"There are 360 days,"--a slightly inaccurate calculation

Since we wish the divisions of our day to be equal, the hour lines on the board must be of unequal length. The Sun gains far more altitude between 8:00 A.M. and 9:00 A.M. than between the hours of 11:00 and noon. In fact for a short while at midday the change in the Sun's altitude is so slight that it becomes useless as a gauge of time.

Similarly in the afternoon there is only a slight drop until 1:00 P.M. and then the length of shadow increases more and more rapidly until sunset.

However refined such a dial of the Thutmose-type may be, it is always dependent upon the altitude of the Sun, and therefore it suffers from a number of disadvantages. For each observation it must be turned until the shadow of the gnomon falls at right angles to the graduated rule, and it must be set horizontal. At a time considerably after Thutmose, the Egyptians added a plumb bob to their sundials, to keep the ruler level.

Denver is approximately forty degrees north of the equator, and here the days vary considerably in their length. The midsummer days are fifteen hours long; the midwinter days nine. Karnak was near the tropics; and Thutmose hardly needed lines to mark the difference between months on his dial. A few seasonal guide lines would suffice to show the change. Yet even in Karnak there was a difference between summer and winter, easily seen in the variable length of days. The mechanism of their time measurement depended upon the Sun itself, not upon whirling dials and springs and wires. We adjust ourselves to the routine of mechanical necessity. They adjusted themselves to the variations of nature.

Many daily newspapers have the habit of announcing the number of sunlight hours which their city will enjoy upon any one day. They scorn any weather considerations and in the late autumn, they publish boldly under their letter head, "There will be nine hours and twenty-one minutes of sunlight for our city today." The next day the amount will be reduced to "nine hours and twenty minutes," and so forth until the winter solstice, when the hours of sunlight begin to increase.

Had there been newspapers in ancient Egypt, they could never have advertised their country in this fashion. Day after day, summer and winter, the heading would have been alike. "There are twelve hours of sunlight for Egypt today. There are likewise twelve hours of dark." Had they been honest, they might have added: "The actual sunlit hours themselves will be shorter than yesterday's hours; nevertheless there will be twelve in number."

Because they adjusted their time to the Sun, the Egyptians divided their days into "unequal" or "temporary" hours. On any one day, all twelve hours were of equal length, but this length varied at different times of the year.

Early dials were divided, like ours, into twelve divisions. At first sight, twelve seems a curious number to choose. Primitive people, like children, always count on their fingers, and we cannot assume that all their mathematicians were born, like Anne Boleyn, with double thumbs. Nevertheless they had a reason in choosing the number twelve, a reason very arbitrary when applied to hours, but duly and thoroughly astronomical in origin.

Long before the Egyptians began to build pyramids, the people who lived near the Tigris and Euphrates had counted the number of days in the year, and the number of times that the Moon waxed and waned in the same period. They had no precise way of reckoning, and quite possibly they distorted their figures a little in an effort to please the gods. "There are twelve lunar months," they said. "There are 360 days,"--a slightly inaccurate calculation, but for a beginning it did well enough, and it had the additional advantage of reconciling two systems of arithmetic. Count off their number of months on the fingers of both hands three times, and you have the number of days in their year. Sixty is the lowest common multiple of the number of fingers and the number of months, so sixty became their unit; and sixty has the great advantage of being divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. A great boon that number must have been to their school children, for they had practically no fractions. It is a very simple system, this Babylonian notation, and we only regret that it is not more scientific in its origin but, scientific or not, it is responsible for the number of degrees in our circle, the seconds in our minute, the minutes in our hour, and the twelve hours in our day.

The hours of darkness were also twelve in number, equal in any one night, but unequal throughout the year. Since the nights shorten as the days become longer, and lengthen as the days become shorter, the hours in any one night would not have the same length as the hours in the preceding or succeeding day. Only at the Equinoxes would a night hour be the same length as a day hour; and the Equinoxes derive their name from that very equality.