Well, that's just axiomatic. if n is the number of relics per unit volume, that comes out to be N/V, so the equation becomes N=N/V*V, which is N=N
Seems like a pretty stupid point to make.
Also, who cares about the velocity if you are sampling a certain volume in a certain period?
When N=1, we know with certainty that we are not the only technological civilization that has ever existed.