improved that Dr. Maskelyne considered them available for attaining
this long-wished-for object. The method which I think was then, for the
first time, proposed was the now familiar one of lunar distances.
Several trials of the method were made by accomplished gentlemen who
considered that nothing was wanting to make it practical at sea but a
Nautical Ephemeris. The tables of the moon, necessary for the purpose,
were prepared by Tobias Mayer, of Gottingen, and the regular annual
issue of the work was commenced in 1766, as already stated. Of the
reward which had been offered, three thousand pounds were paid to the
widow of Mayer, and three thousand pounds to the celebrated
mathematician Euler for having invented the methods used by Mayer in
the construction of his tables. The issue of the Nautical Ephemeris was
intrusted to Dr. Maskelyne. Like other publications of this sort this
ephemeris has gradually increased in volume. During the first sixty or
seventy years the data were extremely meagre, including only such as
were considered necessary for the determination of positions.
In 1830 the subject of improving the Nautical Almanac was referred by
the Lord Commissioners of the Admiralty to a committee of the
Astronomical Society of London. A subcommittee, including eleven of the
most distinguished astronomers and one scientific navigator, made an
exhaustive report, recommending a radical rearrangement and improvement
of the work. The recommendations of this committee were first carried
into effect in the Nautical Almanac for the year 1834. The arrangement
of the Navigator's Ephemeris then devised has been continued in the
British Almanac to the present time.
A good deal of matter has been added to the British Almanac during the
forty years and upwards which have elapsed, but it has been worked in
rather by using smaller type and closer printing than by increasing the
number of pages. The almanac for 1834 contains five hundred and
seventeen pages and that for 1880 five hundred and nineteen pages. The
general aspect of the page is now somewhat crowded, yet, considering
the quantity of figures on each page the arrangement is marvellously
clear and legible.
The Spanish "Almanaque Nautico" has been issued since the beginning of
the century. Like its fellows it has been gradually enlarged and
improved, in recent times, and is now of about the same number of pages
with the British and American almanacs. As a rule there is less matter
on a page, so that the data actually given are not so complete as in
some other publications.
In Germany two distinct publications of this class are issued, the one
purely astronomical, the other purely nautical.
The astronomical publication has been issued for more than a century
under the title of "Berliner Astronomisches Jahrbuch." It is intended
principally for the theoretical astronomer, and in respect to matter
necessary to the determinations of positions on the earth it is rather
meagre. It is issued by the Berlin Observatory, at the expense of the
government.
The companion of this work, intended for the use of the German marine,
is the "Nautisches Jahrbuch," prepared and issued under the direction
of the minister of commerce and public works. It is copied largely from
the British Nautical Almanac, and in respect to arrangement and data is
similar to our American Nautical Almanac, prepared for the use of
navigators, giving, however, more matter, but in a less convenient
form. The right ascension and declination of the moon are given for
every three hours instead of for every hour; one page of each month is
devoted to eclipses of Jupiter's satellites, phenomena which we never
consider necessary in the nautical portion of our own almanac. At the
end of the work the apparent positions of seventy or eighty of the
brightest stars are given for every ten days, while it is considered
that our own navigators will be satisfied with the mean places for the
beginning of the year. At the end is a collection of tables which I
doubt whether any other than a German navigator would ever use. Whether
they use them or not I am not prepared to say.
The preceding are the principal astronomical and nautical ephemerides
of the world, but there are a number of minor publications, of the same
class, of which I cannot pretend to give a complete list. Among them is
the Portuguese Astronomical Ephemeris for the meridian of the
University of Coimbra, prepared for Portuguese navigators. I do not
know whether the Portuguese navigators really reckon their longitudes
from this point: if they do the practice must be attended with more or
less confusion. All the matter is given by months, as in the solar and
lunar ephemeris of our own and the British Almanac. For the sun we have
its longitude, right ascension, and declination, all expressed in arc
and not in time. The equation of time and the sidereal time of mean
noon complete the ephemeris proper. The positions of the principal
planets are given in no case oftener than for every third day. The
longitude and latitude of the moon are given for noon and midnight. One
feature not found in any other almanac is the time at which the moon
enters each of the signs of the zodiac. It may be supposed that this
information is designed rather for the benefit of the Portuguese
landsman than of the navigator. The right ascensions and declinations
of the moon and the lunar distances are also given for intervals of
twelve hours. Only the last page gives the eclipses of the satellites
of Jupiter. The Fixed Stars are wholly omitted.
An old ephemeris, and one well known in astronomy is that published by
the Observatory of Milan, Italy, which has lately entered upon the
second century of its existence. Its data are extremely meagre and of
no interest whatever to the navigator. The greater part of the volume
is taken up with observations at the Milan Observatory.
Since taking charge of the American Ephemeris I have endeavored to
ascertain what nautical almanacs are actually used by the principal
maritime nations of Europe. I have been able to obtain none except
those above mentioned. As a general rule I think the British Nautical
Almanac is used by all the northern nations, as already indicated. The
German Nautical Jahrbuch is principally a reprint from the British. The
Swedish navigators, being all well acquainted with the English
language, use the British Almanac without change. The Russian
government, however, prints an explanation of the various terms in the
language of their own people and binds it in at the end of the British
Almanac. This explanation includes translations of the principal terms
used in the heading of pages, such as the names of the months and days,
the different planets, constellations, and fixed stars, and the
phenomena of angle and time. They have even an index of their own in
which the titles of the different articles are given in Russian. This
explanation occupies, in all, seventy-five pages--more than double that
taken up by the original explanation.
One of the first considerations which strikes us in comparing these
multitudinous publications is the confusion which must arise from the
use of so many meridians. If each of these southern nations, the
Spanish and Portuguese for instance, actually use a meridian of their
own, the practice must lead to great confusion. If their navigators do
not do so but refer their longitudes to the meridian of Greenwich, then
their almanacs must be as good as useless. They would find it far
better to buy an ephemeris referred to the meridian of Greenwich than
to attempt to use their own The northern nations, I think, have all
begun to refer to the meridian of Greenwich, and the same thing is
happily true of our own marine. We may, therefore, hope that all
commercial nations will, before long, refer their longitudes to one and
the same meridian, and the resulting confusion be thus avoided.
The preparation of the American Ephemeris and Nautical Almanac was
commenced in 1849, under the superintendence of the late Rear-Admiral,
then Lieutenant, Charles Henry Davis. The first volume to be issued was
that for the year 1855. Both in the preparation of that work and in the
connected work of mapping the country, the question of the meridian to
be adopted was one of the first importance, and received great
attention from Admiral Davis, who made an able report on the subject.
Our situation was in some respects peculiar, owing to the great
distance which separated us from Europe and the uncertainty of the
exact difference of longitude between the two continents. It was hardly
practicable to refer longitudes in our own country to any European
meridian. The attempt to do so would involve continual changes as the
transatlantic longitude was from time to time corrected. On the other
hand, in order to avoid confusion in navigation, it was essential that
our navigators should continue to reckon from the meridian of
Greenwich. The trouble arising from uncertainty of the exact longitude
does not affect the navigator, because, for his purpose, astronomical
precision is not necessary.
The wisest solution was probably that embodied in the act of Congress,
approved September 28, 1850, on the recommendation of Lieutenant Davis,
if I mistake not. "The meridian of the Observatory at Washington shall
be adopted and used as the American meridian for all astronomical
purposes, and the meridian of Greenwich shall be adopted for all
nautical purposes." The execution of this law necessarily involves the
question, "What shall be considered astronomical and what nautical
purposes?" Whether it was from the difficulty of deciding this
question, or from nobody's remembering the law, the latter has been
practically a dead letter. Surely, if there is any region of the globe
which the law intended should be referred to the meridian of
Washington, it is the interior of our own country. Yet, notwithstanding
the law, all acts of Congress relating to the territories have, so far
as I know, referred everything to the meridian of Greenwich and not to
that of Washington. Even the maps issued by our various surveys are
referred to the same transatlantic meridian. The absurdity culminated
in a local map of the city of Washington and the District of Columbia,
issued by private parties, in 1861, in which we find even the meridians
passing through the city of Washington referred to a supposed Greenwich.
This practice has led to a confusion which may not be evident at first
sight, but which is so great and permanent that it may be worth
explaining. If, indeed, we could actually refer all our longitudes to
an accurate meridian of Greenwich in the first place; if, for instance,
any western region could be at once connected by telegraph with the
Greenwich Observatory, and thus exchange longitude signals night after
night, no trouble or confusion would arise from referring to the
meridian of Greenwich. But this, practically, cannot be done. All our
interior longitudes have been and are determined differentially by
comparison with some point in this country. One of the most frequent
points of reference used this way has been the Cambridge Observatory.
Suppose, then, a surveyor at Omaha makes a telegraphic longitude
determination between that point and the Cambridge Observatory. Since
he wants his longitude reduced to Greenwich, he finds some supposed
longitude of the Cambridge Observatory from Greenwich and adds that to
his own longitude. Thus, what he gives is a longitude actually
determined, plus an assumed longitude of Cambridge, and, unless the
assumed longitude of Cambridge is distinctly marked on his maps, we may
not know what it is.
After a while a second party determines the longitude of Ogden from
Cambridge. In the mean time, the longitude of Cambridge from Greenwich
has been corrected, and we 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 of Washington. The division of the matter without serious
duplication is more easy than might at first be imagined. In explaining
it, I will take the ephemeris as it now is, with the small changes
which have been made from time to time.
One of the purposes of any ephemeris, and especially of that of the
navigators, is to give the position of the heavenly bodies at
equidistant intervals of time, usually one day. Since it is noon at
some point of the earth all the time, it follows that such an ephemeris
will always be referred to noon at some meridian. What meridian this
shall be is purely a practical question, to be determined by
convenience and custom. Greenwich noon, being that necessarily used by
the navigator, is adopted as the standard, but we must not conclude
that the ephemeris for Greenwich noon is referred to the meridian of
Greenwich in the sense that we refer a longitude to that meridian.
Greenwich noon is 18h 51m 48s, Washington mean time; so the ephemeris
which gives data for every Greenwich noon may be considered as referred
to the meridian of Washington giving the data for 17h 51m 48s,
Washington time, every day. The rule adopted, therefore, is to have all
the ephemerides which refer to absolute time, without any reference to
a meridian, given for Greenwich noon, unless there may be some special
reason to the contrary. For the needs of the navigator and the
theoretical astronomer these are the most convenient epochs.
Another part of the ephemeris gives the position of the heavenly
bodies, not at equidistant intervals, but at transit over some
meridian. For this purpose the meridian of Washington is chosen for
obvious reasons. The astronomical part of our ephemeris, therefore,
gives the positions of the principal fixed stars, the sun, moon, and
all the larger planets at the moment of transit over our own meridian.
The third class of data in the ephemeris comprises phenomena to be
predicted and observed. Such are eclipses of the sun and moon,
occultations of fixed stars by the moon, and eclipses of Jupiter's
satellites. These phenomena are all given in Washington mean time as
being most convenient for observers in our own country. There is a
partial exception, however, in the case of eclipses of the sun and
moon. The former are rather for the world in general than for our own
country, and it was found difficult to arrange them to be referred to
the meridian of Washington without having the maps referred 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 considered
necessary by Ptolemy in order to represent the inequalities in the
motions of the planets around the sun.
The next great advance made in the theory of the planetary motion was
the discovery by Kepler of the celebrated laws which bear his name.
When it was established that each planet moved in an ellipse having the
sun in one focus it became possible to form tables of the motions of
the heavenly bodies much more accurate than had before been known. Such
tables were published by Kepler in 1632, under the name of Rudolphine
Tables, in memory of his patron, the Emperor Rudolph. But the laws of
Kepler took no account of the action of the planets on one another. It
is well known that if each planet moved only under the influence of the
gravitating force of the sun its motion would accord rigorously with
the laws of Kepler, and the problems of theoretical astronomy would be
greatly simplified. When, therefore, the results of Kepler's laws were
compared with ancient and modern observations it was found that they
were not exactly represented by the theory. It was evident that the
elliptic orbits of the planets were subject to change, but it was
entirely beyond the power of investigation, at that time, to assign any
cause for such changes. Notwithstanding the simplicity of the causes
which we now know to produce them, they are in form extremely complex.
Without the knowledge of the theory of gravitation it would be entirely
out of the question to form any tables of the planetary motions which
would at all satisfy our modern astronomers.
When the theory of universal gravitation was propounded by Newton he
showed that a planet subjected only to the gravitation of a central
body, like the sun, would move in exact accordance with Kepler's laws.
But by his theory the planets must attract one another and these
attractions must cause the motions of each to deviate slightly from the
laws in question. Since such deviations were actually observed it was
very natural to conclude that they were due to this cause, but how
shall we prove it? To do this with all the rigor required in a
mathematical investigation it is necessary to calculate the effect of
the mutual action of the planets in changing their orbits. This
calculation must be made with such precision that there shall be no
doubt respecting the results of the theory. Then its results must be
compared with the best observations. If the slightest outstanding
difference is established there is something wrong and the requirements
of astronomical science are not satisfied. The complete solution of
this problem was entirely beyond the power of Newton. When his methods
of research were used he was indeed able to show that the mutual action
of the planets would produce deviations in their motions of the same
general nature with those observed, but he was not able to calculate
these deviations with numerical exactness. His most successful attempt
in this direction was perhaps made in the case of the moon. He showed
that the sun's disturbing force on this body would produce several
inequalities the existence of which had been established by
observation, and he was also able to give a rough estimate of their
amount, but this was as far as his method could go. A great improvement
had to be made, and this was effected not by English, but by
continental mathematicians.
The latter saw, clearly, that it was impossible to effect the required
solution by the geometrical mode of reasoning employed by Newton. The
problem, as it presented itself to their minds, was to find algebraic
expressions for the positions of the planets at any time. The latitude,
longitude, and radius-vector of each planet are constantly varying, but
they each have a determined value at each moment of time. They may
therefore be regarded as functions of the time, and the problem was to
express these functions by algebraic formulae. These algebraic
expressions would contain, besides the time, the elements of the
planetary orbits to be derived from observation. The time which we may
suppose to be represented algebraically by the symbol t, would remain
as an unknown quantity to the end. What the mathematician sought to do
was to present the astronomer with a series of algebraic expressions
containing t as an indeterminate quantity, and so, by simply
substituting for t any year and fraction of a year whatever--1600,
1700, 1800, for example, the result would give the latitude, longitude,
or radius-vector of a planet.