out of Greek into Arabic, in the year 827, and again into Latin in

corrected the tables of Ptolemy, and composed those which were denominated from him the Alphonsine Tables. About the same time also Roger Bacon, an English monk, wrote several tracts relative to astronomy, particularly of the lunar aspects, the solar rays, and the places of the fixed stars. And about the year 1270, Vitello, a Polander, composed a treatise on optics, in which he showed the use of refraction in astronomy.

grave of Hesse-Cassel, made a great | discovered, by trials, that the cubes number of observations, published of the distances of the planets from by Snelius in 1618, and preferred the sun were in the same propor. by Hevelius to those of Tycho Brahe. From these observations he formed a catalogue of 400 stars, with their latitudes and longitudes, and adapted them to the beginning of the year 1593.

Tycho Brahe, a Dane, began his observations about the same time with the Landgrave of Hesse, and observed the great conjunction of Jupiter and Saturn: but finding the usual instruments very inaccurate, he constructed many others, much larger and more exact. In 1571, he discovered a new star in the chair of Cassiopeia; which induced him, like Hipparchus on a similar occasion, to make a new catalogue of the stars; which he composed to the number of 777, and adapted their places to the year 1600. Tycho invented a system to account for the planetary motions; but he is more to be noted on account of his accurate observations, which tended much to the discovery of the real nature of the planetary_orbits.

tion as the squares of their periodical times of revolution. By observations also on comets, he concluded that they are freely carried about among the orbits of the planets, in paths that are nearly rectilinear; but which he could not then determine. See Dr. Small on the discoveries of Kepler.

About this time much was done by Wright, Napier, Bayer, Mercator, Maurolycus, Magnius, Homelius, Schulter, Steven, Galileo, Thomas and Leonard Digges, John Dee, Robert Hood, Harriot, &c.

The beginning of the seventeenth century was particularly distinguished by the invention of telescopes, and the application of them to the purposes of astronomy.

Hevelius, from his own curious observations, furnished a catalogue of fixed stars, much more complete than Tycho's. Huygens and Cassini discovered the satellites of Saturn and his ring. And Gassendus, Horrox, Bullialdus, Ward, Ricciolus, Gascoign, &c. each contributed very considerably to the improvement of astronomy.

Newton demonstrated, from physical consideration, the great law that regulates all the heavenly mo tions, sets bounds to the planetary orbs, determined their greatest excursions from the sun, and their nearest approaches to him. It was he who first discovered whence arose that constant and regular proportion, observed by both pri mary and secondary planets, in their circulation round their central bodies; and their distances compared with their periods. He also gave a new theory of the moon, which accounts for all her' inequalities from the laws of gra vity and mechanics.

While Tycho resided at Prague, with the emperor, he prevailed on Kepler to leave the University of Glatz and to come to him; and Tycho dying in 1601, Kepler enjoyed the title of mathematician to the emperor; who ordered him to finish the tables of Tycho Brahe, which he published in 1627, under the title of Rodolphine. He died about the year 1630, at Ratisbon, where he was soliciting the arrears of his pension. From his own observations, and those of Tycho, Kepler discovered several of the true laws of nature, by which the motions of the celestial bodies are regulated. He discovered that all the planets revolve about the sun, not in circular but in elliptical orbits, having the sun in one of the Mr. Flamstead was appointed foci of the ellipse; that their mo- the first astronomer royal at Greentions are not equable, but varying wich in 1675. He observed, for quicker or slower, as they are near forty-four years, all the celestial to the sun, or farther from him; phenomena, the sun, moon, planets, that the areas described by the and fixed stars; of all which he variable line drawn from the planet gave an improved theory and to the sun are equal in equal times, tables. Cassini also, the first and always proportional to the French astronomer royal, very times of describing them. He also much distinguished himself, mak

ing many observations on the sun, It was found, by those who went moon, planets, and comets, and to the south, that the attraction of greatly improved the elements of their motions. He also erected the gnomon, and drew the celebrated meridian line in the church of Petronia, at Bologna.

the mountains of Peru had a sensible effect on the plumb-lines of their large instruments, which af forded an experimental proof of the Newtonian doctrine of gravitation, that has since been completely verified by the observations of Dr. Maskelyne, made on the moun.

In 1719, Mr. Flamstead was succeeded by Dr. Halley, who had been sent, at the early age of 21, to the island of St. Helena, to obtain Schehallien, in Scotland. On serve the southern stars, a cata- the death of Dr. Halley, in 1742, he logue of which he published in was succeeded by Dr. Bradley, 1679; and, a few years afterward, who has rendered himself celebrahe gave to the public his "Synop- ted by two of the finest discoveries sis Astronomia Cometicæ," in which that have ever been made in astrohe ventured to predict the return nomy,-the aberration of light, of a comet in 1758, or 1759. He was and the nutation of the earth's the first who discovered the acce- axis. Among other things he also leration of the moon's mean mo- formed new and accurate tables of tion; and is the author of a very the motions of Jupiter's satellites, ingenious method for finding her as well as the most correct table parallax, by three observed places of refractions yet extant. Also, of a solar eclipse: he also showed with a large transit instrument, and the use that might be made of the a new mural quadrant of eight feet approaching transit of Venus, in radius, constructed by Bird, in 1761, in determining the distance 1750 he made an immense number of the sun from the earth; and re- of observations for settling the commended the method of deter-places of all the stars in the Brimining the longitude by the moon's tish catalogue, together with near distance from the sun and certain 150 places of the moon, the greater fixed stars, which has since been part of which he compared with carried into execution at the in- Mayer's tables. Dr. Bradley was stance of the late Astronomer Roy-succeeded in 1762, in his office of al. Dr. Halley also composed astronomer royal, by Mr. Bliss; tables of the sun, moon, and pla- but who died in 1765, and was sucnets, with which he compared the ceeded by Nevil Maskelyne, D. D. observations he made of the moon who rendered very considerable at Greenwich, amounting to near services to the science, by his pub1500, and noticed the differences.lication of the "Nautical AlmaAbout this time, an attempt wasnac," the "Requisite Tables," &c.; made in France to measure a de- and more particularly by his great gree of the earth, which was the assiduity and zeal, in bringing the occasion of a warm dispute con- lunar method of determining the cerning its figure. M. Cassini con- longitude at sea into general praccluded, from the measurement of tice. Picard, that it was an oblong sphe- In the mean time, many other roid; but Newton, from a conside-eminent mathematicians were asration of the laws of gravity, and siduously employed in endeavourthe diurnal motion of the earth, ing to promote the science of ashad determined its figure to be tronomy. Amongst these may be that of an oblate spheroid, flattened particularly distinguished, Clairat the poles, and protuberant at aut, d'Alembert, Euler, Simpson, the equator. To determine this Walmsley, Mayer, de la Cailie, point, Louis XV. ordered two de- Manfredi, Lambert, &c. grees of the meridian to be mea- Such was the state of astronomy sured; one under or near the equa- when Dr. Herschel, by augmenttor, and the other as near as pos-ing the powers of telescopes be sible to the pole: the result-of this yond the most sanguine expecta. arduous undertaking was a confir- tions, opened a scene altogether mation of Newton's investigation. unlooked for, by the discovery of

a new planet, 12th March, 1781, the Georgium Sidus, or Uranus.

when infinitely produced, or at an infinite distance. Two curves On the 1st of January, 1801, ano- are also said to be asymptotical, ther new planet was discovered when they thus continually ap between Mars and Jupiter, by M.proach indefinitely to a coinci Piazzi, of Palermo, which is named dence: thus two parabolas, placed Ceres; and since this time three with their axis in the same right others have been observed, revolv- line, are assymptotes to each ing also between Mars and Jupiter, other. viz. Pallas, discovered by Dr. Olbers, March 28, 1802; Juno, first observed by Mr. Harding, at the observatory at Lilienthal, near Bremen, Sep. 1, 1804; and Vester, discovered by Dr. Olbers, 29th of March, 1807, being the second that we owe to this eminent astronomer. For the particular elements of these new planets, see the respective articles URANUS CERES, PALLAS, JUNO, and VESTER.

Of lines of the second kind, or curves of the first kind, that is, the conic sections, only the hyper bola has asymptotes, which are two in number. All curves of the second kind have at least one asymptote, but they may have three; and all curves of the third kind may have four asymptotes, and so on. The conchoid, cissoid, and logarithmic curve, though not geometrical curves, have each one asymptote; and the branch or leg of the curve that has an asymptote, is said to be of the hyperbolic kind.

The nature of an asymptote is very difficult to be conceived, by persons who are not acquainted with the higher geometry: they

Hence it appears, that within a few years the number of planets in our system have been nearly doubled, and many other important and interesting discoveries have been made during the same period: yet it must be acknowledged,that we are still unacquainted with many particulars, and cannot comprehend how two lines which therefore still remain to exercise the talents of modern astronomers. We have not yet determined the times of rotation, and the proper figures of some of the planets and their satellites; nor do we know, with sufficient precision, the masses of those bodies. The theory of their motions also consists in a series of approximations, of which the convergence depends both upon the perfection of the instruments and the progress of analysis, and which for that reason ought to acquire continually new degrees of exactness.

shonld always continually ap proach each other, without the possibility of touching or coinciding; this mystery, however, may be elucidated, and the nature of these lines readily comprehended, by considering the generation of the conchoid of Nicomedes. See Conchoid.

ASYMPTOTES, by some are distinguished into various orders. The asymptote is said to be of the first order, when it coincides with the base of the curvilinear figure; of the 2d order, when it is a right line parallel to the base; of the 3d order, when it is a right line oblique to the base; of the 4th order, when it is the common parabola, having its axis perpendicular to the base; and, in general, of the n + 2 order, when it is a parabola whose ordinate is always as the n ASYMPTOTE, a right line to power of the base. The asymptote which some curve continually ap-is oblique to the base, when the proaches nearer, in such sort, that ratio of the first fluxion of the ordiwhen they are both indefinitely nate to the fluxion of the base, approduced, they are nearer together proaches to an assignable ratio, as than by any assignable finite dis-its limit; but it is parallel to the tance; or it may otherwise be con- base, or coincides with it, when sidered as a tangent to the curve, this limit is not assignable.

ASTROSCOPE, an astronomical instrument, composed of two cones, on whose surfaces are exhibited the stars and constellations, by means of which they are both easily found in the heavens.

The areas bounded by curves and their asymptotes, though indefinitely extended, have some times limits to which they may approach indefinitely near: and this happens in hyperbolas of all kinds, except the first or Apollonian, and in the logarithmic curve. But in the common hyperbola, and many other curves, the asymptotical area has no such limit, but is infinitely great. Solids, too, generated by hyperbolic areas, revolving about their asymptotes, have sometimes their limits; and sometimes they may be produced till they exceed and given, solid. Also the surface of such solid, when supposed to be infinitely produced, is either finite or infinite, according as the area of the generating figure is finite or infinite.

The way of discovering whether any proposed curves have asymptotes, and the manner of drawing them when they are inclined to the axis, may be easily derived from the method of tangents.

ATMOSPHERE, that gaseous or aeriform fluid which every where invests the surface of the terraqueous globe; and partakes of all its motions, both annual and diurnal. We have already considered the mechanical properties of this fluid, under the article AIR; and it therefore only remains to treat of it as forming one body, viz. its figure, pressure, altitude, &c.

figure of the atmosphere must become that of an oblate spheroid, because the parts that correspond to the equator have a greater centrifugal force than the parts which correspond to the poles. Besides, the figure of the atmosphere must represent such a spheroid, in consequence of the sun striking the equatorial regions more directly than those about the poles: whence it follows, that the mass of air, or part of the atmosphere, about the polar regions, being less heated, cannot expand so much, nor reach so high; nevertheless, as the same force which contributes to elevate air, diminishes the pressure on the surface of the earth, higher columns of it at or near the equator, all other circumstances being the same, will not be heavier than those of the lower belonging to the poles; but, on the contrary, without some compensation they would be lighter, in consequence of the diminished gravity of the upper

strata.

Weight or Pressure of the Atmos· phere.-Torricelli found that the pressure of the atmosphere sustains a column of quicksilver, of an equal base and 39 inches height; and as a cubical inch of quicksil ver is found to weigh near half a pound avoirdupoise, therefore the whole 30 inches, or the weight of the atmosphere on every square inch, is nearly equal to 15lb. Again, it has been found that the pressure of the atmosphere balances, in the case of pumps, &c. a column of water of about 344 feet high; and,

Figure of the Atmosphere.-As the atmosphere envelopes all parts of the surface of the earth, if both the one and the other were perfectly at rest, and were not en-the cubical foot of water weighing dowed with a diurnal motion round their axis, the atmosphere would be exactly spherical, according to the universal laws of gravity; for the parts of the surface of a fluid in a state of rest, must be equally remote from its centre. But the earth and the ambient atmosphere are invested with a diurnal motion, which carries them round their common axis of rotation; and the different parts of both having a centrifugal force, the tendency of which is more considerable, and that of the centripetal force less, arts are more remote from nd, consequently, the

just 1000 ounces, or 624lb. 34 tinies 62, or 215815. will be the weight of the column of water, or of the atmosphere on a base of a square foot; and, consequently, the 144tl. part of this, or 15lb. is the weight of the atmosphere on a square inch; the same as before. Hence the pressure of this ambient fluid on the whole surface of the earth, is equivalent to that of a globe of lead of 60 miles in diameter. And hence also it appears, that the pressure upon the human body must be very considerable; for, admitting the surface of a man's body to be about 15 square feet,