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From what is the term comet derived? Why are comets so called? What are comets? Whence do they seem to come, and what to do? How have they been considered by the unlearned? Had any of the ancients just views of comets? How do astronomers of the present day view them? What is the general appearance of comets? Is there much variety in their appearance? How large have some comets appeared? What number of comets has been seen within the solar system? How near the Sun have some comets approached? How large a space have the tails of some comets occupied? What have been the different opinions of authors respecting the tails of comets? Whose opinion seems best supported? May the Earth ever have had the appearance of a comet? When did the aurora borealis appear

most brilliant in the United States?

CHAPTER V.

Equation of Time.

THOUGH the apparent motion of the Sun has been used as a measure of time from the greatest antiquity, yet accurate observation has shown it is far from being uniform. The Sun is either faster or slower than a well-regulated clock or watch, during most of the year. At four times only do they coincide, viz. the 14th of April, the 15th of June, the 31st of August, and the 23d of December. From the 14th of April to the 15th of June, the Sun is fast of clock; from the 15th of June to the 31st of August, it is slow of clock; from the 31st of August to the 23d of December, it is fast of clock; from this time to the 14th of April, it is slow of clock. From the difference of longitude, the days of coincidence are not all the same in the United States as in Europe. About the 1st of November, the Sun is 16 m. 14 or 15 s. fast of clock. This is the

greatest inequality. The difference is caused by the /elliptical figure of the Earth's orbit, and the obliquity of the equator to the plane of the ecliptic.

The orbit of the Earth being elliptical, like the other planetary orbits, with the Sun in one of the foci, the Earth, in its annual revolution, moves more slowly in the aphelion than in the perihelion, as has been before shown. But, the motion on its axis being perfectly uniform, any given meridian will come round to the Sun sooner at the aphelion than at the perihelion. Hence the solar day will be shorter at the former, and longer at the latter, than that measured by an accurate time-keeper.

Let S be the Sun, [Plate v. Fig. 8,] E the Earth; AMP the Earth's orbit; A the aphelion, P the perihelion; the line M S the mean proportional between the semi-axes of the orbit; m a point in the equator represented by the external circle of the Earth, E. Let the spaces A Sa, MS n, P S p, represent equal areas of the orbit. The arches of these, by the great law of Kepler, represent the Earth's motion in equal times, as a solar day. It is evident that the point m, when the Earth is at a, at n, or at p, must pass from m to the line ES to complete a solar day. It is also evident, that it must pass farther when the Earth is at p than when it is at a, the distance at n being a mean between the extremes. A day, therefore, measured by the Sun, will agree with that shown by a good timekeeper when the Earth is at M. At A it will be shorter, and at P longer, than the true day of the clock.

By this equation the Sun would be faster than the clock, while the Earth is passing from the aphelion to the perihelion of its orbit; slower than the clock, while the Earth is passing from the perihelion to the aphelion. At either apsis the Sun and clock would coincide. The difference between the Sun and clock would increase, while the Earth is passing from the aphelion or perihe

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lion to the mean distance between them, and decrease while it is passing to the other apsis. The greatest difference arising from this equation is 7'43". The Earth being in the aphelion on the first or second day of July, in the present century, and in the perihelion on the last day of December, or the first day of January, the equation is nothing in those days.

A still greater inequality, in the measure of time, is produced by the obliquity of the equator to the plane of the ecliptic. The vernal equinox happens about_the 21st of March; the autumnal, the 23d of September; the summer solstice, about the 21st of June; the winter, the 22d of December. From either equinox to the succeeding solstice, the Sun, on account of the obliquity, would be faster than the clock. From a solstice to an equinox, it would be slower than the clock. When greatest, this equation is about 9′ 54′′.

To render this familiar, let a wire be bent into a circle, to represent the Earth's orbit; let it be marked into equal spaces or arches, to show the daily motion of the Earth in its orbit. It is not essential that these spaces or arches should be degrees, or exactly so far as the Earth moves in a day, but any convenient distance. In or near the centre of the wire, let a lamp be suspended, in the middle of a large room or hall, to represent the Sun. Let a small globe be holden at a distance from the floor equal to that of the lamp, and on the west side of it, the axis perpendicular to the floor. Keeping the globe in this position, let it be moved upwards, and turned on its axis so as to perform one rotation in the time of its moving one space on the wire or supposed orbit. Both motions being kept equable, and the globe being moved completely round the lamp, it will be found that any meridian of the globe will perform a revolution, and come round to the lamp in the same time that the globe moves one arch of the wire, in all parts of it, except two points, when it is directly over and directly under the lamp. In those points, a meridi

an must move once and a half round, in order to come to the lamp. The motion of the globe from one mark to another on the wire, may represent a solar or natural day; a rotation on the axis, the sidereal day; the two points where the globe must be turned once and a half round, the summer and winter solstices. Were the axis of the Earth in the position in which that of the globe is supposed, it would coincide with the plane of the ecliptic, and the solar and sidereal days would be equal throughout the year, except at the solstitial points, where, as in the hypothesis, the solar day would be equal to one and a half sidereal days.

Let the axis of the globe be placed perpendicular to the plane of the wire, or supposed orbit, carried up, and turned round as in the former case. It will be found, that a meridian, which was towards the lamp at the commencement of a revolution, on the axis of the globe, will not, by being turned once round, be brought to the lamp again, but must, in every part of the supposed orbit, be turned a little farther, or more than once round, before it will become opposite to the lamp. It will also be found, that, if the spaces or arches on the wire, or supposed orbit, be marked as in the former supposition, and a revolution on the axis of the globe be completed in each of these, an additional turn will be requisite to bring a meridian round to the lamp, and that the differences will be equal in the whole revolution round the supposed orbit; and that, if the spaces, in which a revolution on the axis is completed, be taken to represent sidereal days, in the annual revolution of the Earth, an addition must be made to each of these spaces, in order that they may represent solar days.

A still different position of the globe may be conceived, in which the axis may be placed obliquely to the plane of the supposed orbit. In this case, the differences would not be at two points, as in one of the

above suppositions, nor equable, as in the other; but longer at those points, and shorter farther distant, the less the inclination of the axis to the plane of the supposed orbit. A position may be taken which would be a true representation of the Earth in its different motions. In such a position, the axis of the globe would be inclined to the axis of its supposed orbit in an angle of about 23° 28'. From this, it would appear, that the differences of the days are not wholly at the solstices, nor equable throughout the annual revolution, but are longer at the solstices, and shorter at the equinoxes, than the true solar days.

The common mode of explaining this equation by a supposed real and fictitious Sun, is on the principle of the Ptolemaic system, and gives no consistent idea concerning the cause of this equation.

The following table shows the difference between a true time-keeper and the Sun for every day in the year. To prevent an error from bissextile, it is calculated for four years. Altered from European tables, it corresponds to the time at Washington, and will answer, without essential error, in any part of the United States.

Is the apparent motion of the Sun an exact measure of time? At how many times in a year does the Sun coincide with a good clock in the measure of time? What are those times? When is the Sun fast and when slow of the clock? At what time is the greatest difference between the Sun and the clock? How much is the difference? What causes the difference between the Sun and a well-regulated clock? How do you account for the equation arising from the elliptical figure of the Earth's orbit? By this equation, when would the Sun be faster and when slower than a clock? What is the greatest difference arising from this equation? When is the Earth in the aphelion and when in the perihelion of its orbit? When is the vernal and when the autumnal equinox? When is the summer and when the winter solstice? When, on account of the obliquity of the equator to the ecliptic, would the Sun be faster and when slower than the clock ? What is the greatest equation arising from this cause? How can you, by a familiar representation, explain the principles on which this equation is founded? What objection can be made to the common mode of explaining this equation?

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