Clepsydra - is a water-clock, or instrument to measure time by the fall of a certain quantity of water, and is constructed on the following principles. - Suppose a cylindrical vessel, whose charge of water flows out in twelve hours, were required to be divided into parts, to be discharged each hour. 1. As the part of time is to the whole time, Twelve, so is the same time Twelve to a fourth proportional Hundred-and-forty-four. Divide the altitude of the vessel into one hundred and forty-four equal parts: here the last will fall to the last hour; the three next above, to the last part but one; the five next, to the tenth hour; lastly, the twenty-three last to the first hour. For since the times increase in the series of the natural numbers 1, 2, 3, 4, 5, etc. and the altitudes, if the numeration be in a retrograde order from the twelfth hour, increase in the series of the unequal numbers 1, 3, 5, 7, 9, etc. the altitudes computed from the twelfth hour will be as the squares c£ the times 1, 4, 9, 16, 25, etc. Therefore the squares of the whole time, one hundred and forty-four, comprehend all the parts of the altitude of the vessel to be emptied. But a third proportional to 1 and 12, is the square of twelve, and consequently it is the number of equal parts in which the altitude is to be distributed, according to the series of the unequal numbers, through the equal interval of hours:

There were many kinds of clepsydrae among the ancients; but they all had this in common, that the water ran generally through a narrow passage, from one vessel to another, and in the lower was a piece of cork, or light wood, which, as the vessel filled, rose up by degrees, and showed the hour.