. But before we proceed further this last statement must be subjected to a correction, for we temporarily assumed above that there was an equal distribution of molecules and velocities throughout the whole volume. Now at the start, in defining the contemplated state, it was distinctly announced that there was an unequal distribution of such elementary conditions, the law of their distribution being given by the known number of molecules in each elementary volume
and in each constructed elementary velocity volume
. This correction is effected by the introduction of a finite proportionality factor,
which can be any given function of the location and velocity co-ordinates, so long as it fulfills the one condition (put in abbreviated form),
where