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