count, from the centre of the drum, which would also be in its centre of gravity, if it were empty, on which account it would, in that case, revolve to the left, in the direction F G H downwards, from the cord being at the remote side of the centre, as represented by NO; but conceive the water to be included now and then, it would be elevated to the right, till its weight became a counterpoise to the gravity of the heavier side of the drum, in which situation all motion would cease, and the drum would remain, suspended, indeed, by the cords, but in a state of equilibrio. Conceive again a small hole perforated in the partition pressed upon by the water near the circumference of the large circle, and also at the points F, G, H, I, K, L, M, and the consequence will be, that the water will first force its way slowly through the perforation at K, from the more elevated to the lower compartment, which effect will diminish its power as a counterpoise, and give such an advantage to the heavy side, FGH, of the drum, considered as empty, as will occasion a small degree of motion towards the left, and consequently carry the water once more towards the right; but now the water passes through the perforation of the next partition also at I, and produces again the same effect as has been described with respect to K, and will continue to do so, at the successive perforations, till all the compartments have been filled and emptied by means of these perforations, in succession, which kind of motion of the drum, contrary to that of the water, it is now not difficult to conceive, will be pretty regular, if all the partitions are perforated exactly alike. The difference of the pressures of the water in cells, nearly full and nearly empty, will occasion some little deviation from regularity; but these will be periodic, and must be allowed for in the hour divisions, which ought to be made by a comparison of the spaces fallen through, with the time indicated by a clock or watch. About nine ounces of distilled water will suffice for a clepsydra of six inches diameter, and two inches depth, and the velocity of the fall may be limited, either by varying the quantity of water, or by hanging a small metallic cup F, to receive weights, by a cord wound in a direction contrary to the cords of suspension, to act as a counter poise in aid of the water, if the fall be too rapid, or vice versa. It is necessary that the arbor should fit the central square hole so well as to prevent the escape of water from the drum, otherwise the instrument would continue to gain velocity, till at length it would no longer afford a true indication of time.

Sometimes a cord, cd, with a weight, P, is made to pass round a pulley fixed to an arbor at the top of the frame, with a noose passing over the axis near u, as is seen in the same figure, which arbor, projecting through a dial-plate or face, turns round and carries a hand to indicate the hours like an ordinary clock; when this construction is preferred, it is an indispensable requisite that the circumference of the pulley's groove be exactly of the same dimensions as the fall of the drum in twelve or twenty-four hours, accordingly as the dial is divided. This clepsydra, it is said, goes faster in summer than in

winter, which is owing to the drum being relatively heavier in rarefied than in dense air; we can hardly suppose that any alteration in the fluidity of the water, as formerly imagined, would make any difference. The minute hand, and also the striking part of a common clock, might easily be superadded to this clepsydra.

Another, and more simple, form of the modern clepsydra is derived 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 twelve 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. Now if, instead of the vessel itself being divided by hourlines as above directed, the stem 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.

a parabola of the fourth degree, the method of describing which, he gives thus:-Let A BS, be a common parabola, the axis of which is PS, and the summit S. Draw, in any manner, the line, Rr T, parallel to that axis, and then draw any ordinate of the parabola A P, intersecting RT, in R; make PQ a mean proportional between PR and PA, and let pq be a mean proportional also between pr and pa; and so on. The curve passing through all the points Qq, &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 equalising the scale, so as to correspond to equal times while the water is running out. Mr. Varignon has given a geometrical and general me

thod of determining the scale for a clepsydra, whatever may be the shape and magnitude of the vessel. (See Memoires de l'Academie Royale des Sciences, p. 78, 1699.)

A still more simple water-clock with equidistant hour-lines, in any regular vessel, is constructed 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.

We conclude with extracting the construction and action of a clepsydra, published in the 44th volume of the Philosophical Transactions by the Hon. 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 4, which shows only the interior mechanism; ab and c d are two columns of wood so floating in water that their counterpoises, F and G, just keep their 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 slips 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,, 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 dialplate; 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 CD require to be alternately filled; near the top of each of these vessels is inserted a long syphon or tantalus, 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 fastened to the end of the trough under it, and 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 cord 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 CD; during this action the counterpoise, F, rises, and its pulley, f, produces no effect on the ratchet by reason of the click, hy 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 CD 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 quantity of pure water.

CLERC (George le), count de Buffon. See BUFFON.