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A special quaternion representation is constructed for a pair of relativistic vectors and skew-symmetric tensors on the basis of the group theory of Lorentz transformations. The construction has considerable advantages over the conventional vector-tensor description. It is pointed out that pairs of Minkowski vectors as well as certain scalars and skew-symmetric tensors can also be interpreted as simple components of more complex physical quantities, each of them expressed by a single quaternion. As an example a concise relativistic quaternion formulation of Maxwell's electrodynamics is presented. The relativistic covariance can be maintained even for the existence of magnetic monopoles.

A variational method is shown to derive the equations describing the propagation of surfaces of weak discontinuity, i.e. of those surfaces across which at least one of the derivatives of the field variables suffer a jump. From the point of view of the calculus of variations this is the case of the broken extremals. The equations are derived from that variational principle which accounts for the non-broken extremals. The variational principle must be formulated at least in the frame of the special relativity.

The fundamental equations of an ideal—entropy current conserving—fluid are obtained from a Hamilton Principle. The Lagrangian is formulated in the usual way. The physical situation, however, requires the introduction of some constraints in the variational principle to restrict the variations of the original field quantities. The Lagrange multipliers entering in such a way are shown to lead to the possibility of vortices in the velocity field.

After giving a brief review of the fundamental equations of magnetofluido-dynamics and their limits of validity, the basic equations are derived for the case of media characterized by anisotropic conductivity, electric and magnetic permeability. The material quantities are supposed to be given tensor expressions with a nonvanishing determinant.

The relativisticCrocco-Vazsonyi equation is based on, and derived from the energymomentum tensor of an ideal fluid given byTaub. The contribution of a possible external field is taken into account. Three of the four components of theCrocco—Vazsonyi equation are the corresponding classical ones with corrections of the orderc −2. The fourth component equation provides the equqtion of continuity for the specific entropy.

Waves of small amplitude and the propagation of the surfaces of weak discontinuity (jumping derivatives) are studied in relativistic fluid dynamics. It is shown that in analogy with classical fluid dynamics, small amplitude waves and weak discontinuities have similar character. Both small amplitude waves, and surfaces of weak discontinuity are propagated with the velocity of sound, which, however, contains a relativistic correction.

Es werden die magnetohydrodynamischen Wellen kleiner Amplituden in unendlichen, zylindrischen Wellenleitern rechtwinkeligen bzw. kreisformigen Querschnittes untersucht. Mit einer ahnlichen Methode werden die stehenden magnetohydrodynamischen Wellen in einem Torus naherungsweise beschrieben. Es ergibt sich, das in beiden Fallen longitudinale, transversale und gemischte Wellen auftreten konnen.

The classical relativistic equations of motion of a pole particle subjected to scalar fields are investigated. It can be shown that in the case of a free particle the equations of motion admit a rigorous solution which corresponds to the uniform rectilinear motion. The probable existence of the runaway solutions is mentioned. It is shown that in a special case the particle can move uniformly along a straight line even under the action of a constant external field. The variation of the rest mass is studied on hand of this example and it is pointed out that the proper field of the particle gives no contribution to the rest mass. An analogue ofEliezer’s integral theorem is derived for a particle moving in a central scalar field. Finally it is shown in a certain approximation that the particle cannot perform a uniform circular motion under the action of the force derived from the Yukawa potential.