hich
observations of any exactness were made. Only a few observations
were used, because Hansen, with the limited computing force at
his command,--only a single assistant, I believe,--was not able to
utilize a great number of the observations. The rapid motion of the
moon, a circuit being completed in less than a month, made numerous
observations necessary, while the very large deviations in the
motion produced by the attraction of the sun made the problem of the
mathematical theory of that motion the most complicated in astronomy.
Thus it happened that, when I commenced work at the Naval Observatory
in 1861, the question whether the moon exactly followed the course
laid out for her by Hansen's tables was becoming of great importance.

The same question arose in the case of the planets. So from a
survey of the whole field, I made observations of the sun, moon,
and planets my specialty at the observatory. If the astronomical
reader has before him the volume of observations for 1861, he will,
by looking at pages 366-440, be able to infer with nearly astronomical
precision the date when I reported for duty.

For a year or two our observations showed that the moon seemed
to be falling a little behind her predicted motion. But this soon
ceased, and she gradually forged ahead in a much more remarkable way.
In five or six years it was evident that this was becoming permanent;
she was a little farther ahead every year. What could it mean?
To consider this question, I may add a word to what I have already
said on the subject.

In comparing the observed and predicted motion of the moon,
mathematicians and astronomers, beginning with Laplace, have been
perplexed by what are called "inequalities of long period." For a
number of years, perhaps half a century, the moon would seem to be
running ahead, and then she would gradually relax her speed and fall
behind. Laplace suggested possible causes, but could not prove them.
Hansen, it was supposed, had straightened out the tangle by showing
that the action of Venus produced a swinging of this sort in the
moon; for one hundred and thirty years she would be running ahead
and then for one hundred and thirty years more falling back again,
like a pendulum. Two motions of this sort were combined together.
They were claimed to explain the whole difficulty. The moon, having
followed Hansen's theory for one hundred years, would not be likely
to deviate from it. Now, it was deviati