sun.

to the north pole P about the 21st of June, and consequently he will be immediately over the point H in the tropic of Cancer, and all the places of the earth situated under the parallel G H will pass in their diurnal revolution directly under the Six months after, the earth will be found on the other side of the sun in the point t of her orbit, diametrically opposite to the point T. Suppose then (which nearly takes place) that the axis p a is parallel to the axis P A, so as to point exactly to the same part of the heavens to which it pointed six months before. Now it is evident that the terminator M N, or m n, (drawn at right angles to It) will divide the parallels to the equator or the circles of daily motion into unequal parts-those on the same side of the equator with the sun having a greater portion within the illumined than within the dark hemisphere. All the countries of the earth, therefore, which lie on this side of the equator will employ a longer portion of the diurnal rotation in passing through the illuminated than through the darkened parts of their respective parallels, and will, therefore, have their days longer than their nights, and of course enjoy summer. On the contrary, all the countries on the other side of the equator, having a greater portion of their parallels included within the dark than the illumined hemisphere, must occupy a longer time in passing through those dark parts, and have their nights longer than their days; consequently it will be their winter.

This is not only the case when the sun is at his greatest distances from the equator, or when he is in either of the tropics, but it takes place, though in a less degree, at all his intermediate distances from it, the terminator continually dividing the parallels unequally, so as to comprehend a greater or a less portion of them within the illuminated part of the earth, according as the sun is on the same or a different side of the equator from that on which the parallels lie. When he is in the equator, the terminator will be in the direction P A, or p a, and will manifestly divide the parallels equally, so as to make day and night of the same length throughout the globe. This is the time of spring to the inhabitants of that part of the earth who are placed on the same side of the equator on which the sun is passing, and autumn to those who are placed on the other side of the equator from which he is retiring.

It is easy, therefore, to see that it is the inclination of the axis of the earth to the plane of the ecliptic, which occasions the change of the seasons; and the constancy of that inclination their constant succession.

The sun and moon being of all the heavenly bodies the most familiar to us, and the most easy of observation, have from the earliest ages furnished us with the measure of time. Time is divided into ages, years, months, weeks, days, hours, minutes, and seconds: of which the month originated in the motions of the moon; the year

and the day in the apparent motions of the sun; the hours, minutes, &c. have been introduced to facilitate the estimation of the subdivisions.

That space of time is called a day in which the earth performs one rotation on its axis, and in which consequently the sun appears to make an entire revolution round the earth from east to west. The natural or astronomical day is that in which the sun appears to revolve from the meridional line which passes through any given place to the same meridian again. The astronomical days are, however, not always of the same length, while the civil day is always of equal duration. This difference has given rise to a distinction which is necessary to be known. The former, which is usually measured by the sun-dial, is called solar, and the latter, which is measured by the clock, is called mean or equal time.

The difference between mean and solar time depends upon three causes.

1st, The earth (according to the third law o Kepler) does not pass equal portions of its orbit in equal times. It proceeds sometimes quicker, and sometimes slower, and consequently the sun appears to advance more or less rapidly in the ecliptic. In the first case the day will be somewhat longer, because the earth to rejoin the sun, or to present to him the same meridian, must make somewhat of a larger turn upon its axis,

In the second case (for the opposite reason) the day will be in some degree shorter.

2dly, The earth's motion on its own axis is always equal and regular; and if the plane of the ecliptic were parallel to the equator, there would be no difference in the time marked by either of these circles, for fifteen degrees of each of these circles passing over any meridian would be equivalent to an hour in time. But, from the inclination of the earth's axis, as already described, the ecliptic is oblique to the equator, and consequently the earth's rotation on its axis carries unequal portions of the ecliptic over the meridian in equal times, and the difference is proportional to the obliquity. If a sun or star were, therefore, supposed to move in the circle of the equator, it would always return to the same meridian in twenty-four hours, as measured by the clock; but the sun, which moves in the ecliptic, will sometimes return sooner, and sometimes later. It is therefore only on four days in the year that these two luminaries would come both together to the same meridian, and on these days only the dial and the clock will be found exactly to agree.

A diagram will perhaps serve better to explain what I have now said. Let Pl. I. fig. 2, represent a part of the concave sphere of the heavens. Let DE be a part of the celestial equator, FG a part of the ecliptic, A the intersection of the two circles at the vernal equinox, AB a degree

upon the equator. Suppose the plane of the meridian to pass from the situation M M into the situation N N, in going through the arc A B, one degree of the equator, it will go through the arc C more than one degree of the ecliptic. For in the triangle A B C, the angle at B is a right angle, and the hypothenuse A C is consequently the longest side.

At the solstices, the obliquity of the ecliptic has a contrary effect, and contributes to lengthen the solar days. Thus, (in fig. 3) TT is part of the tropic of Capricorn, CD part of the ecliptic, coincident with the tropic for some distance on each side of the solstitial point, viz. from A to B, and therefore meridians which are perpendicular to the tropic may be considered so far as perpendicular to the ecliptic. A meridian, then, in going from A to B will go through as large an arc in the tropic as in the ecliptic; but the tropic not being so great a circle, any arc, as a b, taken in both these circles will measure more minutes than in the ecliptic, and that in proportion as the ecliptic exceeds the tropic in dimensions. The circumference of the ecliptic is to that of the tropic as 60 to 55, and therefore the arc ab of 55 minutes on the ecliptic, will be 60 in the tropic. As every meridian, therefore, passes in the same time through similar arcs in the celestial equator, and all circles parallel to the equator, and such are the tropics, at the solstices every arc of the ecliptic passed through by any