an instrument or machine serving to measure time by the fall of a certain quantity of water. The word comes from κλείνω, condo, and ἀπό, aqua, water; though there have likewise been clepsydrae in which mercury was used. The Egyptians, by this machine, measured the course of the sun. Tycho Brahe made use of it to measure the motion of the stars; and Dudley used the same contrivance in making his maritime observations. Clepsydrae were invented in Egypt under the Ptolemies, as were also sun-dials. Their use was chiefly confined to the winter. The sun-dials served in the summer. They had two great defects; the one, that the water ran out with a greater or less facility, as the air was more or less dense; the other, that the water flowed out more readily at the beginning than towards the conclusion.

Construction of a Clepsydra. To divide any cylindric vessel into parts to be emptied in each division of time; the time in which the whole, and that in which any part, is to be evacuated, being given. Suppose, for example, a cylindric vessel, whose charge of water thrown out in twelve hours was required to be divided into parts to be evacuated each hour. 1. As the part of time one is to the whole time twelve, so is the same time twelve 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, &c.; and 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 numeration be in retrograde order from the twelfth hour, increase in the series of the unequal numbers 1, 3, 5, 7, 9, &c., the altitude, computed from the twelfth hour, will be as the squares of the times 1, 4, 9, 16, 25, &c.; therefore the square of the whole time 144 comprehends all the parts of the altitude of the vessel to be evacuated. But a third proportional to one and twelve is the square of twelve, and consequently it is the number of equal parts into which the altitude is to be divided, to be distributed according to the series of the unequal numbers, through the equal intervals of hours. But since in lieu of parts of the same vessel, other less vessels equal thereto may be substituted, the altitude of a vessel emptied in a given space of time being given, the altitude of another vessel to be emptied in a given time may be found, viz. by making the altitudes as the squares of the times.