From these we have, also, for the expression of either time in terms of the other and the equation of time,

The equation of time is given in the Nautical almanac, for every day in the year, with instructions whether to add or subtract in changing one time to the other.

172. Times at which the equation of time is nothing. When the effects of the two causes on which the equation of time depends (170), are opposed to each other and are equal, the equation of time must be nothing; apparent and mean time must then be the same. This occurs four times in the year; about the 15th of April, 15th of June, 1st of September, and 24th of December.

173. Sidereal time. The arc EM of the equator, converted into time, expresses the sidereal time (142). But EM = EH + HM. Hence, the sidereal time is obtained by adding the apparent time to the sun's true right ascension, expressed in time.

Again, EM GS' + EG + S'M. Consequently, the sidereal time is also obtained, by adding the mean time to the sum of the sun's mean longitude and the equation of the equinoxes in right ascension, expressed in time.

As EM is the right ascension of the zenith Z, it follows that the sidereal time expresses the right ascension of the zenith, in time.

174. Solar Spots. When the sun is viewed with a telescope furnished with a coloured glass to protect the eye, a number of dark spots are usually seen on his surface. Each spot generally consists of a central part of irregular form, which is black, surrounded by a margin or border, called the penumbra, of much lighter colour, as represented in Fig. 28. The spots differ greatly in size and form. Some are occasionally observed, so large as to be visible to the naked eye, when in consequence of intervening

light clouds, or of the sun being near the horizon he can be thus viewed. The breadth of some of these as ascertained from measurements with a micrometer, is found to be nearly or quite 50,000 miles.

When the spots are examined from hour to hour or day to day, they are found to vary in size and form and also to change their positions on the disc; all of them moving towards the western edge. Some increase in size and others diminish. Some are formed and come into view where none were before visible; others after gradually diminishing entirely disappear; the central part being that which first becomes invisible. Sometimes a spot is seen suddenly to separate or as it were to burst asunder. The change of form is sometimes gradual and sometimes rapid. None of the spots are permanent in their continuSome remain only for a few hours or days; and there are seldom any that continue longer than six or seven weeks. There are generally some spots to be seen on the disc, and at times as many as forty or fifty have been observed at once; but there have been periods of months or even years, during which none were visible. When a spot remains for several weeks it is seen to traverse the disc from east to west in about 13 days, and after being invisible during about the same time, to re-appear on the eastern side; it being thus about 27 days in returning to the same position on the disc.

ance.

175. Sun's rotation on his axis. By observations of the right ascensions and declinations of the centres of the sun and of a spot, or by observations with a position micrometer (50), either being repeated from day to day, the positions of the spot with reference to the centre of the disc and the plane of the ecliptic, and thence the form of its path, may be determined .At two nearly opposite times in the year, in June and December, the paths are found to be nearly straight lines inclined in an angle of 7° to the plane of the ecliptic. Except at these times they are nearly semi-ellipses of great eccentricity; the eccentricity

however, though always great, varying with the sesaon of

From the motions of the spots and the paths they describe, it is inferred that the sun revolves from west to east on a fixed axis, inclined at an angle of about 71° to a perpendicular to the plane of the ecliptic. Let EEE", Fig. 29, represent the earth's orbit, epqp' the sun, fg a perpendicular to the plane of the ecliptic through S, the sun's centre, pp' his axis and enq a circle, called the sun's equator, the plane of which passes through his centre at right angles to the axis. A spot on the sun's surface must by his revolution on his axis, describe either the circle enq or some other as amb parallel to it. These circles being perpendicular to the axis pp', must be inclined to the ecliptic in the same small angle, in which the axis is inclined to the perpendicular fg. They are therefore, in very oblique positions with regard to an observer on the earth, and consequently, the spots describing them must appear to move in ellipses of large eccentricity. This would be accurately the case, if the earth were at rest; but in consequence of its motion in its orbit, the apparent paths must deviate somewhat from accurate elliptical arcs, as they are found to do. When the earth is at those opposite points of its orbit through which the plane of the sun's equator passes, the observer being then in that plane, the spots must appear to move in straight lines, excepting so far as deviations. are produced by the earth's motion.

It has been stated that a spot returns to the same position on the disc in about 27 days. This is not, however, the time of a revolution on the axis. For while the sun makes a revolution on his axis, the earth advances nearly a sign in the ecliptic; and, consequently, the sun must make more than a complete revolution, before the spot will appear to an observer on the earth to occupy its former position on the disc. By investigations and computations which may be omitted here, the real time of revolution can be determined from the observed positions of the same spot at different times. According to Delambre the period of the

sun's revolution on his axis is 25d. Oh. 17m. Some astronomers make it rather greater.

It is also ascertained that the position of the sun's axis is such, that when his longitude is about 170° 21', it coincides with the plane ESf, passing through the centres of the earth and sun at right angles to the ecliptic, the northern half Sp of the axis being then inclined towards the earth.

176. Hypotheses relative to the solar spots. Various hypotheses to account for the solar spots have been proposed. None of them are, however, entirely satisfactory. One of the most probable is that by Sir W. Herschel. He supposed that the mass of the sun is an opaque globular body, surrounded by an atmosphere of luminous matter; that this luminous atmosphere is not in contact with the body of the sun, but is sustained far above it by a transparent, elastic medium, in which, floats a stratum of cloudy matter; and that from the operation of local causes, cavities or openings are formed both in the cloudy stratum and luminous part of the atmosphere, the opening in the latter being larger than that in the former. According to these assumptions, the part of the solid body of the sun that is under an opening, being shaded by the cloudy stratum and thus receiving little or no light from the luminous part of the atmosphere, must appear as a black spot. The part of the cloudy stratum contiguous to its aperture and under the larger opening, reflecting light received from the latter, would form the border or penumbra of the spot.

177. Zodiacal Light. A faint light somewhat resembling that of the milky way, or more nearly that of the tail of a comet, and being nearly in the form of a cone with its base towards the sun, and its axis nearly in the direction of the ecliptic, is frequently seen at certain seasons of the year in the west, after the close of twilight in the evening, or in the east before its commencement in the morning. This is called the zodiacal light.

The state of the air and other circumstances being the same, the zodiacal light is most distinctly scen, when its direction or the direction of the ecliptic is most nearly perpendicular to the horizon. This, for places whose latitudes are from 40° to 50° north, occurs about the 1st of March for the evening and about the 10th of October for the morning. In some years the zodiacal light is very perceptible in the evening for several weeks contiguous to the former time, and in the morning, for a like period contiguous to the latter time.

The distance to which the zodiacal light extends varies from 20 or 30° to 70 or 80'. No satisfactory explanation of this phenomenon has as yet been given.

CHAPTER XI.

PARALLELISM OF THE EARTH'S AXIS-VARIATIONS IN THE LENGTHS OF DAY AND NIGHT-SEASONS-ASTRONOMICAL PROBLEMS.

178. Parallelism of the earth's axis. In the annual motion of the earth round the sun, its axis continues very nearly in the same direction, or in other words, it continues parallel to itself very nearly, the small deviation from parallelism being that which corresponds to the slow motion of the poles of the equator about those of the ecliptic (126). The axis being perpendicular to the plane of the equator, it is evident that it must continually make with the axis of the ecliptic, an angle equal to the obliquity of the ecliptic. On this inclination of the axis, and on its parallelism depend the variations in the lengths of day and night and the changes of the seasons.