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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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