cording as we suppose the star to be distant in longitude 10 or 15 degrees, respectively, from the sun when it first, in Egypt, becomes disengaged from the rays of that luminary before his rising. At the former of these epochs, the longitude of Regulus was 86 degrees, and at the latter, 80 degrees; consequently the star must, at either epoch, have been situated within a few degrees of the solstitial colure. Now the four intersections of the colures with the ecliptic taking place at the beginning of the first, seventh, fourteenth and twenty-first lunar mansions, it will follow that, in the age just mentioned, the circles of longitude passing through the two extremities of each of those four mansions respectively, passed also near the four principal fixed stars Regulus, Antares, Fomalhaut and Aldebaran: a disposition likely enough to have excited attention, and which probably had some influence in determining the number of the mansions.

Since the first considerable star in the constellation Aries (now marked 7,) has less longitude than Regulus by about 116° 30′, it must have happened that, at the time of the supposed invention of the lunar mansions, the circle of longitude passing through the former star coincided with the commencement of the nineteenth lunar mansion; and an opinion has been advanced, unsupported indeed by direct evidence, yet nevertheless, not destitute of probability, that when, by the retrogradation of the equinoctial points, the equinoctial colure passed through the same star, which was about the year 390 Before Christ, the commencement of the year was, by the Greeks and Asiatics, changed from the epoch of the summer solstice to that of the vernal equinox; a circumstance which did not prevent the origins of the dodecatemories and lunar mansions from being still coincident. In the second volume of the Asiatic Researches is contained an Essay by Sir William Jones, shewing that the ancient Hindus divided the zodiac into twenty-seven Nak-chatras or lunar mansions, of which the first includes the three stars in the head of Aries; and consequently, is coincident with the first of the zodiacal signs: and, in the ninth volume, is a dissertation by Mr. Colebrook, in which the writer endeavours to prove that these Nak-chatras coincide with the lunar

mansions of the Arabs, as they are described by Ulug Beg. Mr. Bentley, in the eighth volume, states that the Hindus ascribe the invention of this division of the ecliptic to Daesha, who, like Atlas in the Greek mythology, is said to have been a grandson of the daughter of the Ocean: a circumstance which gives some force to the opinion that the Hindu astronomy was derived from Greece or Egypt. M. Bailly observes that though the number of the lunar mansions, according to the Hindus, is less by one than that assigned by the Egyptians and other people; yet, as the former subdivided each of the twenty-seven mansions into four parts, and the Egyptians subdivided each of the twelve zodiacal signs into nine parts, the whole number of divisions is the same, according to both people; which may further serve to strengthen the opinion that the astronomies of India and Egypt had a common origin.

Hitherto we have described merely the apparent intersections of the planes of the equator and ecliptic in the heavens, and shewn how the primitive divisions of these circles were estimated: we have now to mention the steps by which the positions of the principal circles of the sphere were determined; the manner of expressing the measure of any portion of their circumferences, and the means of ascertaining with precision the values of any angular distances between the apparent places of the celestial bodies.

A very slight knowledge of geometry would suffice to shew the extent, from north to south, of the sun's annual path in the heavens. The length of the gnomon, and that of its shadow, form two sides of a right angled triangle from which the value of the angle at the vertex, between the gnomon itself and the ray passing from its summit to the extremity of the shadow, might be determined by a graphical construction according to a method which appears to have been used by Archimedes, and probably was that by which such measurements were first made; that is, by taking with compasses the chord of the are subtending the angle, and finding how often it could be inscribed in the circumference of the whole circle. The difference between the two angles taken on the days when the sun's shadow was the greatest and the least, which is the measure of

the sun's annual movement from south to north in the heavens, might thus be found equal to about one-eighth of the circumference of a circle of the sphere; and this, indeed appears to have been the result originally obtained. But the method of estimating the value of an angle by a fractional part of the whole circumference of a circle seems early to have given place to one more accurate; which was to consider the circumference of a circle as divided into a certain number of equal parts or degrees, 360 for example, and to ascertain the number of those degrees which were contained in the arc subtending the angle: according to this method the difference of the angles made by the rays, with the gnomon, would be found to be equal to about forty-seven degrees; and the inclination of the planes of the ecliptic and equator, which is equal to half that quantity, would be about 23° 30'.

The division of the circumference of a circle into 360 parts, or degrees, may be almost considered as universal among mathematicians, and it is probable enough that, when from the first and rudest observations, the length of the year appeared to be equal to 360 days, the division of the circle into as many degrees was immediately adopted on account of the convenience of expressing the daily movement of the sun in longitude by one of those degrees: after a more correct length of the year had been ascertained, a perception of the advantages of that division, arising from the many simple divisors contained in the number 360 (which rendered it possible to express various arcs by a certain number of degrees without fractions) caused it, with a sexagesimal subdivision, to be retained, and it has ever since continued in use. The great political revolution which took place in France near the end of the eighteenth century brought forth, indeed, a new graduation of the circle, in which each quadrant is divided into 100 parts and each part is decimally subdivided; but, however advantageous this method may be, it has only yet been able to obtain a very partial adoption.

a

It appears from a treatise of Proclus that on some occasions the ancients expressed the values of arcs or angles by numbers founded on a division of the circumference of a circle into sixty · a De Sphæra, sect. IX.

parts, and Eudoxus is said to have used that mode of expression; agreeably to which Proclus makes the distance from the pole of the world to the northern point of the horizon equal to six parts (=36°); which is equal to the latitude of Rhodes; the distance of the pole from the point of summer solstice he makes equal to five parts (30°), and the distance of the equator from either tropic, or the obliquity of the ecliptic, equal to four parts (24°). It is probable, however, that such numbers were often employed merely as reductions of the proportions of arcs of circles to their lowest terms. The Chinese have from the earliest period of their history divided the circumference of each great circle of the sphere into 365 equal parts, so that the daily motion of the sun from west to east is nearly equal to one of their degrees; which shews, at the same time, the reason of using that graduation, and that when astronomy was first cultivated in their country, the length of the year was known to be equal to that number of days.

The circle which limits the view of the spectator on the earth's surface, having its plane extended every way to the celestial sphere, was doubtless the first of those which were imagined to be described in the heavens, for the purpose of designating the places of the fixed stars and planets, though it is remarkable that the term horizon, which is applied to that circle, occurs only for the first time in an astronomical work written by the celebrated Euclid. The position of the north point of the horizon, and the direction of the meridian, must have been immediately determined, and this could be done with tolerable accuracy by a method which has been stated above": a line passing through the place of the observer, at right angles to the meridian, would cut the horizon in the east and west points; and the diurnal path of any star, which might be observed to rise in the former and set in the latter of those points, would serve to indicate the position of the equator in the heavens; then, as soon as means were obtained of taking the elevation of a celestial body above the horizon, it would be found that such star, on arriving in the plane of the meridian, had the same elevation as the sun on those two days of the year when he appears, also,

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a

to rise in the east; consequently the sun, on each of those days, appears to describe the circumference of the equator, by his diurnal movement, and these days are found to be equally distant from those on which the shadow of a gnomon is the longest and the shortest; but, as soon as the two days were determined on which the sun rises in the east, a comparison of the angles which, at noon, the gnomon makes with the solar ray projecting the extremity of the shadow, would shew that the deviations of the sun, northward and southward, from the equator were equal to each other on the days of the greatest and least lengths of the shadow; and it would be, no doubt, immediately concluded, by combining the motion of that luminary from west to east with his declinations from the equator, that he must appear to describe, annually, in the heavens a route whose circumference crosses that of the equator in two points diametrically opposite to each other, and whose plane is inclined to that of the latter circle in an angle equal to half the whole movement of the sun from south to north; that is, to about 23 degrees. The year is, consequently, divided nearly, into four equal parts by the two times at which the sun crosses the equator, and those two at which he attains his greatest declinations: these days might naturally, then, serve to mark the commencements of the four seasons of the year; and, because an equality in the lengths of day and night is observed to take place when the sun is in the equator, the two points in the heavens which the sun occupies on those days received the name of equinoxes, while the term solstice was, as we have said, applied to each of those days on which the sun's declination is the greatest. The circles which the sun appears to describe, in his diurnal course, on the days of the solstices, received the name of tropics from a word signifying a return, because, from the solstitial points, the sun seems to return towards the equator. To the oblique route described annually by the sun through the heavens the name of ecliptic was given because the eclipses of the sun and moon take place, always, in or near its circumference.

The positions of the equator and ecliptic being determined, it was easy to conceive the existence of other circles in the celestial sphere respectively perpendicular and parallel to the