If for and 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 are omitted while those with itself are preserved.
When this is done reduces to
and, taking into consideration (44) and (48), we find after division by
In the second term of (44) we have interchanged here the indices and .
If for shortness' sake we put, for
we may write
The set of quantities will be called the complex and the set of the four quantities which stand on the left hand side of (54) in the cases , the divergency of the complex. It will be denoted by and each of the four quantities separately by .
The equation therefore becomes
- Einstein uses the word "divergency" in a somewhat different sense. It seemed desirable however to have a name for the left hand side of (54) and it was difficult to find a better one.