Landau & Lifschitz, Classical Theory of Fields

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Landau & Lifschitz, "Classical Theory of Fields"

The above titled book is useful in many regards, but occasionally I find what I think are errors in the text. I have the Third Revised English edition (1971). On p. 231, for example, an unnumbered equation E = J e. I have omitted the superscripts; E and e are 4-pseudotensors and J is the determinant (Jacobian) of the transformation. To my understanding, all of the quantities are determinants, or otherwise they are all tensor-type elements. Down the page, further, the metric tensor g in arbitrary coordinates is related to g in galilean coordinates. The transformation, this time, is a product of two derivatives with the latter g. In this case, it seems that the product determinant is called J-squared, rather than just J as in the prior case.

Are my observations off the mark?

 

[goedelite]

PS I ask this apparently uninteresting question, because there are other equations in the same discussion that I find doubtful and I am wondering whether an errata exists that may have fallen out of my text or if a better edited book would be a good idea, if it exists.