$\Delta N$ appears on the graph with values of +4 and -12. These are the numbers of seconds (or rather 'ticks') gained or lost each day. So $N$ must be the number of 'ticks' of the clock each day.
86400 is the number of seconds in one day, so we should have $NT=84600$ where $T$ is the time for each 'tick'. I don't understand why there is an extra factor of 2, I cannot see a reason for it.