d to the same
meridian. Since, however, the meridian of Greenwich is most convenient
outside of our own territory, and since but a small portion of the
eclipses are visible within it, it is much the best to have the
eclipses referred entirely to the meridian of Greenwich. I am the more
ready to adopt this change because when the eclipses are to be computed
for our own country the change of meridians will be very readily
understood by those who make the computation.

It may be interesting to say something of the tables and theories from
which the astronomical ephemerides are computed. To understand them
completely it is necessary to trace them to their origin. The problem
of calculating the motions of the heavenly bodies and the changes in
the aspect of the celestial sphere was one of the first with which the
students of astronomy were occupied. Indeed, in ancient times, the only
astronomical problems which could be attacked were of this class, for
the simple reason that without the telescope and other instruments of
research it was impossible to form any idea of the physical
constitution of the heavenly bodies. To the ancients the stars and
planets were simply points or surfaces in motion. They might have
guessed that they were globes like that on which we live, but they were
unable to form any theory of the nature of these globes. Thus, in The
Almagest of Ptolemy, the most complete treatise on the ancient
astronomy which we possess, we find the motions of all the heavenly
bodies carefully investigated and tables given for the convenient
computation of their positions. Crude and imperfect though these tables
may be, they were the beginnings from which those now in use have
arisen.

No radical change was made in the general principles on which these
theories and tables were constructed until the true system of the world
was propounded by Copernicus. On this system the apparent motion of
each planet in the epicycle was represented by a motion of the earth
around the sun, and the problem of correcting the position of the
planet on account of the epicycle was reduced to finding its geocentric
from its heliocentric position. This was the greatest step ever taken
in theoretical astronomy, yet it was but a single step. So far as the
materials were concerned and the mode of representing the planetary
motions, no other radical advance was made by Copernicus. Indeed, it is
remarkable that he introduced an epicycle which was not