we change the velocity of our system by an infinitely small value . (It can of course be presupposed, that these infinitely small changes occur suddenly.)
Let
Thus at the beginning, within there is a total relative radiation (with respect to ) of radiation intensity or . According to (10), this radiation is corresponding to an absolute radiation of intensity
or .
And to this radiation, a total relative radiation with respect to is corresponding again, of intensity
or ,
where the index 1 supplemented to the quantities means, that these quantities are to be formed by and instead of and .
Thus we can say: At the beginning, the total relative radiation in with respect to , is given by the expressions
or
.
The density of these radiations is obtained by division by or . Thus the energy amount of these emphasized radiations in is equal to (density times volume):
(31a)
or
(31b)
Now, the relation of the total to the true relative radiation (the latter is actually absorbed) was equal to or ; thus when the velocity is equal to