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duced to 2", and two days before sunset it has increased to about 3".5. It will be noticed in the above table the first three measures made upon the fifth and seventh days are larger than any of the others.

The first reading made upon the date of the eclipse as compared with its two successors made immediately afterwards, is unaccountably large. This is probably due in part to the inferior seeing, which would have this effect, and in part to accidental errors. Omitting it from consideration for the present, we find that before the eclipse the mean diameter of the spot was 2.00, immediately after the eclipse it was 2".11, and soon after that it was reduced to 1".95. The mean of the first two and the last two is 1".97, which, subtracted from the reading made immediately after the eclipse is 0".14, corresponding to 0.17 miles or 0.26 kilometers. That is to say, owing to the eclipse, the white spot surrounding Linné apparently increased in diameter by about one-sixth of a mile. Including the rejected measure, the mean of the five readings, to be compared with that taken immediately after the eclipse is 2".03, giving an enlargement due to the eclipse of 0".08.

Although these results certainly cannot be called conclusive, still, they tend to confirm those already obtained by Mr. Douglass during the previous year, both in the fact of the existence of an enlargement, and also in the observation that the effect is of short duration; and perhaps that is all that can be expected, when we consider how small a quantity is involved. There seems to be a strong reason to believe, as has been already stated, that the size of Linné increases as the Sun approaches its horizon, and if this is so, it certainly seems natural to suppose that it should increase in size if the Sun's light were withdrawn from it altogether. At all events that is the effect which has been observed at two different eclipses, by two different observers, one of whom had no personal bias, since he did not know what to expect.

HARVARD COLLEGE OBSERVATORY,

December 24, 1899.

CONCERNING THE EARTH'S MOTIONS.

GEORGE S. HODGINS.

FOR POPULAR ASTRONOMY.

The expression, so often used in everyday conversation, "Immovable as the Earth;" is after all, only relatively true, and could not be accepted for a moment, as a scientific statement of fact. Equally open to a little friendly criticism, in this regard, are the well known words, in which Juliet adjures her lover: "O swear not by the Moon, the inconstant Moon, that nightly changes in her circled orb, lest that thy love prove likewise variable." The Moon is, however, not more inconstant than the very globe upon which Juliet stood. Investigation by astronomers has revealed the fact that the Earth is circling and swinging and changing its course in a manner that is well nigh baffling to the understanding.

In the first place our Earth revolves upon its axis, as any school boy knows, just as an orange may be made to rotate round a knitting needle, thrust through its volume. It is, of course, this motion which gives us the endless succession of day and night. If the equator be regarded as a huge wheel, it makes one complete revolution in about 23 hours and 56 minutes. During this period of time, the Sun has moved forward in its course, over a million miles, so that the Earth requires to continue its rotations for 4 minutes longer, in order that it may bring the same meridian, under the central beam of light from the Sun, which shone on it, at the beginning of any one of its rotations. It thus makes the period of rotation 24 hours for each day and night. The period of 23 hours 56 minutes is called the sidereal day; and the 24-hour period is the solar day.

Passing on to the annual motion of the Earth round the Sun, we find that this revolution is the one which produces the seasons, in regular succession. The path or orbit of the Earth round the Sun follows a line, which is simply a vast ellipse. The major axis of this ellipse, is given, by some authorities, so as to place the Sun, approximately, three and a half millions miles, nearer one end of the ellipse than the other.

It may be advantageous, just here, to glance at one of the properties common to all ellipses. There are, in every true ellipse, two points, situated on the greater diameter, called foci. An ellipse has been shortly defined, as a plane curve, such that the sum of the distances from any point of the curve, to the two fixed

points, is a constant. It may be added, that the two foci, are, of course, always separated by a line of constant length.

The Earth, then, swings round the Sun in a path called an ellipse, the Sun occupying one of the foci. As the Earth swings past the Sun, at the nearer end, one would expect that at this portion of its path, it would receive more heat, than when at the farther end, as it is then about three and a half millions of miles nearer the great source of heat and light. Paradoxical as it may seem, northern countries experience, at this nearer approach to the Sun, their winter season. At the more distant end of the orbit these northern lands enjoy their summer weather. The reason for this lies in the fact that the axis of the Earth is tilted, and makes an angle with the plane of its own orbit of about 66%0. The consequence of this axial tilt is, that when the Earth is closer to the Sun, the rays of heat fall more obliquely on the northern hemisphere, than they do when the Earth assumes its more distant position. The rapidity of the Earth's motion about the Sun has been estimated at about 19 miles per second.

Glancing now, very briefly at another, and more complex motion of our planet, one may say that the above holds good on the assumption that the inclined axis of the Earth always moves parallel to itself, during the entire cycle round the Sun. Though the axis does approach very close to absolute parallelism, all the way round, yet, strictly speaking, it is not so. The tilt of the axis, and the Earth's peculiar shape give rise to a curious and interesting motion, which astronomers have called the precession of the equinoxes.

The shape of the Earth is not that of a perfect sphere. It is in reality that of an oblate spheroid, or in other words, it is slightly flattened at the poles and bulges out in the neighborhood of the equator. The polar diameter of the Earth is somewhere about 26 miles shorter than its equatorial diameter. This equatorial protuberance, is at times, above and again below, the line joining the centres of Earth and Sun, owing to the tilt of the axis of the former. The effort of the Sun's attraction, acting along the line of centres, on this protuberant mass, tends to draw the Earth into such a position that the axis of the later shall be perpendicular to the plane of its orbit about the Sun. This cffort, directed upon a rapidly rotating body, like our Earth, causes each pole to describe a circle, traced out in the heavens, in a manner similar to that of a spinning top, whose axis revolves slowly, in a cone. The revolution of the Earth's axis round this circle, which, if the poles be supposed to be prolonged until they

reach the stars, above and below the Earth, is a very slow one indeed, and in marked contrast to the rapid diurnal rotation and annual rates of revolution. The complete revolution of the axis, or the precession of the equinoxes, requires a period of no less than 25,827 years.

From this it will be evident that the true polar point in the heavens is slowly and gradually shifting its place among the stars. The star in the northern heavens which we know as Polaris, or the Pole Star, is only a close approximation to the true north point. No one point, therefore, remains permanently as our celestial pole.

It has been calculated by competent authorities, and found, that at the date of the construction of the Great Pyramid of Egypt, in the year 2170 B. C., the pole star of that remote epoch was the first star in the Dragon, more correctly called, a Draconis. At the present time a Ursa Minoris, or the brightest star in the Little Bear, is the nearest observable point to our true north, and is in more than name, the North Star. In the southern celestial hemisphere, there is no conspicuous star to mark the polar point. The precession of the equinoxes is so called because the equinoxial points on the Earth's orbit revolve slowly around, with the circling poles.

In considering this motion, one is compelled to notice, the modification of it, which is effected through the agency of the Moon's attraction. This modification is called nutation, or the nodding of the pole. The path of the Moon is inclined to that of the Earth at an angle of about 5°, and her attraction when above and below the protuberance at our equator, is able to modify the lines traced by the poles, on the heavens, due to the Sun's attraction. The Moon's attractive force, though much less than the Sun's, by reason of her inferiority of mass, is yet very considerable, owing to her comparative proximity to our planet. By the delicate balancing of her power with that of the Sun, it is found that she is able to compel the otherwise circular line, traced by our poles on the heavens, to assume a sinuous form. The deviation from the circle which the Sun would cause our pole to trace, passes as much outside it as it does within, so that the resulting figure is really a scalloped circle, if one may so say; forming an exquisitely beautiful and sinuous line. The period required to make one "nod" in the pole's course is about 18 years. The motion, or rather, modification of motion which we call nutation, effects a series of slight undulations in the otherwise theoretical circle, traced by the pole in its "precession."

Next in order comes that motion of the Earth called the advance of the apsides. In order to properly consider it, we must here go back to our great ellipse or path of the Earth around the Sun. The apsides are the two points on this ellipse having, respectively the greatest and least distance from the Sun. They are, in fact the ends of the major diameter of the ellipse. When at either of these points, the Earth is said to be, as the case may be, in perihelion, when near the Sun, and in aphelion, when away from the Sun. These two points together with the whole ellipse or Earth path, move slowly forward in the direction of the Earth's motion.

The Earth revolves round the Sun in its diurnal motion from west to east, turning upon its axis, just as if it were being rolled over and over, on the outer surface of the Sun. In its annual motion round the central luminary, it moves in exactly the same direction, as if rolled over the Sun's surface. In the same direction also the apsides advance. This motion is caused by the attraction of Jupiter, and the other planets. It amounts to about 1° 23′ per century, so that in about 26,024 years, the advancing apsides would complete one cycle. When computed with reference to time, we find that there is a difference in the length of the year, as measured by the advance of the apsides and that of the sidereal This latter is the time required by the Earth, leaving any point in the heavens, and returning to it again. The year measured by this apsidal motion is 4 minutes and 39 seconds longer than the sidereal year, which latter is 365 days, 6 hours, 9 minutes and 10 seconds.

year.

Another modification of the Earth's motion is caused by the tilting or swaying of the ecliptic. This is also due to the attraction of our giant neighbor, Jupiter, and his fellow planets. The ecliptic is the name given to the plane of the Earth's orbit. It may be supposed that this plane is extended outward in all directions until its edges touch the fixed stars, exactly like the surface of a level liquid, with the Earth floating, half immersed in it. The Earth's axis stands, as has been said above, at an angle of about 66% to the ecliptic and it therefore makes the complementary angle of 23° with a line standing perpendicular to the ecliptic. The ecliptic does not, however, lie motionless like the surface of a level liquid; but is moved up and down, or tilted about a line joining the equinoxial points, just as a table might be tilted up at one end, and down at the other, about a line drawn straight across it, in the middle, from side to side. This tilting up and down, of the ecliptic, will necessarily alter the angles 662° and 231⁄2° just given. The limits of the tilting

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