We also want, after we have passed to the new coordinates, use the sign instead of for a differentiation with respect to time at constant relative coordinates, so that
(18)
The derivative with respect to time, which occurs in the basic equations (I) - (V), are all of the kind indicated by . We will maintain this sign as an abbreviation for the longer term (18).
In contrast, a point over a letter shall henceforth — such as - indicate a differentiation with respect to time at constant relative coordinates. Thus the terms and in (4) and (IV) may not be left unaltered. By , for example, we understood a vector with components
or
We can suitably write this vector
while
or
will mean the vector with components
Based on the system of axes associated with ponderable matter, eventually the fundamental equations become