It is by means of proper observations of these spots, and the calculations founded upon them, that the elements of rotation are determined; that is, its duration, the position of the axis about which it is accomplished; that of the equator, its nodes, and its inclination to the ecliptic. The time of rotation may be found by observing the arc described by any spot in a given time, and then finding, by proportion, the time of describing the whole circle; or the return of the spot to the same position with respect to the earth may be observed, which will give the time of the entire rotation. But the most accurate method is to observe the difference of right ascension between the centre of the spot and the limb of the Sun, from which the difference of right ascension between the centre of the spot and that of the Sun is immediately obtained. The same observation made with respect to the declination gives the dif ference of declination between the centre of the spot and that of the Sun. These results fix the position of the spot upon the disc; and by repeating these observations several times during its appearance, its apparent course over the disc may be traced with considerable accuracy, provided the time of this appearance be of sufficient duration. From having the difference of right ascension and declination, the difference of latitude and longitude of the centres of the spot and the Sun is found by calculation. Numerous observations, combined with all the circumstances connected with them, lead to the conclusion, that the Sun has a rotary motion from east to west, about an axis inclined to the ecliptic. A plane drawn through the centre of the Sun, perpendicular to that axis, determines the solar equator by its intersection with the surface of that body. The line formed by the intersection of this plane with that of the ecliptic is called the line of the nodes of that equator. The nodes themselves are the points in which that right line, indefinitely produced both ways, would meet the celestial sphere. To know the position of this axis of rotation, the angle of inclination of the solar equator with the ecliptic must be determined, as well as that which the line of the nodes makes with some other fixed line, supposed to be drawn in the plane of the ecliptic; that of the equinoxes is usually selected for this purpose. The angle is called the longitude of the node. M. Delambre, after performing the necessary calculations with all the care and accuracy of which the subject admits, arrives at the following conclusions relative to the rotary elements of the Sun, viz. By the result of another variety of combinations of the elements of calculation afforded by the observations he has considered, he makes the time of the real rotation of the Sun 25.01154 days, or 25 d. 0 h. 16 m.; a result extremely near the former. The delicacy of the observations, and the variation to which the spots are subject, are sufficient sources of error, however, to prevent implicit reliance being placed upon the above results. The rotation of the Moon is much slower than that of the Sun; and it presents phenomena more singular. But the spots on her disc are permanent, which allows the observations to be multiplied indefinitely. By following nearly the same processes, both of observation and calculation, as for the Sun, it is found that the lunar equator is inclined to the ecliptic in an angle of 1° 43′; and as that of the orbit is about 5° 9′, it follows that the orbit and the equator are inclined to each other in an angle of 3° 26'; and also, that the plane of the lunar equator is therefore between that of the orbit and ecliptic. The duration of the rotation is 27 d. 7 h. 43 m. 3 s., the same as the lunar month. The Moon, therefore, turning on its axis in the same time that it makes a revolution of 360° about the Earth by its mean motion, if her motion were uniform, and she always remained in the plane of the ecliptic, she would always present exactly the same face to us, and the spots on her disc would appear permanently fixed, as they would always be seen in exactly the same situation. But her motion in her orbit round the Earth is not uniform, and she is sometimes about 5° above the ecliptic, and at others as much below that circle; and therefore the spots on her surface appear to vary, their positions corresponding to the irregularity of her motions and the difference of her situations. These phenomena are denoted by the name libration, or balancing; and are again distinguished into libration in latitude and longitude; in right ascension and declination. The same methods of ascertaining the elements of rotation of the Sun and Moon are also employed in finding those of the planets. Mercury, however, is so small and bright, that it is difficult to fix upon any point of his disc sufficiently distinct for making the requisite observations, and his nearness to the Sun also prevents these observations from being continued with the required regularity. Notwithstanding these diffi culties, M. Schroëter has distinguished spots and mountains, which he has assiduously followed, till he has arrived at the subsequent conclusions: that the apparent diameter of the planet is about 6"; that it does not present any sensible ellipticity; that the mountains it contains are proportionally larger than those of Venus and the Earth; that the highest are, as in these two bodies, in the southern hemisphere; that the angle which the equator makes with its orbit is very considerable; that the difference of days and seasons ought to be much greater in Mercury than it is on the Earth; that its atmosphere, like that of Venus, is very dense; and, lastly, that its rotation about its axis is 24 h. 5 m. 30 s. The rotation of Venus is also very difficult to be observed. M. Schroëter, however, found her rotation to be 23 h. 21 m. 19s. ; the inclination of her equator about 75°, and the longitude of the node 10. 15°. He did not perceive any ellipticity. In fact, supposing it to be like that of the Earth, there would be only about the tenth of a second of difference between the two semiaxes, which it would be impossible to ascertain by observation. According to this astronomer, the atmosphere is sufficiently dense to produce a refraction of 30′ 24′′. Cassini found the rotation of Mars to be 24 h. 40 m.; the inclination of the equator appeared to him to be very small. Maraldi assigned 24 h. 39 m. for the rotation. Herschel gives 24 h. 39 m. 22 s.; the inclination of the equator to the ecliptic he makes 30° 18′; and the node in 2. 17° 47'. The elliptieity 16. The rotation of Jupiter, according to Cassini and Maraldi, is 9 h. 56 m.; according to Dr. Herschel, it is from 9 h. 51 m. 46 s. to 9 h. 56 m. 40 s. Schro êter makes it 9 h. 55 m. 33 s. He also supposes the inclination to be 2° or 3o, and the ellipticity, which is sensible to the sight. But from the eclipses of his satellites, and the theory of Laplace, M. Delambre found the inclination equal to 3° 12′ 24′′, and the ellipticity about th. Jupiter is remarkable for two belts parallel to the equator: he has also four satellites which revolve about him, in planes very little inclined to his equa❤ tor. The rotation of Saturn has not been satisfactorily observed. Dr. Herschel thinks it is a little more than 10 h., and that the ellipticity of this planet is about 4th. He also thinks that his greatest diameter is not that of the equator, but that it is inclined to it in an angle of about 46°. The most remarkable circumstance, however, which is peculiar to Saturn, is his being encompassed by a flat ring, resembling the wooden horizon of an artificial globe. This is, perhaps, one of the most curious objects which the invention of the telescope has presented to the view of the astronomer; and will therefore form a suitable subject for a separate article, in a subsequent part of this volume. The Naturalist's Diary For MAY 1818. Returning Spring, Borne on the balmy zephyr's fragrant wing, MAY is usually considered as the most delightful month of the whole year, and has long been the Muse's favourite theme; although much that is said of its beauties applies better to more southern climates, or, indeed, to our month of JUNE, which is, commonly, entitled to all the praises that the poets have lavished upon MAY. This month, however, is remarkable for the profusion of verdure which it exhibits nature's carpet is fresh laid, and nothing can be more grateful than to press its velvet surface. The scenery of a May morning is, not unfrequently, as beautiful as possibly can be conceived; a serene sky, a refreshing fragrance arising from the face of the earth, and the melody of the feathered tribes, all combine to render it inexpressibly delightful, to exhilarate the spirits, and call forth a song of grateful adoration. Yet May, like its predecessór April, is often very changeful, and cold winds and a gloomy atmosphere have, of late, usurped the place |