1. Here, as in the preceding paper, we shall describe the gravitational field by means of a simple scalar potentialG. Such a description, although not sufficient to deal with the subtler gravitational effects to which general relativity addresses itself, is nevertheless covariant and adequate for the needs of magnetofluid dynamics. As in the preceding paper, everything we shall do here will be within the framework ofspecial, rather thangeneral, relativity. The metric tensor is taken to beg 00=−g jj=1,j=1, 2, 3;g jk=0,j ≠k. The notation used (with the exceptions noted at the beginning of the preceding paper) is that introduced in the first paper of this series (L. A. Schmid:Nuovo Cimento, 47 B, 1 (1967). This paper will be referred to in the text as I. As noted above, the paper immediately preceding the present one will be referred to as II.
2. Cited in footnote (1).
3. See, for example,L. Brand:Vector and Tensor Analysis (New York, 1947), p. 227.
4. For discussions of the familiar nonrelativistic Clebsch transformation of the fluid velocity, seeH. Lamb:Hydrodynamics, 6th ed. (Cambridge, 1932), p. 248;H. Bateman:Partial Differential Equations of Mathematical Physics (Cambridge, 1932), p. 164;J. Serrin:Encyclopedia of Physics, vol.8/1 (Berlin, 1959), p. 169. A relativistic Clebsch transformation of the usual canonical momentumµv j + (q/c)A j, rather than of the generalized canonical momentumP j, has been used byC. C. Wei:Phys. Rev.,113, 1414 (1959).
5. This has been discussed in somewhat greater detail elsewhere:L. A. Schmid:Phys. of Fluids,9, 102 (1966).