THEORETICAL ASTRONOMY. i09 
towards the south. If, for instance, we suppose the sun on June 2lst to 
have reached the point L, it is evident that while the earth rotates about 
her axis, az, from west to east, or in the direction from Q to U, it will 
seem as if the sun in the same time, but from east to west, had described 
the parallel circle, VOLV (or the tropic of Cancer), about the earth ; wher 
the sun is at R, he will appear to describe the equator CREFC; and on 
December 2Ist, the tropic of Capricorn or the circle DHMD. The planes 
of the equator and tropics intersect the earth in circles, which are respec- 
tively the terrestrial equator and the terrestrial tropics. It is further to be 
observed that the poles, N, K, of the ecliptic, during the apparent daily 
rotation of the heavens, describe two small circles, of which the northern, 
AN, is called the arctic, the southern, BK, the antarctic. The polar circles 
of the earth corresponding to these are u, y, and fh, b. 
The rotation of the earth on its axis, and the inclination of the ecliptic to 
the equator, explain without any difficulty the inequality of days and nights, 
and the succession of the seasons. For when the sun on the 21st June 
traverses the tropic of Cancer, he remains much longer above the horizon 
zz than when describing the tropic of Capricorn on Dec. 21. In this latter 
case we readily perceive that the sun remains much longer below the hori-. 
zon, and that consequently the nights are much longer than on the 21st 
of June. It is further evident, that about the 20th of March and 23d of 
September, when the sun is on the equator, an equality of days and nights 
must take place. Figs. 1 and 3, pl. 9, also show that during the six months 
that the sun is north of the equator, spring and summer must take place in 
the northern hemisphere, autumn and winter in the southern; but during 
the six months that this luminary is south of the equator the case must be 
reversed, spring and summer now happening in the southern hemisphere, 
autumn and winter in the northern. 
28. All that has hitherto been said with regard to phenomena occurring 
in connexion with the earth, can only be explained by the assumption of a 
rotatory motion of the earth about an axis at the same time with a revolution 
about the sun in an elliptical orbit (pl. 9, fig. 1). The inequality of the: 
seasons is a necessary consequence of the elliptic motion of the earth, and 
of the inclination of its axis of rotation to the plane of the ecliptic. If, for 
instance, the axis of rotation were perpendicular to the plane of the ecliptic, 
then there would be no change of seasons, but rather a single continuous 
torrid, temperate, or frigid zone. In this case also the planes of the equator 
and ecliptic would coincide, and as the sun would remain constantly in this 
plane, the days and nights would be equal the whole year through, and the 
poles of the earth be illuminated by only half the sun’s disk. The equatorial 
regions would have a burning summer continually, the temperate zones 
would have an eternal spring, and the polar lands would experience without 
intermission intense cold, in which ice would never melt. But the axis of 
the earth, ever parallel to itself, is inclined to the plane of the ecliptic 66° 33’, 
and thence follows,—Ist, a progressive difference in the length of the days 
and nights for all points of the earth’s surface from the equator to the poles, 
and from the first day of the year to the last; 2dly, an increase and diminu-- 
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