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time axis could be detected. Hence, one concludes that if the deformation introduced changes in the elastic constants C33 or C44 these changes must be less than one or two percent for strains up to 10-' radian. Such a result is to be expected since the appearance of slip bands on the surface indicates that the deformation was confined to numerous very narrow bands. Within these bands one might expect very diGerent elastic modulii but since their total thickness is small compared to the total thickness of undisturbed crystal, the sound wave spends most of its time traveling in an undeformed lattice. The author is particularly indebted to Professor E. P. T. Tynda11 for his encouragement and valuable suggestions throughout the development and performance of this experiment.

Both the unusually large magnitude and strong temperature dependence of the extraordinary Hall effect in ferromagnetic materials can be understood as effects of the spin-orbit interaction of polarized conduction electrons. It is shown that the interband matrix elements of the applied electric potential energy combine with the spin-orbit perturbation to give a current perpendicular to both the field and the magnetization. Since the net effect of the spin-orbit interaction is proportional to the extent to which the electron spins are aligned, this current is proportional to the magnetization. The magnitude of the Hall constant is equal to the square of the ordinary resistivity multiplied by functions that are not very sensitive to temperature and impurity content. The experimental results behave in such a way also.

The most general form of the Hamiltonian of an electron or hole in a semiconductor such as Si or Ge, in the presence of an external homogeneous magnetic field, is given. Two methods of obtaining the corresponding energy levels are discussed. The first should yield very accurate values for the magnetic field in the (111) direction for either Si or Ge. The second is a perturbation method and is expected to give good results only for Ge.

An exactly soluble model of a one-dimensional many-fermion system is discussed. The model has a fairly realistic interaction between pairs of fermions. An exact calculation of the momentum distribution in the ground state is given. It is shown that there is no discontinuity in the momentum distribution in this model at the Fermi surface, but that the momentum distribution has infinite slope there. Comparison with the results of perturbation theory for the same model is also presented, and it is shown that, for this case at least, the perturbation and exact answers behave qualitatively alike. Finally, the response of the system to external fields is also discussed.

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calculated from Kasuya's formula, for the most pure samples above 3. 0'K and the dependence of Ho and Jo/Ao on carrier concentration, are under investigation.We wish to acknowledge the technica, l assistance provided by Mr. C. D. Wilson. We thank Mr. M. P. Mathur for providing Ge (grown by Miss L. Roth) which he found suitable for lowtemperature thermometers, and Professor H. Yearian for x-ray orientations of the samples. This is not quite the expectation for the very purest g-InSb due to its carrier concentration not being sufficiently degenerate; see Eq. (1) obtained from V. A.

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