We will deal with the sun first. From the motions of the sun we can observe the time. This is done in every garden by means of sun-dials, and I will now describe how they are constructed. If a light, such as the light of a candle, be moved round in a circle at a uniform pace so as to go round once in some given period, such as twenty-four hours, it is obvious that it would serve to measure time. Thus, for example, if a sheet of white paper be placed upon the table, and a pencil be stuck on to it upright with some sealing wax, or a pen propped up in an ink-pot, then a candle held by anyone will cast the shadow of the pen on the paper.
Fig. 5.
If the person holding the candle walk round the table at a uniform speed, the shadow will go round like the hand of a clock, and might be made to mark the time. If the candle took twenty-four hours to go round the table, as the sun takes twenty-four hours to go round the earth, then marks placed on the paper would serve to measure the hours, and the paper and pen would serve as a sort of sun-dial.
But the sun does not go round the earth as the candle round the table. Its path is an inclined one, like that shown by the dotted line. Sometimes it is above the level of the table, sometimes below it. And, moreover, its winter path is different from its summer path. Whence then it follows that the hour-marks on the paper cannot be put equidistant like the hours on the dial of a clock, and that some arrangement must be made so that the line as shown by the summer sun shall correspond with the time as shown by the winter sun.
Fig. 6.
Let us suppose that N O S is the axis of the heavens, and the lines N A S, N B S, N C S, are meridian lines drawn from one of the poles N of the heavens round on the surface of a celestial sphere whose centre is at O. Let A B C be a circle also on this sphere, passing through O, the centre of the sphere, in a plane at right angles to N S, the axis. Then A B C is called the equatorial. It is a circle in the heavens corresponding to the equator on the earth. At the vernal and autumnal equinox, namely on March 25 and September 25, the sun is in the equatorial. In midsummer and midwinter it is on opposite sides of the equatorial. In midsummer it is nearer to N, as at V; in midwinter it is nearer to S, as at W. Suppose we were on an island in the midst of a surrounding ocean, we should only have a limited range of view. If the highest point on the island were 100 feet, then from that altitude we should be able to see about thirteen miles to the horizon. More than that could not be seen on account of the rotundity of the earth.
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.
