distance of the center of force were the same in both cases; but since the attraction of a sphere is the same as though all the matter were collected in the center, consequently, the weight of a body, so far as it depends on its distance from the center of force, would be the square of 112 times less at the sun than at the earth. Or, putting W for the weight at the earth, and W' for the weight then

at the sun,

1

W: W'

12

Hence a body would weigh nearly 28 times as much at the sun as at the earth. A man weighing 200 lbs. would, if transported to the surface of the sun, weigh 5,580 lbs., or nearly 2 tons. To lift one's limbs, would, in such a case, be beyond the ordinary power of the muscles. At the surface of the earth, a body falls through 16

feet in a second; and since the spaces are as the velocities, the times being equal, and the velocities as the forces, therefore a body would fall at the sun in one second, through 16×27%=448.7 feet.

SOLAR SPOTS.

147. The surface of the sun, when viewed with a telescope, usually exhibits dark spots, which vary much, at different times, in number, figure, and extent. One hundred or more, assembled in several distinct groups, are sometimes visible at once on the solar disk. The greatest part of the solar spots are commonly very small, but occasionally a spot of enormous size is seen occupying an extent of 50,000 miles in diameter. They are sometimes even visible to the naked eye, when the sun is viewed through colored glass, or, when near the horizon, it is seen through light clouds or vapors. When it is recollected that 1" of the solar disk implies an extent of 400 miles, (Art. 143,) it is evident that a space large enough to be seen by the naked eye, must cover a very large extent.

A solar spot usually consists of two parts, the nucleus and the umbra, (Fig. 27.) The nucleus is black, of a very irregular shape, and is subject to great and sudden changes, both in form and size. Spots have sometimes seemed to burst asunder, and to project fragments in different directions. The umbra is a wide margin of lighter

shade, and is often of greater extent than the nucleus. The

spots are usually confined to a zone extending across the central regions of the sun, not exceeding 60° in breadth. When the spots are observed from day to day, they are seen to move across the disk of the sun, occupying about two weeks in passing from one limb to the other.

Fig. 27.

After an absence of about the same period, the spot returns, having taken 27d. 7h. 37m. in the entire revolution.

Fig. 28.
a

S

148. The spots must be nearly or quite in contact with the body of the sun. Were they at any considerable distance from it, the time during which they would be seen on the solar disk, would be less than that occupied in the remainder of the revolution. Thus, let S (Fig. 28,) be the sun, E the earth, and abc the path of the body, revolving about the sun. Unless the spot were nearly or quite in contact with the body of the sun, being projected upon his disk only while passing from b to c, and being invisible while describing the arc cab, it would of course be out of sight longer than in sight, whereas the two periods are found to be equal. Moreover, the lines which all the solar spots describe on the disk of the sun, are found to be parallel to each other, like the circles of diurnal revolution around the earth, and hence it is inferred that they arise from a similar cause, namely, the revolution of the sun on his axis, a fact which is thus made known to

us.

E

But although the spots occupy about 27 days in passing from one limb of the sun around to the same limb again, yet this is not the period of the sun's revolution on his axis, but

exceeds it by nearly two days. For, let AA'B (Fig. 29,) represent the sun, and EE'M the orbit of the earth.

earth is at E, the visible disk of the sun will be AA'B; and if the earth remained stationary at E, the time occupied by a spot after leaving A until it returned to A, would be just equal to the time of the sun's revolution on his axis. But during the 27 days in which the spot has been performing its apparent revolution, the earth has been advancing in his orbit from E to

A

Thus, when the

Fig. 29.

M

E

B

B

E', where the visible disk of the sun is A'B'. Consequently, before the spot can appear again on the limb from which it set out, it must describe so much more than an entire revolution as equals the arc AA', which equals the arc EE'. Hence,

365d. 5h. 48m.+27d. 7h. 37m. : 365d. 5h. 48m.::27d. 7h. 37m. 25d. 9h. 56m. the time of the sun's revolution on his axis.

149. If the path which the spots appear to describe by the revolution of the sun on his axis left each a visible trace on his surface, they would form, like the circles of diurnal revolution on the earth, so many parallel rings, of which that which passed through the center would constitute the solar equator, while those on each side of this great circle would be small circles, corresponding to parallels of latitude on the earth. Let us conceive of an artificial sphere to represent the sun, having such rings plainly marked on its surface. Let this sphere be placed at some distance from the eye, with its axis perpendicular to the axis of vision, in which case the equator would coincide with the line of vision, and its edge be presented to the eye. It would therefore be projected into a straight line. The same would be the case with all the smaller rings, the distance being supposed such that the rays of light come from them all to the eye nearly parallel. Now let the axis, instead of being perpendicular to the line of vision, be inclined to that line, then all the rings being seen obliquely would be projected into ellipses. If, however, while the sphere remained in a fixed position, the eye were carried around it,

(being always in the same plane,) twice during the circuit it would be in the plane of the equator, and project this and all the smaller circles into straight lines; and twice, at points 90° distant from the foregoing positions, the eye would be at a distance from the planes of the rings equal to the inclination of the equator of the sphere to the line of vision. Here it would project the rings into wider ellipses than at other points; and the ellipses would become more and more acute as the eye departed from either of these points, until they vanished again into straight lines.

150. It is in a similar manner that the eye views the paths described by the spots on the sun. If the sun revolved on an axis perpendicular to the plane of the earth's orbit, the eye being situated in the plane of revolution, and at such a distance from the sun that the light comes to the eye from all parts of the solar disk nearly parallel, the paths described by the spots would be projected into straight lines, and each would describe a straight line across the solar disk, parallel to the axis of vision. But the axis of the sun is inclined to the ecliptic about 710 from a perpendicular, so that usually all the circles described by the spots are projected into ellipses. The breadth of these, however, will vary as the eye, in the annual revolution, is carried around the sun, and when the eye comes into the plane of the rings, as it does twice a year, they are projected into straight lines, and for a short time a spot seems moving in a straight line inclined to the plane of vision 710. The two points where the sun's equator cuts the ecliptic are called the sun's nodes. The longitudes of the nodes are 80° 7′ and 260° 7', and the earth passes through them about the 12th of December, and the 11th of June. It is at these times that the spots appear to describe straight lines. We have mentioned the various changes in the apparent paths of the solar spots, which arise from the inclination of the sun's axis to the plane of the ecliptic; but it was in fact by first observing these changes, and proceeding in the reverse order from that which we have pursued, that astronomers ascertained that the sun revolves on his axis, and that this axis is inclined to the ecliptic 8230.

151. With regard to the cause of the solar spots, various hypotheses have been proposed, none of which is entirely satisfactory. That which ascribes their origin to volcanic action, appears to us the most reasonable.*

Besides the dark spots on the sun, there are also seen, in different parts, places that are brighter than the neighboring portions of the disk. These are called facula. Other inequalities are observable in powerful telescopes, all indicating that the surface of the sun is in a state of constant and powerful agitation.

ZODIACAL LIGHT.

152. The Zodiacal Light is a faint light resembling the tail of a comet, and is seen at certain seasons of the year following the course of the sun after evening twilight, or preceding his approach in the morning sky. Figure 30 represents its appearance as seen in the evening in March, 1836. The following are the leading facts respecting it.

1. Its form is that of a luminous pyramid, having its base towards the sun. It reaches to an immense distance from the sun, sometimes even beyond the orbit of the earth. It is brighter in the parts nearer the sun than in those that are more remote, and terminates in an obtuse apex, its light fading away by insensible gradations, until it becomes too feeble for distinct vision. Hence its limits are at the same time, fixed at different distances from the sun by different observers, according to their respective powers of vision.

Fig. 30.

2. Its aspects vary very much with the different seasons of the year. About the first of October, in our climate (Lat. 41° 18') it becomes visible before the dawn of day, rising along north of

* In the system of instruction in Yale College, subjects of this kind are discussed in a course of astronomical lectures, addressed to the class after they have finished the perusal of the text-book.