Leap seconds are exactly analogous to leap days. One additional unit is added to the calendar, shifting everything down. For leap days we add a day 29 when normally we wrap after 28. For leap seconds we add second 60 when normally we wrap after 59.

Imagine a timestamp defined as days since January 1, 1970, except that it ignores leap years and says all years have 365 days. Leap days are handled by giving February 29 the same day number as February 28.

If you do basic arithmetic with these timestamps to answer the question, “how many days has it been since Nixon resigned? then you will get the wrong number. You’ll calculate N, but the sun has in fact risen N+13 times since that day.

Same thing with leap seconds. If you calculate the number of seconds since Nixon resigned by subtracting POSIX timestamps, you’ll come up short. The actual time since that event is 20-some seconds more than the value you calculate.