Page:LorentzGravitation1916.djvu/49

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of the second derivatives of those quantities. This latter involves that, if we replace (91) by

the second and the third term annul each other. Thus

(92)

If now we define a complex by the equation

(93)

we have

(94)

If finally we put

we infer from (90) and (94)

(95)

and from (88), (89), (93) and (92)

(96)

and for

(97)

Formula (95) shows that the quantities can be taken just as well as the expressions (88) for the stress-energy-components and we see from (96) and (97) that these new expressions contain only the first derivatives of the coefficients ; they are homogeneous quadratic functions of these differential coefficients.

This becomes clear when we remember that is a function of this kind and that only contributes something to the second term of (96) and the first of (97); further that the derivatives of occurring in the following terms contain only the quantities and not their derivatives.


§ 55. Einstein's stress-energy-components have a form widely different from that of the above mentioned ones. They are