But now let us suppose we were living at the north pole. In this case the north pole would be directly overhead, the south pole directly under our feet. At the vernal and autumnal equinoxes the sun would appear with half its disc above the ocean, and go round the ocean horizon, always appearing with half its disc above the sea. In summer it would appear at a point _s_ nearer to the pole _N_. It would go round in the heavens, always appearing above the horizon, and would never set at all. As the summer waned the sun would become lower and lower, still, however, going round and round without setting till at the autumn equinox it reached the horizon. So that for six months it would never have set. But when it did set, there would then be six months without a sun at all. [Illustration: FIG. 9.] Thus then all over the world the period of darkness and light is equivalent. At the tropics the days and nights are always equal. At the poles light for six months is followed by darkness for six months. In the intermediate temperate regions nights of varying lengths follow days of varying lengths, a short night following a long day and _vice versâ_. [Illustration: FIG. 10.] It is evident that for a person living on the north pole a sun-dial would be an easy thing to make. All that would be needful would be to put a post vertically in the ground, and observe its shadow as the sun went round (Fig. 10). [Illustration: FIG. 11.] In latitudes such as that of England, where the pole of the earth is inclined at an angle to the horizon, it is necessary that the rod, or “style” as it is called, of the sun-dial should be inclined to the horizontal. For if we used an upright “style,” as _O A_, then when the sun was in the south, at midday, the shadow would lie along the same direction, _O B_, whether the sun were high in summer, as at _S_, or low in winter, as at _s_. But at other hours, such as nine o’clock in the morning, the shadow of the “style” _O A_ would, when the sun was at its summer position _T_, lie along _O D_, whereas when the sun was at its winter position _t_ the shadow would lie along _O C_. Thus the time would appear different in summer and in winter; and the dial would lead to errors. But if the “style” is inclined in the direction of the poles, then, however, the sun moves from or towards the pole. As its position varies in winter and summer, the shadow still remains unchanged for any particular hour, and it is only the circular motion of the sun round in its daily path that affects the position of the shadows. [Illustration: FIG. 12.] Therefore the first condition of making a sun-dial is that the “style” which casts the shadow should be parallel to the earth’s axis, that is to say should point to the polar star. This is the case whether the sun-dial is horizontal or is vertical, and whether it stands on a pillar in the garden or is attached to the wall of a house.