small piece of time, which I will call an
instant, per day; a locality on the earth will come up to a given
position one instant late on the first day after an event. On the
next day it would come up two instants late by reason of the
previous loss; but it also loses another instant during the course
of the second day, and so the total lateness by the end of that day
amounts to three instants. The day after, it will be going slower
from the beginning at the rate of two instants a day, it will lose
another instant on the fresh day's own account, and it started
three instants late; hence the aggregate loss by the end of the
third day is 1 + 2 + 3 = 6. By the end of the fourth day the whole
loss will be 1 + 2 + 3 + 4, and so on. Wherefore by merely losing
one instant every day the total loss in _n_ days is (1 + 2 + 3 +
... + _n_) instants, which amounts to 1/2_n_ (_n_ + 1) instants;
or practically, when _n_ is big, to 1/2n^2. Now in thirty-six
centuries there have been 3600 x 365-1/4 days, and the total loss
has amounted to an hour; hence the length of "an instant," the loss
per diem, can be found from the equation 1/2(3600 x 365)^2 instants
= 1 hour; whence one "instant" equals the 240 millionth part of a
second. This minute quantity represents the retardation of the
earth per day. In a year the aggregate loss mounts up to 1/3600th
part of a second, in a century to about three seconds, and in
thirty-six centuries to an hour. But even at the end of the
thirty-six centuries the day is barely any longer; it is only 3600
x 365 instants, that is 1/180th of a second, longer than it was at
the beginning. And even a million years ago, unless the rate of
loss was different (as it probably was), the day would only be
thirty-five minutes shorter, though by that time the aggregate
loss, as measured by the apparent lateness of any perfectly
punctual event reckoned now, would have amounted to nine years.
(These numbers are to be taken as illustrative, not as precisely
representing terrestrial fact.)

What can have caused the slowing down? Swelling of the earth by reason
of accumulation of meteoric dust might do something, but probably very
little. Contraction of the earth as it goes on cooling would act in the
opposite direction, and probably more than counterbalance the dust
effect