To divide the dial, we have only to imagine it surrounded by a sort of cage formed of twenty-four arcs drawn from the north pole to the south pole, and equidistant from one another. In its course the sun would cross one of them every hour. Hence the points to which the shadows _o a_, _o b_, _o c_, _o d_, of the inclined “style” _O N_ would point are the points where these arcs meet the horizontal circle. This consideration leads to a simple method of constructing a sun-dial, which is given at the end of this chapter in an appendix. Sun-dials were largely in use in ancient times. It is thought that the circular rows of stones used by the Druids were used to mark the sun’s path, and indicate the times and seasons. Obelisks are also supposed to have been used to cast sun-shadows. The Greeks were perfectly acquainted with the method of making sun-dials with inclined “styles,” or “gnomons.” [Illustration: FIG. 13.] Small portable sun-dials were once much used before the introduction of watches, and were provided with compasses by which they could be turned round, so that the “style” pointed to the north. Sun-dials were only available during the hours of the day when the sun was shining. The desire to mark the hours of the night led to the adoption of water clocks, which measured time by the amount of water which escaped from a small hole in a level of water. Some care, however, is required to secure correct registration. For suppose that we have a vessel with a small pipe leading out near the bottom, then the amount of water which will run out of the pipe in a given time depends upon the pressure of the water at the pipe, and this depends in its turn upon _P Q_, the head of water in the vessel. Whence it follows that the division _Q R_, due to say an hour’s run of the clock at _Q R_, will be more than _q r_, the division corresponding to an hour, at _q_, a point lower down between _P_ and _Q_, and hence the divisions marked on the vessel to show the hours by means of the level of the water would be uneven, becoming smaller and smaller as the water fell in the vessel. To avoid the inconvenience of unequal divisions, the water to be measured was allowed to escape into an empty vessel from a vessel in which its surface was always kept at a constant level. Inasmuch as the pressure on the pipe or orifice in the vessel in which the water was always kept at a constant level was always constant, it followed that equal volumes of water indicated equal times, and the vessel into which the water fell needed only to be equally divided.