Let us suppose then such an island surrounded for thirteen miles distant on every side by an ocean, and let us consider what would be the apparent motions of the sun when seen from such an island. At the vernal and autumnal equinoxes, when the sun is on the equatorial, it would appear to rise out of the ocean at a point _E_, due east; it traverses half the equatorial and sets in the ocean at a point _W_, due west. The day is twelve hours long, from 6 a.m. to 6 p.m. [Illustration: FIG. 7.] In summer the sun is higher, and nearer to the pole _N_, say at a point _s_. It rises at a point _a_ in the ocean more to the north than _E_, the eastern point, and sets at a point _b_, also more north than _W_, the western point, and traverses the path _a s b_. But to traverse this path it takes longer than twelve hours, for _a s b_ is more than half the circle _a s b_. Hence then it rises say at 4.30 a.m. and sets at 7.30 p.m. The night, during which the sun moves round the path from _b_ to _a_, is correspondingly short, being only nine hours in length, from 7.30 p.m. till 4.30 a.m. So you have a long summer day and a short summer night. But in winter, when the sun gets nearer to the south pole of the heavens, it rises at a point _C_ in the ocean at 7.30 a.m., and traverses the arc _c t d_, and sets at the point _d_ at 4.30 p.m. So that the winter day is only nine hours long. But the winter night lasts from 4.30 p.m. till 7.30 a.m., and is therefore fifteen hours long, the sun going round the path _d r c_ in the interval. It is therefore the obliquity of the poles _N S_, coupled with the fact that the sun’s position is nearer to one pole, _N_, in summer, and nearer to the other pole, _S_, in winter, that produces the inequality of days and nights in our latitudes. Suppose our island were on the equator. The north pole and the south pole would appear to be on the horizon, and then whether the sun moved in the circle _a s b_ in the summer, or _E S W_ at the vernal or autumnal equinoxes, or _c t d_ in the winter, in each of these cases, though the places of rising and setting in the ocean might vary in summer from _a_ and _b_ to _c_ and _d_ in winter, yet in each of these cases the path from _a_ to _b_, _A_ to _B_, and _c_ to _d_ would still always be a half-circle and occupy twelve hours. Hence at the equator the days and nights never vary in length, but the sun always rises at six and sets at six. And, besides, it always rises straight up from the ocean and plunges down vertically into it, so that there is but little twilight and dawn. [Illustration: FIG. 8.]