where j is the angular momentum per unit mass and S is the entropy per unit mass. We can thus rewrite Eq. (3.80) in the compact form

Note that the vectors $0 and are always directed along the outer normal to the surfaces m = constant and p = constant, respectively. Similarly, the vectors $ and ^ are orthogonal to the surfaces j = constant and S = constant, respectively, although we do not know a priori whether they are directed along the inner or outer normal.

Since the vectors (3.82)-(3.85) and the tensor (3.86) play an essential role in the subsequent discussion, we shall briefly summarize their main properties. First, taking the curl of Eq. (3.48), we obtain grad — x gradp = —- grad(—2m4) x 1m- (3.87)

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