Page:LorentzGravitation1916.djvu/35

 If for $$\delta_{1}Q$$ and $$\delta_{2}Q$$ the expressions (48) and (44) are taken, the equation

is an identity for every choice of the variations.

It will likewise be so in the special case considered and we shall also come to an identity if in (50) the terms with the derivatives of $$\xi$$ are omitted while those with $$\xi$$ itself are preserved.

When this is done $$\delta Q$$ reduces to

$-\frac{\partial Q}{\partial x_{h}}\xi$|undefined

and, taking into consideration (44) and (48), we find after division by $$\xi$$

In the second term of (44) we have interchanged here the indices $$e$$ and $$f$$.

If for shortness' sake we put, for $$e\ne h$$

and for $$e=h$$

we may write

The set of quantities $$\mathfrak{s}_{h}^{e}$$ will be called the complex $$\mathfrak{s}$$ and the set of the four quantities which stand on the left hand side of (54) in the cases $$h=1,2,3,4$$, the divergency of the complex. It will be denoted by $$div\mathfrak{s}$$ and each of the four quantities separately by $$div_{h}\mathfrak{s}$$.

The equation therefore becomes