the point in question. It is concluded that the speed of propagation of gravitation is the same as that of light.

An instrument for time‐resolved spectroscopy with an effective time resolution capability of 2×10−7 sec has been built using a pulsed photomultiplier and the stroboscopic time resolution technique. Because of the higher voltages allowable in pulsed operation, the photomultiplier gain is found to be increased by more than two orders of magnitude and the dark current is reduced by a factor of about five. Therefore, the apparatus is very useful for analyzing weak fluorescence and absorption spectra of microsecond duration. Fluorescence rise and decay times of fractions of a microsecond have also been measured. The instrument was found to be very suitable for analyzing the fluorescence properties of rare‐earth chelate laser materials.

Ungefahr 200 Praparate von basischem Bleisulfat sind nach verschiedenen Verfahren hergestellt worden.

In this paper a periodic solution of the gravitational equations is examined. The solution, which is valid throughout all space, is such that the internal and external fields and their derivatives are continuous at the boundary of a spheroid rotating about an axis other than that of symmetry. At great distances from the system the solution has the same form as the field due to a rotating rod and can be applied to problems like the determination of the velocity of propagation of gravitational waves and the loss of energy of a rotating cohesive system.

SummaryIn classical mechanics the mass of a system of gravitating particles can be denned to be the mass of an equivalent particle which gives the same field at great distances, or alternatively the mass can be defined by means of Gauss' Theorem. Reference to the former procedure was made by Eddington and Clark (1938) in a discussion on the problem of n bodies. The relativistic extension of Gauss' Theorem has been investigated by Whittaker (1935) for a particular form of the line-element and for more general fields by Ruse (1935). The latter, treating the problem from a purely geometrical point of view, expressed the integral of the normal component of the gravitational force as the sum of two volume integrals. The physical significance of one of these integrals was quite obvious but the meaning of the other was far from clear. In this paper the terms in Ruse's result are examined as far as the order m2 in the case of a fundamental observer at rest and the 1938 discussion modified to bring the two investigations into line. It is concluded that the surface integral of the normal component of the gravitational force taken over an infinite sphere is –4π × the energy of the system.

In this paper an investigation is made of the properties of material which is under isotropic stress p when in a strained state, and is such that the relation between the stress and the dilatation Δ iswhere α is the density, assumed constant in the unstrained state, and c is the velocity of light. It is shown that in this material the waves of dilatation travel with the velocity of light and that a disk or cylinder composed of this kind of matter suffers no change in radius when it is made to rotate.It is suggested that it is not unreasonable to attach the label incompressible to matter having these properties.

Hamilton’s principle is applied to an invariant integral in which the field variables, regarded as independent, are the coefficients Γμνα defining a symmetric affine connection, the metric tensorgμνand the electromagnetic four-vectorxμ. Variation of the Γμνα yields an expression for the Γμνα in terms ofgμνandxμVariations with respect to thexμand thegμνlead respectively to the field equations\(\begin{gathered} F^{\mu \nu } _{i\nu } \hfill \\ G_{\mu \nu } - \frac{1}{2}g_{\mu \nu } G + \lambda g_{\mu \nu } = B\left( {F_{\mu \alpha } F_\nu ^\alpha - \frac{1}{4}g_{\mu \nu } F_{\alpha \beta } F^{\alpha \beta } } \right) \hfill \\ \end{gathered} \)% MathType!End!2!1! whereB is a constant which experience requires to be positive,\(F_{\mu \nu } = \frac{{\partial _{\kappa _\mu } }}{{\partial _{x_\mu } }} - \frac{{\partial _{\kappa \nu } }}{{\partial _{x_\mu } }}\)% MathType!End!2!1! and a semi-colon denotes covariant differentiation.

SummaryLittle progress has been made in the development of a relativity theory of elasticity, although it has been realised that no disturbance can be propagated with a velocity greater than that of light. In 1917 Lorentz (1) gave a relativistic formulation of the laws of elasticity in the case of small strain and, applying the theory to the problem of a rotating, incompressible, homogeneous disc, he claimed that the radius as measured by an observer at rest on the disc undergoes a contraction. His result was accepted by Eddington (4) but was attacked by others. A great deal has been written on the subject, but it has never been pointed out that both Lorentz and Eddington were considering material in which the waves of dilatation travel with an infinite velocity. In this paper we define “incompressible” matter as that in which these waves are propagated with the velocity of light and Poisson's ratio tends to the value ½. This gives an upper limit to the modulus of compression k, which in this case is the elastic constant λ, and as a result the expansion determined by the ordinary classical theory has to be taken into account. It is found that the “relativity contraction” is exactly cancelled by the “classical expansion”. Throughout the discussion on the rotating disc the analysis is restricted to the case of small strain.The equations of equilibrium of a continuous static distribution of matter are also investigated in the case of weak fields for which the fourth power of the density may be neglected.

SummaryThe gravitational field of a system of particles was investigated by de Sitter as far back as 1916. A minor alteration to the analysis was made by Eddington and Clark in 1938. The amended value of the potential g44 is the same as that derived by Einstein, Infeld and Hoffmann without making use of the energy-tensor; this agreement suggests that the revised de Sitter argument is correct. In this paper we show that this is not the case, for the de Sitter analysis completely overlooked any possible interaction terms in the stress components of the energy-tensor. We find the value of these terms, pmn, and show that the agreement mentioned above is due to the fact that the volume integral of pu vanishes.

The radiographic illustrations which are presented in this article prove that x-rays can be produced for experimental purposes with a unit which can be built for a very small fraction of the cost of installation of a standard x-ray unit. The apparatus consists essentially of a 1/10 hp. motor which operates a rotor whose function is to raise the frequency of the current; a set of brushes for conducting the current from the rotor to the block of condensers (0.16 MF) ; a “kick coil” of 24-ohm capacity; a resonator for building up the voltage, and an old 01-A radio tube. The schematic plan of the apparatus is given in Figure 1. The construction of the apparatus is very simple. A “kick coil” consisting of one and one-quarter pound of No. 24 silk covered wire is wound on a bakelite core five-eighths inch in diameter and three inches long. The purpose of this coil is to excite the primary circuit of an Oudin resonator which consists of six turns of No. 10 cotton-covered space-wound wire which is connected to two...