an instrument or machine serving to measure time by the fall of a certain quantity of water.

The word comes from κλεπτόν, condo, and ἀνάγειν, aqua, "water;" though there have likewise been clepsydrae made with mercury.

The Egyptians, by this machine, measured the course of the sun. Tycho Brahe, in our days, made use of it to measure the motion of the stars, &c., and Dudley used the same contrivance in making all his maritime observations. The use of clepsydrae is very ancient; they were invented in Egypt under the Ptolemies, as were also sun-dials. Their use was chiefly in 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 ran more readily at the beginning than towards the conclusion. M. Amontons has invented a clepsydra free from both these inconveniences; and which has these three grand advantages, of serving the ordinary purpose of clocks, of serving in navigation for the discovery of the longitude, and of measuring the motion of the arteries.

Construction of a CLEPSYDRA. To divide any cylindrical vessel into parts to be emptied in each division of time; the time wherein the whole, and that wherein any part, is to be evacuated, being given.

Suppose, for example, a cylindrical vessel, whose charge of water throws out in 12 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, &c.; lastly, the 23 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 1 and 12 is the square of 12, 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. 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 time. For a further description, see HYDRODYNAMICS Index.