In most applications would be the velocity of the earth in its yearly motion.
§ 4. Now, in order to simplify the equations, the following quantities may be taken as independent variables
The last of these is the time, reckoned from an instant that is not the same for all points of space, but depends on the place we wish to consider. We may call it the local time, to distinguish it from the universal time t.
If we put
we shall have
will be denoted by
We shall also introduce, as new dependent variables instead of the components of and , those of two other vectors and , which we define as follows
In this way I find by transformation and mutual combination of the equations (Ib)—(Vb):