year 1762. Contemporary with La Caille lived several very eminent astronomers, of whom may be mentioned Cassini, Bouguer, Condamine, Maupertuis, and Clairaut, who were all employed soon after this, in measuring degrees of the meridian in different parts of the world. Professor Mayer, of Gottingen, deserves also to be mentioned, as contributing greatly to the improvement of the science, by the excellent set of tables which he calculated for finding the place of the moon, &c. These tables are now used in making the calculations of the Nautical Almanack. His widow received 30007. for them from the British Government, on account of their great accuracy. Mayer died in 1762, aged 41 years. D'Alembert also rendered great service to astronomy by his indefatigable labours, particularly in resolving the problem of the precession of the equinoxes. He died

1783.

Euler, one of the greatest geniuses and calculators that any age or nation can boast of, ought to be associated with the history of astronomy, as one of its most distinguished votaries and improvers. By his many and accurate calculations, he has rendered the most essential service, not only to astronomy, but to all the physical sciences; but his labours are too numerous to be detailed here. The eighteenth century was distinguished by many other eminent astronomers; viz. Maclaurin, Simpson, Bernoulli, Lambert, Mason, Boscovich, De Lisle, Bailly, La Lande, &c.

The celebrated La Grange, who outlived most of his contemporaries, was born at Turin in 1736, and has enriched astronomy with some of the most splendid discoveries of which it can boast. The subjects of his researches in this science were, the theory of Jupiter's satellites, the motions of the planets, and their action on each other, which he determined with great accuracy.

As the labours of the most distinguished astronomers that have appeared in the world have now been briefly noticed, and of whom their labours are the only memorials that exist; all that remains to complete this short account of the improvements that have taken place in the science, down to the present day, is to mention the labours of a few individuals still alive.

La Place has also distinguished himself by his labours to improve astronomy, particularly in solving the problem of the tides, in adding some new corrections to the lunar tables, and some discoveries respecting the precession of the equinoxes, He also ascertained the mean depth of the sea to be four leagues.

The name of Troughton ought also to be mentioned; for to no individual of the present age is practical astronomy more indebted than to this distinguished artist. The great improvements he has made upon astronomical instruments, has rendered his name celebrated in every country in Europe. There is scarcely an observatory of note to be found that does not contain some of Mr. Troughton's instruments.

The labours of Dr. Olbers, Harding, and Piazzi, will be noticed in treating of the new planets.

SUPPLEMENT

ΤΟ

ASTRONOMY

AS IT IS, COMPARED WITH WHAT IT WAS;

CONTAINING,

THE USE OF ASTRONOMICAL INSTRUMENTS,

THE

Method of computing the Notes of the Calendar,

THE MAGNITUDES, PERIODS, AND DISTANCES OF THE SUN, MOON,
PLANETS, &c.

INTRODUCTION.

THE Work, to which the following pages form a Supplement, being entirely confined to what may be termed the Descriptive and Historical parts of Astronomy, it was thought it might tend to make the work still more generally useful if it contained a description of Astronomical Instruments, and a short account of the Calendar. In order to accomplish this, without interfering with the plan proposed for treating of the various branches of Astronomy in a systematic and popular manner, it was found that a Supplement was neces sary. This has therefore been added, and will be found to form a very valuable addition to the Work itself.

The principal instruments used in the practical part of Astronomy are not only represented by figures and described at considerable length, but many other subjects connected

with Astronomy have been introduced, which could not have been noticed in a work purely astronomical. Among these will be found several interesting essays on Meteorology and Physical Geography, accompanied with diagrams, which cannot fail to render the subjects perfectly level to the understanding of the humblest inquirer after scientific information.

An acquaintance with the Calendar, and the manner of computing the common Notes of the year, is so useful to every class of society, that the rules contained in the following pages, for effecting this, cannot fail to gratify all who wish to possess the slightest acquaintance with Astronomy.

The manner of calculating most of the fundamental Elements employed in Practical Astronomy have been added, with the view of rendering the work not only more complete, but to induce the astronomical reader to enter more deeply, into this beautiful and highly interesting branch of the science. To those who have made some progress in the study of Astronomy, and who are in some degree judges of works which treat of the practical parts of the science, this will perhaps be considered the most valuable part of the Work.

ASTRONOMY,

AS IT IS KNOWN AT THE PRESENT DAY.

Miscellaneous Subjects.

On Astronomical Tables.

IN constructing tables for computing, at any given instant, the places of the sun, moon, and planets, the first step is to determine, from a series of accurate observations, the time in which those bodies describe a space of 360°, or perform a complete revolution round the sun, or the primary planet.

When this important element is exactly ascertained, we can easily find, by simple proportion, the space which the planet describes in any number of years, months, days, minutes, or seconds, upon the supposition that it moves uniformly, or describes equal spaces in equal times in the circumference of a circle. This is called the mean motion of the body.

The next thing to be settled is the epochs, or radical places of the planet, which is nothing more than its longitude upon the supposition of its motion being uniform, at certain epochs of time, from which the calculations are supposed to commence. These epochs of time, or mean longitudes, are generally put down in Astronomical tables of the noon of the 1st of January of each year. These elements are all which would be necessary for computing the longitude of a planet, if it moved uniformly in a circular orbit; but as all the bodies of the solar system move in eliptical orbits round the sun, or their primary planet, placed in one of their foci, we must next determine the form of their orbits, or the nature of the elipse which they describe. This may be done in the case of the sun and moon, by observing the variations of their apparent diameters during a complete revolution; their distance from the earth being inversely proportional to the angle they subtend.

The ratio of their greatest and least diameters is a measure of the relation between their greatest and least distances, and consequently enables us to ascertain the eccentricity of their orbits. The same results may be obtained by observing the spaces described by the planets during equal intervals of time. As the areas described by the radius vector of a planet are proportional to the times, equal areas will correspond to equal angles, if the planet moves in a circular orbit. The observed inequalities, therefore, in the case of an eliptic orbit, being the effect of the eccentricity of the orbit, will

enable us to determine that important element. If we, therefore, suppose that the real planet moves with different velocities in an eliptical orbit, while a fictitious planet sets off from the peregee at the same instant, and describes a circular orbit, with an uniform motion, in the same time that the real planet describes the eliptical orbit, we shall obtain a simple explanation of the inequalities arising from the eliptical motion of the body. At no place of the orbit will these two planets be together, but when they are in Peregee and Apogee, or when the real planet is at its greatest and least distances from the sun. The angular distance, at any time, between the real and fictitious planet, is called the Equation of the Centre.

This is greatest when the fictitious planet is at that part of its orbit, where a line drawn from it to the line of the Apsides forms a right angle, or where the real planet is at its mean distance. From the Perihelion to the Aphelion, the real planet will be before the fictitious; but from its Aphelion to its Perihelion, it will be behind the fictitious planet. During the motion of the real planet from the Aphelion to its Perihelion, the mean place has been farther advanced than the true place; and therefore the equation of the centre must be subtracted from the mean longitude, to obtain the true longitude of the planet; but from the Perihelion to the Aphelion it must be added, because the mean place is behind the true. The equation of the centre obviously depends on the mean anomaly of the planet, or its distance from the apogee, which, in all the primary planets except Venus, has a motion according to the order of the signs. By determining, therefore, the place of the apogee, and subtracting its longitude from that of the planet, we obtain the mean anomaly of the planet; with which, as an argument, we find from the Tables the corresponding equation of the centre, which, applied to the mean place of the planet, gives its longitude in an eliptical orbit.

This result would be the true place of the planet in its orbit, if its motion were not influenced by any disturbing force; but, owing to the mutual action of the planets, their motions are sometimes accelerated, and at others retarded; and therefore the longitudes of these bodies must be still farther corrected.

In determining the places of the planets, we must compute also their latitudes or distances from the ecliptic, which must evidently depend on the distance of the planet from its node. As the nodes of all the planetary orbits have a retrograde motion along the ecliptic, the radical place of the node, or its position at any particular time, must first be ascertained; and its retrograde motion being known, we can obtain the longitude of the node at any time, and consequently the distance of the planet from the node. When the distance from the node is 0, the latitude will be nothing; and when the distance from the node is a maximum, or 3 or 9 signs, the latitude is also a maximum, or equal to the inclination of the planet's orbit to the ecliptic.

The places of the primary planets computed in the manner which is here described, are evidently their heliocentric places, or their places as seen from the sun. The geocentric place of the planet, or