ffects
by repeated observations under a variety of conditions.

A necessary conclusion from all this is that the work of all observing
astronomers, so far as it could be used, must be combined into a
single whole. But here again difficulties are met at every step.
There has been, in times past, little or no concert of action among
astronomers at different observatories. The astronomers of each
nation, perhaps of each observatory, to a large extent, have gone
to work in their own way, using discordant data, perhaps not always
rigidly consistent, even in the data used in a single establishment.
How combine all the astronomical observations, found scattered
through hundreds of volumes, into a homogeneous whole?

What is the value of such an attempt? Certainly if we measure value
by the actual expenditure of nations and institutions upon the work,
it must be very great. Every civilized nation expends a large annual
sum on a national observatory, while a still greater number of such
institutions are supported at corporate expense. Considering that
the highest value can be derived from their labors only by such a
combination as I have described, we may say the result is worth an
important fraction of what all the observatories of the world have
cost during the past century.

Such was, in a general way, the great problem of exact astronomy
forty or fifty years ago. Its solution required extended cooperation,
and I do not wish to give the impression that I at once attacked it,
or even considered it as a whole. I could only determine to do my
part in carrying forward the work associated with it.

Perhaps the most interesting and important branch of the problem
concerned the motion of the moon. This had been, ever since the
foundation of the Greenwich Observatory, in 1670, a specialty
of that institution. It is a curious fact, however, that while
that observatory supplied all the observations of the moon,
the investigations based upon these observations were made almost
entirely by foreigners, who also constructed the tables by which the
moon's motion was mapped out in advance. The most perfect tables
made were those of Hansen, the greatest master of mathematical
astronomy during the middle of the century, whose tables of the
moon were published by the British government in 1857. They were
based on a few of the Greenwich observations from 1750 to 1850.
The period began with 1750, because that was the earliest at w