  1. It seems to me that Boltzmann here adopts an (implicit) identification of probability and relative duration, At the very least, he does not indicate any difference in meaning between phrases like “During the greater part of that time, \(H\) will be very near to its minimum” and “It is extremely probable that \(H\) lies near its minimum”. Also, it seems that to me that his claim (ii) that peaks in the curve are “very rare”, and his claim (iii) that they are “very improbable” are intended as synonymous. This way of reading Boltzmann would indeed not fall out of tune with his previous interpretations of probability.