have a longitude of Ogden which will be
discordant with that of Omaha, owing to the change in the longitude of
Cambridge. A third party determines the longitudes of, let us suppose,
St. Louis from Washington, he adds the assumed longitudes of Washington
from Greenwich which may not agree with either of the longitudes of
Cambridge and gets his longitude. Thus we have a series of results for
our western longitude all nominally referred to the meridian of
Greenwich, but actually referred to a confused collection of meridians,
nobody knows what. If the law had only provided that the longitude of
Washington from Greenwich should be invariably fixed at a certain
quantity, say 77 degrees 3', this confusion would not have arisen. It
is true that the longitude thus established by law might not have been
perfectly correct, but this would not cause any trouble nor confusion.
Our longitude would have been simply referred to a certain assumed
Greenwich, the small error of which would have been of no importance to
the navigator or astronomer. It would have differed from the present
system only in that the assumed Greenwich would have been invariable
instead of dancing about from time to time as it has done under the
present system. You understand that when the astronomer, in computing
an interior longitude, supposes that of Cambridge from Greenwich to be
a certain definite amount, say 4h 44m 30s, what he actually does is to
count from a meridian just that far east of Cambridge. When he changes
the assumed longitude of Cambridge he counts from a meridian farther
east or farther west of his former one: in other words, he always
counts from an assumed Greenwich, which changes its position from time
to time, relative to our own country.

Having two meridians to look after, the form of the American Ephemeris,
to be best adapted to the wants both of navigators and astronomers was
necessarily peculiar. Had our navigators referred their longitudes to
any meridian of our own country the arrangement of the work need not
have differed materially from that of foreign ones. But being referred
to a meridian far outside our limits and at the same time designed for
use within those limits, it was necessary to make a division of the
matter. Accordingly, the American Ephemeris has always been divided
into two parts: the first for the use of navigators, referred to the
meridian of Greenwich, the second for that of astronomers, referred to
the meridian