MATHEMATICAL AND PHYSICAL SCIENCE ming in an erect position. The stem or neck is divided into degrees or parts, which are numbered, to show the specific gravity by the depth of its descent. ARGUMENT, in Astronomy, is in general a quantity upon which another quantity or equation depends; or it is an arch, whereby we seek another unknown arch, bearing some proportion to the first: hence ARGUMENT of Inclination, or ARGUMENT of Latitude, of any platiet, is an arch of a planet’s orbit, intercepted between the ascending node and the place of the planet from the sun, numbered according to the succession of the signs. Menstrutal ARGUMENT of Latitude, is the distance of the moon’s true place from the sun's true 1 lace; by which is found the quantity of the real obscuration in eclipses. Annual ARG UMENT of the Moon's Apogee, or simply Annual Argument, is the distance of the sun’s place from the place of the moon’s apogee ; that is, the arc of the ecliptic comprised between those two places. ARGUMENT of the Parallar, demotes the effect it produces on an observation, and which serves for determining the true quantity of the horizontal parallax. ARGUMENT of the Equation of the Centre, is the anomaly, or distauce, from the apogee or aphelion; because this equation is calculated in an elliptic orbit for every degree of anomaly, and varies according to the variation of the anomal v. ARIES, or the Ram, in Astronomy, the first of the old 12 signs of the different nations among whom it has been used. Its origin, like that of all sciences, is involved in obscurity; nor is it fully ascertained to whom we are indebted for the improved system now im use. Arithmetic is divided into various kinds, according to the nature of the numbers that form the subject of it; but the most simple form, and that which is the root or foundation of all the others, is the arithmetic of abstract or simple numbers. A number is called abstract when it merely answers to the question, “how many (" and has no allusion to the value of the said many, and no reference to things of any kind, but which admits of having the name and value of any kind of things whatever applied to it. In this sense, one is the smallest and simplest number that can be mentioned; and the other numbers proceed by constant additions of one, without limit. This being the case, the first thing requisite for the formation of an arithnetical language, is the invention of a limited number of original names, which shall comprehend a great and almost endless variety of numbers. For this purpose, what is usually called a “scale of numbers,” becomes necessary, and the limits of this scale are the powers of any number, m which is taken as the modulus or root. Thus mo, m1, m2, m3, m*, will form five ranks or places in the scale, any number whatever being taken for on 5 and the scale will receive its name according to the mumber so taken : thus, it for 11. For the method of changing a number from one scale to another, see Notation. Arithinetic receives various denominations, according to the mature of the numbers treated of: thus, Simple or Integral arithmetic is the method of calculating by simple or abstract numbers. Fractional arithmetic is the method of calculating by numbers which are less than the number 1, and is of two kinds, vulgar and decimal. For these, as well as for the arithmetic of eaponents, logarithms, sines, &c. see those articles. Whatever may be the nature of the numbers which form the subject of arithmetical computation, there are but two changes, of which any number is susceptible, namely, being made greater, and being made less; and, generally speaking, each of these may be performed in two different ways. When a number is increased by adding to it any number or numbers whatever, the process is called addition, and when it is increased by repeating itself any number of times, the process is called multiplication. When a number is diminished by taking away from it any number or numbers whatever, the process is called subtraction; and when it is diminished by taking away one or more numbers equal to that, which is left, or when (which is the same thing,) the number left, if repeated a cer. tain number of times, would produce the given number, the process is called division. These four processes are called the four fundamental operations, and the methods of performing them the four fundamental rules of arithmetic ; and each of the latter is the converse of the corresponding one of the former. Subtraction is the converse of addition, and division the converse of multiplication. For the method of performing each of these, see the articles Addition, Subtraction, &c. ARITHM ETICAL, any thing relating to arithmetic. ARITH METICAL complement of a Logarithm. See Anti-Log AR IT HM and CoMPLE MENT. ARITH METICAL Mean, is the middle term of three quantities in arithmetical progression, or half the sum of any two proposed numbers. ARITHMETICAL Progression and Proportion. See Progression and PRoportion. ARITHMETICAL Ratio, is the difference between any two adjacent terms in arithmetical progresSlon. ARITHMETICAL Scales. Not Ation. ARITHMETICAL Triangle. See TRIANGLE. ARMILLARY Sphere, a name given to an artificial sphere, which represents the several circles of the system of the world, put together in their natural order. The armillary sphere revolves upon an axis, within a horizon, which is divided into degrees, and moveable every way upon a brass supporter. The other parts, are the equinoctial, zodiac, meridian, the two tropics, and the two polar circles. ARTIFICIAL Numbers, a term sometimes used for logarithms, lo garithmic sines, tangents, &c. ASCENDING, in Astronomy, is understood of those stars, &c. which are rising above the horizon, in any parallel of the equator. 'so". "...". latitude of a planet when going towards the north pole. ASCENDING Node, is that point of a planet's orbit where it passes the ecliptic to proceed northward. See ASCENSION, in Astronomy, is either light or oblique. Ičight Ascension of the Sun or of a Star, is that degree of the equinoctial (counted from the beginning of Aries,) which rises with the sum or star in a right spliere. Or, it is that degree and minute of the equinoctial, counted as before, which comes to the meridian with the sum or star. The reason of thus referring it to the meridian is, because that is always at right angles to the equinoctial, whereas the horizon is only so in a right or direct sphere. The right ascension stands opposed to the right descension, and corresponds to the longitude of places on the earth. Two fixed stars, that have the same right ascension, that is, which are at the same distance from the first point of Aries, or which is still the same, are in the same meridian, rise at the same time in a right sphere, or with respect to persons living under the equator. If they be not in the same meridian, the difference between their rising, or coming to the meridian, is the precise difference of their right ascension. But in an oblique sphere, where the horizon cuts all the meridians obliquely, different points of the meridian never rise or set together; so that two stars, on the same meridian, never lise or set at the same time; and the more oblique the sphere is, the greater is the interval of time between them. To the sine of the right ascenSlone The sun’s right ascension in time is useful to the practical astronoiner in regular observations, who adjusts his clock by sidereal time. It serves also for converting apparent into siderial time ; as, for instance, that of an eclipse of Jupiter’s satellites, in order to know at what time it may be expected to happen by the clock. For this purpose, the sun's right ascension for the preceding noon, together with the increase of right ascension from moon, must be added to the apparent time of a known star passing the meridian: then subtract the sun’s right ascension in time at noon, from the star’s right ascension in time, the remainder is the apparent time of the stars passing the meridian nearly : from which the proportional part of the daily increase of the same night ascension from his apparent time from noon being subtracted, leaves the correct time of the star’s passing the meridian. The sun’s right ascension in time is also useful for computing the time of the moon, or a planet’s, passing the meridian. The Arch of Right Ascension, is that portion of the equator, intercepted between the beginning of Aries and the point of the equator, which is the meridian : or it is the number of degrees contained in it. Oblique Ascension, is an arch of the equator, intercepted between the first point of Aries, and that point of the equator which rises, together with the star, &c. in an oblique sphere. The oblique ascension is counted from west to east; and is greater or less, according to the different obliquities of the sphere: Arch of Oblique Ascension, is the arch on which the oblique ascension is measured. ASCENSIONAL Difference, is the difference between the right and oblique ascension. To find the ascensional Difference of the Sun, having the Sun’s Declination and the Latitude of the Place. Say, As radius Is to the tangent of the latitude, So is the tangent of the sun’s When the latitude and declination have the same manne, the difference between the right ascension, and the ascensional disserence, is the oblique ascension; and their sum is the oblique descension; but when they are of contrary names, the sun is the oblique ascension, and the differ. ence is the oblique descension. ASCII, are those inhabitants of the globe, who, at certain times of the year, have no shadow ; such are all those who inhabit the torrid zone. ASPECT, in Astronomy, is the situation of the stars and planets with regard to each other. There are five principal aspects; which, with their respective characters, are as follows: viz. &, Opposition, when the 1so angle becomes When the planets have exactly the distances described above, they are called partile aspects : and when the distances have not precisely these measures, they are called platic aspects. ASPERITY, the roughness or inequality in the surface of bodies. ASSURANCE on Lives. See L1 v Es. ASTEROIDS, in Astronomy, a name given by Dr. Herschel to the four new planets discovered by the foreign astronomers Piazzi, Olbers, and Harding. ASTERISM, in Astronomy, an ancient term, siguifying the same as CoNsts: LLATION. . ASTRAEA, in Astronomy, a name given by some authors to the sign Virgo. ASTRAL, depending or belonging to the..”: as ASTRAL year, &c. ASTRODICTICUM, an astronomical insurument invented by Mr. Weighel, by means of which several persons may view the same star at the same time. A S T R O GNO S 1 A, signifies a knowledge of the fixed stars, their names, ranks, siluations, &c. ASTRO LABE, the man,e of an ancient astronomical instrument, very much resembling our a nillary sphere. It is likewise the name of an instrument formerly inuch used at sea for ascertaining the altitude of the sun, stars, &c. which consisted of a brass ring about fifteen inches in diameter, graduated into degrees and minutes, and fitted with an index moveable about its centre, and carrying two sights ; the whole being attached to a small brass ring for suspending the instrument at the time of observation. Modern astronomers use the term Astrolabe, to demote a stereographic projection of the sphere, either upon the plane of the equator, the eye being supposed to be in the pole of the world ; or upon the plane of the meridian, when the eye is supposed in the point of the intersection of the equinoctial and horizon. ASTRONOMICAL, anything relating to astronomy. ASTRONOMY, a mixed mathematical science, which treats of the heavenly bodies, their motions, periods, eclipses, magnitudes, &c. and of the causes on which they depend. That part of the science which relates to the motions, magnitudes, and periods of revolution, is called Pure or Plain Astronomy : and that which investigates the causes and laws by which these motions are regulated, is called Physical Astronomy. IIistory of Astronomy.—The early history of this science, like that of all others of ancient date, is too much disfigured by fabulous and allegorical representations, to admit of any reguiar or satisfactory elucidation. It is probable, however, that some knowledge of this kind must have been nearly coeval with the formation of society. Many traces of it have been found amongst various nations, which show that several of the most remarkable celestial phenomena must have been observed, and a knowledge of them dissemimated, at a very renuote period. But in what age or country the science first originated, or by whom it was gradually methodised and improved, is extremely uncertain. M. Bailly, in his elaborate history of ancient and modern astronomy, endeavours to trace the origin of this science among the Chaldeans, Egyptians, Persians, Indians, and Chinese, to a very early period. And thence, he maintains, that it was cultivated in Egypt and Chaldea 2800 years before Christ; in Persia, 3209; in India, 3101; and in China, 2952 years before that aera. He also apprehends, that astronomy had been studied even long before this distant period, and that we are only to date its revival from this time. In investigating the antiquity and F. of astronomy among the Indians, M. Bailly examines and compares four different sets of astronomical tables of the Indian philosophers; namely, that of the Siamese, explained by M. Cassini in 1689; that brought from India by M. le Gentil, of the Academy of Sciences; and two other manuscript tables, found among the papers of the late M. de Lisle; all of which he found to accord together, and all referring to the meridian of Benares. It appears that the fundamental epoch of the Indian astronomy, is a remarkable conjunction of the sun and moon, which took place at the distance of 3102 years before Christ: and M. Bailly informs us, that by our most accurate astronomical tables, such a conjunction did really hap. pen at that time. He farther observes, that at present the Indians calculate eclipses by the mean motions of the sun and moon commencing at a period 5000 years distant. The solar year of the Brahmins of Tervalore is divided into twelve unequal months, each being equal to the time the sun occupies in moving through a sign; and in their calculations for a day, they employ the time the sun moves 1* in the ecliptic. Their sidereal year consists of 3654, 6, 12m, 30s; and the tropical, of 3654, 5*, 50m, 35°. They assign inequalities to the motions of the planets, answering very well to the annual parallax, and the equation of the centre. Most authors, however, fix the origin of astronomy and astrology either in Chaldea, or in Egypt; and, accordingly, among the ancients, we find the word Chaldean often used for astronomer, or astrologer. Both of these nations pretended to a very high antiquity, and claimed the honour of producing the first cultivators of this science. The Chaldeans boasted of their temple, or Tower of Belus, and of Zoroaster, whom they placed 5000 years before the desli uction of Troy : while the Egyptians spoke with equal pride of their colleges of priests, where astronomy was taught; and of the monument of Osymandyas, in which, it is said, there was a golden circle of 365 cubits in circumference, and one cubit thick, divided into 365 equal parts, answering to the days of the year, &c. From Chaldea and Egypt, the science of astronomy passed into Phenicia, and was by that people applied to the purposes of navigation, whence they became masters of the sea, and of almost all the commerce in the world. The Greeks, it is probable, derived their astronomical knowledge chief. ly from the Egyptians and Phemicians, by means of several of their country men who visited those nations for the purpose of learning the different sciences. Several of the constellations are mentioned by Hesiod and Homer, who lived 870 years before Christ. The knowledge of the Greeks in this science, was greatly in proved by Thales the Milesian, and others, who travelled into Egypt. Thales was born about 640 years before Christ; and was the first among the Greeks who observed stars, the solstices, the eclipses of the sun and moon, and predicted an eclipse of the sum. The science was far. ther cultivated and extended by |