2. Another form, and that a very simple one, of the modern clepsydra has derived its origin from that law in hydrostatics by which the efflux of water out of an orifice is influenced under different pressures, or which is the same thing, at different depths from the surface, the velocity being directly as the square root of the height of the surface from the aperture. If a glass vessel, like that in fig. 3,


therefore be taken, out of which all the water will flow in exactly 12 hours, from a small aperture in its lower extremity, the whole height must be divided, or supposed to be divided, into the square of 12 or 144 equal parts, of which parts 11 x 11, or 121 measured from the bottom, or 23 measured from the top, will give the division for the hour 11, 10 x 10 or 100 from the bottom will give the line for 10, 81 for 9, 64 for 8, and so on down to the bottom, as represented in the figure ; which scale is in the inverted proportion of that according to which heavy bodies fall in free space by the sole force of gravity.

If, instead of the vessel itself being divided by hour-lines as above directed, the Item of a floating piece like an hydrometer were to have a similar scale kept in a perpendicular direction, by passing through the central hole of a cap or cover of the vessel, the indication of time would be made on the stem at the surface of the cap, which construction would admit of the vessel being of wood or metal.

3. But such a figure might be given to the containing vessel as would require the dividing marks to be equi-distant, which Dr. Hutton, in his recent edition of "Ozanam's Recreations," has asserted to be a paraboloid, or vessel, formed by the circumvolution of a parabola of the fourth degree, the method of describing which, he has given thus :


Let A B S , Plate II. fig. 4, be a common parabola, the axis of which is P S, and the summit S. Draw, in any manner, the line, R v T, parallel to that axis, and then draw any ordinate of the parabola A P, intersecting R T in R ; make P Q a mean proportional between P R and PA, and let p q be a mean proportional also between p r and p a ; and so on; The curve passing through all the points Q q, &c. will be the one required, which, being made the mould for a vessel to be cast by, will produce an instrument, which, when perforated at the apex, will have the singular property of equalizing the scale, so as to correspond to equal times while the water is running out. Mr. Varignon has given a geometrical and general method of determining the scale for a clepsydra, whatever may be the shape and magnitude of the vessel. (See "Memoires de I'Academié Royale des Sciences," p. 78, 1699.)

4. Another method of making a water-clock with equi-distant hour lines in any regular vessel is effected more simply than in the preceding one, by means of the syphon fixed fast in the centre of a broad piece of cork, which is floated in any regular vessel, as the cylindrical one at fig. 5,


for as the power of a syphon to empty any vessel filled with water depends upon the difference of atmospheric pressures at the surface of the water and at the orifice of the longer leg, it is clear that while the shorter leg sinks with the surface of the water in the vessel during its time of emptying, the relative pressures, depending on the distance from the surface of the water to the orifice of the lower leg, will continue unaltered in any state of the atmosphere ; hence equal portions of water will be discharged in equal times ; and a light cock cemented on the lower orifice would afford a means of adjusting its aperture to the size of any vessel that may be fixed upon ; or otherwise a second receiving vessel may be divided into equal spaces for the hours, which would in this case be indicated by the surface of the rising water.

Besides the preceding methods of measuring time by means of water, there are others nearly similar, such as the double jet d'eau, which, like the sand-glass that may be classed with these, requires to be inverted as soon as empty, and it is easy to conceive a variety of ways of applying any liquid to answer the purpose of measuring pretty nearly a given number of hours, but we do not learn that the most accurate of the clepsydra is comparable to an ordinary clock, though it has been asserted, that Amontons constructed one in so accurate a manner, that he hoped to find it useful in ascertaining the longitude at sea by means of its accuracy ; we regret that it is not in our power at present to procure the pamphlet in which the account of it was published. "Remarques & Experiences Physiques fur la Construction d'une nouvelle Clepsydre," &c. Paris. Jombert, 1695.

5. We shall conclude our account of these horological instruments with detailing the construction and action of a clepsydra, published in the 44th volume of the Philosophical Transactions by the Hon. Mr. Charles Hamilton.

A B and C D are two similar oblong vessels attached to a frame of wood, which may easily be conceived to surround figure 6,


which shews only the interior mechanism ; a b and c d are two columns of wood so floating in water, that their counterpoises, F and G, just keep thor superior ends equal with the surface of the water by means of connecting chains passing over the pulley f, and another hid by the dial plate ; the former of these pullies, f, has a click which pushes the ratchet on the barrel, i, when the counterpoise, F, falls, but flips easily over the slopes of the teeth when the said counterpoise rises ; the latter pulley has also a similar click acting in like manner, with a second ratchet at the opposite end of the barrel, i, which ratchet is also hid in the drawing, so that whichever of the two counterpoises shall at any time be falling, the barrel, i, will move forwards in the same direction ; and carry the minute hand along with it on the dial-plate; the hour hand goes round by means of dial-work, as in an ordinary clock or watch, where a diminution of velocity is effected by two wheels and two pinions. The action is thus produced by means of five syphons and two balances.

The water enters with an unvaried influx, drawn from a reservoir, by a syphon of small bore, the longer leg of which is seen at J, into the middle of what may be called a horizontal trough, supported like a balance by a fulcrum at K, in such a manner, that either end of the balance may be elevated accordingly as the long vessels A B and C D require to be alternately filled ; near the top of each of these vessels is inverted a long syphon or tantalus, l and m, the lower legs of which reach down to two small cylindrical vessels, n and o, which are poised by another balance at the fulcrum p ; these cylindrical vessels have, in like manner, each a small syphon, q and r ; lastly, a silken thread tied to the upper end of the cylinder, n, is carried up round a small pulley fast to the frame at s, and is fastened to the end of the trough under it, and a similar thread is fastened in like manner to the cylinder o, and end of the trough under the small pulley t. Now it is easy to conceive, that when the vessel A B, is filled to nearly the head of the tantalus l, the bore of which is larger than of the feeding syphon J, the water will be discharged into the cylindrical vase n, which consequently will preponderate, and by means of the silken chord elevate the end of the trough higher than the horizontal line, and make its opposite end under the small pulley, t, to be depressed, which will therefore conduct the water into the other long vessel C D ; during this action the counterpoise, F, rises, and its pulley, f, produces no effect on the ratchet by reason of the click, h, sliding over the sloping sides of its teeth, but the counterpoise, G, falls, and the click of its pulley (not seen) pushes the second ratchet forwards in the direction of the figures of the face I. II. III. &c.

When C D is nearly full, the long syphon m, begins to discharge its water ; makes the cylindrical vase, o, preponderate, and again elevates by means of its silken string the end of the trough under the small pulley t, and depresses the opposite end to fill the vessel A B, again, during which time the click, h, of the pulley, f, acts with its ratchet ; and thus the alternate increase and decrease of the water in the two vessels are continued without interruption, so long as the feeding syphon continues to supply a sufficient quantify of pure water. We think, however, that the mechanism is nearly as complex as that of a clock itself and consequently prefer a water-clock, such as that made by Perrault in the year 1699, where a pendulum is used as the regulator, and water only as the first mover. For the account, see "Machines Approuvées," tome i. p. 39.

The same Perrault also made a water-clock with a balance: and striking part, an account of which is given in, the vo!ume of "Machines Approuvées," which, we have just referred to; and in the seventh volume of the same work, is a description of a regulator going by water, invented by Peronnier, and improved by Le Roy, the son, in 1746.

CLEPSYDRA is also used for an hour-glass of sand. CLEPSYDRA is also applied to a chemical vessel perforated in the same manner.