This being thoroughly understood, let us place ourselves in the equatorial plane, so as to embrace at a single glance a quarter of the illuminated and a quarter of the darkened hemisphere. If the equator of the photo-adumbrated sphere perpetually coincided with the terrestrial equator,--if, in other words, the earth, in revolving round the sun, invariably occupied the plane of the Equator, which, when prolonged, would pass through the centre of the illuminating orb,--the diurnal rotation would not cease to divide equally the light and the darkness over the earth's surface, as is shown in Fig. 42 _a_, where S indicates the sun, EE the terrestrial equator, and N S the extremities (or North and South Poles) of the axis which divides the globe into an illuminated and a darkened half. This phenomenon of coincidence exists; but only for a very brief period, and is only repeated twice a year,--that is, at the equinoxes. At all other times, the equator of the photo-adumbrated sphere, in whose plane the orb of light is situated, passes sometimes above and sometimes below the terrestrial equator. [Illustration: FIG. 42.--S, the Sun; EE, the Equator; N, North Pole; S, South Pole.] But this alternate movement of northern and southern declination has its limits; it stops at 23° 27' 30" on either side of the Equator; this, too, is the maximum of the distance which the imaginary axis of the photo-adumbrated sphere retires from the axis of terrestrial rotation; it is at the same time the value of the obliquity of the ecliptic, or of the inclined plane which the earth traverses in its annual movement of revolution. Fig. 42 _b_, which represents the photo-adumbrated sphere at the summer solstice, will enable the reader to comprehend with the utmost facility the six months' day of the North Pole, coinciding with the six months' night of the South Pole; for the triangle N C D indicates the amount by which the illuminated moiety increases in the northern hemisphere between the spring equinox and the summer solstice, the amount being equal to that by which the adumbrated moiety overspreads in a contrary direction the South Pole in the southern hemisphere. The superfluous quantity of the photo-adumbrated sphere is _nil_ at the apex of the two opposite triangles, or in the equinoctial region. And then, in effect, both day and night are always twelve hours long. Starting from the equinoctial line, we see how easy it is to calculate for each locality the variable dimensions of the arc which the sun, in its apparent course, traces above the horizon. * * * * *