The optical properties of reflecting echelette gratings, used in the infra-red region of the spectrum, are discussed theoretically. Expressions are derived for various important characteristics including the wave-length relationship, the dispersion and the resolving power of spectrometers using such gratings. The intensity distribution is discussed and illustrated by reference to a particular spectrometer fitted with a grating of 1200 lines to the inch. The relative importance of other factors such as the variation of available energy with wave-length, the dispersion of the preliminary optical system, etc., is considered and tabulated. Particular consideration is given to the properties of such gratings when used in much higher orders of interference than are common at present. With large aperture spectrometers, this possibility of using comparatively coarse gratings with a high order of interference is of great practical importance.

A new and fruitful theory of turbulent motion was published in 1941 by A. N. Kolmogoroff. It does not seem to be as widely known outside the U.S.S.R. as its importance warrants, and the present paper therefore describes the theory in some detail before presenting a number of extensions and making a comparison of experimental results with some of the theoretical predictions.

Kolmogoroff's basic notion is that at high Reynolds number all kinds of turbulent motion, of arbitrary mean-flow characteristics, show a similar structure if attention is confined to the smallest eddies. The motion due to these eddies of limited size is conceived to be isotropic and statistically steady. Within this range of eddies we recognize two limiting processes. The influence of viscosity on the larger eddies of the range is negligible if the Reynolds number is large enough, so that their motion is determined entirely by the amount of energy which they are continually passing on to smaller eddies. This quantity of energy is the local mean energy dissipation due to turbulence. On the other hand, the smaller eddies of the range dissipate through the action of viscosity a considerable proportion of the energy which they receive, and the motion of the very smallest eddies is entirely laminar. The analytical expression of this physical picture is that the motion due to eddies less than a certain limiting size in an arbitrary field of turbulence is determined uniquely by two quantities, the viscosity and the local mean energy dissipation per unit mass of the fluid.

The mathematical method of describing the motion due to eddies of a particular size is to construct correlations between the differences of parallel-velocity components at two points at an appropriate distance apart. Kinematical results analogous to those for turbulence which is isotropic in the ordinary sense are obtained, and then the scalar functions occurring in the expressions for the correlations are determined by dimensional analysis. The consequences of the theory in the case of turbulence which possesses ordinary isotropy are analysed and various predictions are made. One of these, namely that dimensionless ratios of moments of the probability distribution of the rate of extension of the fluid in any direction are universal constants, is confirmed by recent experiments, so far as the second and third moments are concerned. In several other cases it can be said that relations predicted by the theory have the correct form, but further experiments at Reynolds numbers higher than those hitherto used will be required before the theory can be regarded as fully confirmed. If valid, Kolmogoroff's theory of locally isotropic turbulence will provide a powerful tool for the analysis of problems of non-uniform turbulent flow, and for the determination of statistical characteristics of space and time derivatives of quantities influenced by the turbulence.

The velocity distribution in steady rectilinear plastic flow of a Bingham solid between coaxial circular cylinders in relative motion can be obtained exactly by simple arguments. On the basis of the general equations of plastic flow, an approximate velocity distribution is derived below for the case of eccentric circular cylinders as rigid boundaries and zero pressure gradient by making use of a conformal transformation. This approximation is valid only if a dimensionless parameter S (which is proportional to the yield value) is sufficiently small, and there is flow in the whole region between the cylinders. The differences in velocity distribution in the cases of Bingham solid (S finite) and Newtonian liquid (S zero) are illustrated by a particular example. It is shown that the effect of a finite yield value is to cause the contours of equal velocity in a normal section to become more nearly concentric with the inner boundary as the yield value increases from zero.

Some data obtained at Leiden on relaxation effects in a diluted potassium chrome alum are discussed in the light of a paper by Temperley (10), and excellent agreement is found with the conclusions of that paper. The primary effect of diluting the salt is to reduce the magnetic interaction, and the observed effects are a big increase in the relaxation time in zero field, and a decrease of the relaxation time with increasing field instead of an increase. It is predicted that a decrease should set in with an ordinary salt at liquid helium temperatures at fields somewhat higher than have so far been used. Van Vleck's criticisms of Temperley's paper are discussed, and it is concluded that they are not valid in their present form.

The complete set of matrix representations of a set of n quantities β1, β2,…,βn satisfying

is obtained for all values of n. It is found that if n = 2v or n = 2v + 1, there are v + 1 irreducible representations with the respective degrees 1, but if n = 2v + 1 there are in addition two conjugate representations of order , the symbol denoting the binomial coefficient. The explicit representations are given for n = 2, 3, 4, 5.

By electrical analysis of the output from a hot-wire anemometer, it is possible to measure rapidly and accurately all the quantities appearing in the theoretical equations for the decay of isotropic turbulence. The technique for these measurements is described, and possible extensions and limitations of the method are discussed. Measurements have been made of the second and fourth derivatives of the longitudinal double-velocity correlation at the origin, the third derivative of the longitudinal triple-velocity correlation at the origin, the statistical distribution in time of the velocity fluctuations, and the integral scale of turbulence.

The hysteresis losses and demagnetizing coefficients of rectangular Fe-Si strips of various dimensions have been investigated. The hysteresis loss is approximately independent of the value of N, in agreement with a simple theoretical argument. The value of the demagnetizing coefficient is in fair agreement with the value calculated for the inscribed ellipsoid.

It is shown that In113* can be obtained by nuclear excitation of indium by X-rays. The cross-section per nucleus for the production of In113* with 2 MeV. X-rays is of the same order as the cross-section for the production of In115*. The decay period of In115*, for which some discrepancy was apparent in the literature, was definitely proved to be 4·5 hr.

A more detailed analysis has been carried out of earlier results obtained in the scattering of X-radiation by liquid He II. When certain necessary corrections have been applied to these results and a comparison made with theoretical intensity distribution functions to be expected for certain ordered arrangements of atoms in a liquid, it is found that the arrangement of atoms in liquid He II most probably follows either a diamond or a simple cubic configuration. Considerations of energy and atomic volume render the former the more likely arrangement.

1. The theoretical study of the transport phenomena in metals requires the solution of a certain integral equation, which is formed by equating the rate of change of the distribution function of the conduction electrons due to the applied fields and temperature gradients to the rate of change due to the mechanism responsible for the scattering. This integral equation has so far been solved only in the simplest case where the electrons are assumed to be quasi-free, the energy being proportional to the square of the wave vector, and this assumption will be made throughout the present paper. The scattering of the electrons is due to two causes: the thermal vibration of the crystal lattice and the presence of impurities or strains. The scattering due to the impurities can always be described in terms of a free path l (or more conveniently a time of relaxation τ, were l = τν, ν being the average velocity of the conduction electrons), whereas for the scattering due to the thermal vibration this is possible only at high temperatures such that (Θ/T)2 can be neglected, where Θ is the Debye temperature (1). At very low temperatures the scattering due to the thermal vibration can be neglected compared with that due to the impurities. When a time of relaxation exists, the integral equation for the distribution function reduces to an ordinary equation, and its solution is then a comparatively simple matter. In the general case the problem is much more difficult, and no rigorous and generally valid solution has so far been obtained.

It is shown that the algebra of the Duffin-Kemmer matrices can be handled quite neatly by introducing an extra dimension and by using the Γ-formalism of an earlier paper (3). By this means it is possible to derive identities similar to the De Broglie-Pauli identities for the Dirac matrices. To complete the analogy a Γ-formalism is also set up for the Dirac matrices.

The production of by deuteron bombardment of uranium has been established and the radiations of this product have been examined by the absorption method. The normal mode of disintegration involves β-particles having an upper energy limit of 1·20 ± 0·02 MeV. and a low-energy γ-ray of 76 ± 3 keV. quantum energy. Evidence has been found for electrons of less energy (about 0·1 per disintegration) and more penetrating γ-rays of relatively low intensity. Quantum radiations corresponding broadly to the L X-radiations, to be expected to follow the internal absorption of the low-energy γ-ray, have also been detected.

The excitation function for the process has been studied, and the conclusion reached that the Oppenheimer-Phillips mechanism is responsible for the larger part of the yield.

A simple formula is obtained for the visibility of Talbot's bands. This formula shows that the bands occur only if the glass plate is inserted at one particular side of the telescope objective, and that when they occur, their visibility is proportional to the plate thickness up to a certain optimum thickness, and then decreases linearly, vanishing at and beyond twice the optimum thickness.

The physical significance of the parameters which appear in the combinatory factors g(Ni) and g(Ni, Xij) in the statistical mechanics of mixtures is examined. Hitherto, closed ring molecules have been excluded from the jurisdiction of the formulae for these combinatory factors. The means by which this restriction on the validity of the formulae can be removed is indicated. It is concluded that the equations given by Guggenheim are formally applicable in all cases provided that appropriate values, which differ according as the molecules are simple and branched chain or closed ring molecules, are substituted for certain parameters which occur in the equations.

It is shown that the white light fringe obtained with Brewster's fringes or with ‘scatter’ fringes has a breadth which decreases with the reflexion coefficient R of the film surfaces. The decrease of intensity from the centre of the fringe is given by the usual Fabry-Perot formula except that R is replaced by R2.

The radioactivity of the naturally and artificially produced lutecium isotope has been investigated on a number of occasions (l, 2). A 4 hr. activity was observed when lutecium was activated by slow neutrons and later a 6-day period was observed by Hevesi and Levi (3). Heyden and Wefelmeier (4) discovered the natural radioactivity of lutecium, while Libby (5) made measurements indicating that this natural activity consisted of a negative electron spectrum of maximum energy 0·215 MeV. Mattauch and others (6) showed from mass spectrograph evidence that in addition to the main isotope of lutecium of mass 175 there was an isotope of mass 176 with an abundance of 2·5%. The second isotope had been reported previously by Gollnow (7), but not identified. Since Hf176 and Yb176 are known to be stable, whereas Hf175 and Yb175 do not exist in nature, the radioactivity of natural lutecium must be assigned to Lu176. Flammersfeld and Mattauch (8) measured the energy of the natural spectrum by the absorption method and found it to be 0·4 MeV. They observed also a γ-radiation (1–2 quanta per β-particle) of 0·26 MeV. In addition, they investigated the radiations resulting from slow neutron bombardment of lutecium. They estimate the shorter period, previously reported by Hevesi and Levi, to be 3·4 hr. and to consist of a β-spectrum of maximum energy 1·150 MeV. They estimate the longer period to be 6·6 days and to consist of β-spectrum of maximum energy 0·440 MeV. In view of the closeness of this latter energy to 0·4 MeV., Flammersfeld and Mattauch allocate the 6·6 days' activity to an isomeric state of Lu176. The short period is allocated by these authors to Lu177.