The principle of this was applied in several interesting variations. The defect of the Hemicycle, as this hollow type of dial was called, was that it could not be read accurately for short intervals. A shadow moving only a few inches in the whole day must move so slowly that one could hardly see it move at all. To mark the minutes, it must move faster, just as the minute hand of your watch moves faster than the hour hand, and the second hand faster still. One cannot read seconds from the hour hand, however accurately it moves, because it moves so slowly. So the idea was applied by making the shadow move across a street or courtyard, down one side and across and up the other side, as the sun opposite went up and across and down the sky. Sometimes the place was partly roofed over, and a single beam of light admitted through a small hole at the South end. The resulting spot of light would then move in the same way. The long sunbeam or shadow moved faster, and so could be read at shorter intervals. The Hemicycle is not certainly known to have been invented until long after this, about B. C. 350. But the principle of it is so simple and so entirely such as would occur to an intelligent man still ignorant of its mathematical explanation, that we may not unreasonably suppose it to have been discovered by experiments long before. [Illustration: ANCIENT ROMAN HEMICYCLE] The final improvement of the sundial was the discovery that by slanting the gnomon so that it pointed exactly toward the North Pole of the sky, the direction of its shadow could be made to show the solar time correctly. Since the sky is infinitely far away, the line of the gnomon would then lie parallel to the axis of the heavens. And the sun, moving parallel to the celestial Equator, would always move straight across the gnomon. In other words, he would practically revolve around its sloping edge. Therefore the North and South motion of the sun would be as it were along the edge of the gnomon, and would not influence the direction of the shadow at all. His East and West motion alone would govern the swing of the shadow; and the dial would keep true time with the sun for every day in the year. There was no longer any necessity for hollowing out the dial itself into the concave form; it might just as well be the more convenient flat surface, and this might be either vertical or horizontal, so long as the gnomon pointed straight to the Celestial Pole. All that was needed was to mark out on the dial the true direction in which the shadow fell for each hour of the day. [Illustration: OLD ENGLISH DIAL]