CLEPSYDRA, a water-clock, or in strument to measure time by the fall of a certain quantity of water.
The construction of a Clepsydra. To di vide any cylindrical vessels into parts, to be emptied in each division of time, the time wherein the whole, and that where in any part is to be evacuated, being given. Suppose a cylindrical vessel, whose charge of water flows out in twelve hours, were required to be divided into parts to be evacuated each hour. 1. As the part of time 1 is to the whole time 12, so is the same time 12 to a fourth proportional 144. 2. Divide the altitude of the vessel into 144 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, &c. and the altitudes, if the nume ration be in a retrogade order from the twelfth hour, increase in the series of the unequal numbers 1, 3, 5, 7, 9, &c. the al
titudes computed from the twelfth hour will be as the squares of the times 1, 4, 9, 16, 25, &c. Therefore the squares of the whole time, 144, comprehend all the parts of the altitude of the vessel to be evacuated. But a third proportional to 1 and 12 is the square of 12, and conse quently it is the number of equal parts in which the altitude is to be divivided, to be distributed, according to the series of the unequal numbers, through the equal in terval of hours. There were many kinds of clepsydrm 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.