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Ancient Clepsydrae.--According to M. Vitruvius Pollio, the first improver of the ancient clepsydra, or water-clock, was Ctesibius of Alexandria, the son of a barber, who, about 245 years before Christ, spent much time in devising mechanical contrivances for removing not only the obstacle in question, but also another equally formidable one, which arose from the daily inequality of the Egyptian hours. As one-twelfth part of the time elapsed from sun-rise to sun setting on any day, was called an hour of that day ; and as one-twelfth part of the time that passed from full setting to sun-rise was called an hour of the night; not only did the hours of day differ from the hours of night, but from one another, at all times, except at the vernal and autumnal equinoxes ; hence it became necessary, either to make the water fall irregularly into a receiving vessel, with equidistant hour-marks, or to have varying hour-marks for a regular efflux ; the first of these methods (which probably preceded that of Ctesibius) was thus effected, viz. 1. A conical hollow vessel, A, was inverted, or placed like a funnel in a frame C C (Plate I. fig. 1. of Horology)
there being a very small aperture at the apex of the cone, and another solid cone, B, every way similar as to dimensions, was plunged into the hollow one when filled with water to a greater or a smaller depth, accordingly as the efflux was wanted to be more or less rapid, and then adjusting marks, corresponding to every day and night in the year, were put on a long Item D, inserted into the broad end of the solid cone B, and kept in its position by the frame, as represented in the figure, to show how much the inner cone was to be depressed or elevated, to accelerate or retard the issue of the fluid for the corresponding time ; H was the spout which supplied a constant influx of water, and I the waste pipe, connected with the top of the conical vessel, which carried off the superfluous water ; hence the constant influx of water preserved an unvarying height of the surface from the aperture, which aperture was varied at pleasure, by the elevation or depression of the inner cone ; if now we suppose the subjacent vessel to be a cube, cylinder ; or any other regular figure, and equidistant hour-marks to be properly made on its side, the surface of the water or an index borne by it on a piece of cork, would, as it rose, indicate the hours corresponding to those marks.
The imperfections of this clepsydra were these :
Fig. 2. of Plate I. represents an ancient clepsydra with an horary circle and a variable aperture : A is a reservoir, to the top of which is attached a water-pipe, not seen in the drawing, to preserve an equal pressure by carrying off the superfluous water ; B is a pipe projecting from the reservoir into the upper part of the drum, M N, on the front of which drum the ecliptic circle is marked ; O D L is a smaller inner drum, which revolves on a tubed arbor, F, and which is represented as drawn out of its place ; this small drum has a thorough groove, a b varying in breadth all round it, like a hoop tapering throughout from the broadest part both ways to its opposite point, and is of such a diameter that the middle of the groove just reaches to, and coincides with, a perforation under the tube, B, at the upper part of the great drum, so that, as the little drum, which carries the diurnal index, L, and nocturnal index, O, opposite to the former, is turned round by hand, the variation in the breadth of the groove occasions a corresponding variation in the velocity of the efflux of water, by making a larger or smaller aperture, accordingly as the sun's place is more or less advanced in the ecliptic, the largest aperture being when the diurnal index is at the beginning of Capricorn ; a little bason or funnel attached to the upper part of the fixed tube or hollow arbor, F, (not visible), receives the water in its fall within the drum, and transmits it through the said tube by G into the receiving vessel, H, in which is floated the piece of cork, I ; this floating-piece is connected, by a chain, with the counterpoise, K, after it is folded round the arbor, P, which carries the hour-hand of the dial-plate ; consequently, as the water rises in the vessel, H, the piece, I, is raised, and its counterpoise, K, at the same time falling gives motion to the arbor and hour-hand, and the hours are longer or shorter according to the breadth of the groove which is at any time under the perforation of the tube, B, i. e. according to the place in the ecliptic to which the proper index is put. This clepsydra, like the preceding one, composed of two cones, requires two manual adjustments, one in the morning and the other in the evening, and makes no allowance for the (supposed) variation of fluidity occasioned by the different states of the weather ; and the variation in the breadth of the groove or slit, it is presumed, was more plausible in theory, than feasible in practice ; the contrivance, however, was ingenious, and bespoke the inventor's acquaintance with astronomy.
which, according to Perrault and Ferd. Berthoud, exhibits the interior construction of this machine ; A is the end of a tube over which an image stands, which is connected with a full reservoir, and from the eyes of which, considered as invariable apertures, the water continually flows or drops in a regulated manner into it ; this tube conveys the water from M towards B into the top of a long regular vessel, B C D F, which it gradually fills, and raises the cork, D, with its attached light pillar, C D ; on the top of this pillar is surmounted another image holding an index which points to the divisions on the large column above. Now, when the water rises in the vessel that contains the cork, it also rises in the small tube, F B, which constitutes one leg of a syphon, F B E, that is connected with the bottom of the cubic vessel ; consequently, when the index has mounted to the uppermost division on the large column of hour lines, consulting of twice twelve, the water flows over the bent part, B, of the syphon, and, immediately empties the vessel into one of the six troughs or divisions of the water-wheel, K, which is thus turned one-sixth part of a revolution, during which time the image falls with its index to the bottom of the column, to be ready for the next day. This portion of the mechanism would have been sufficient to constitute the machine, if the hours had been considered as of equal length throughout the year, but the Egyptian mode of dividing and reckoning time made it requisite that the hour lines should slope out of an horizontal direction on the surface of the column, so as to make variable spaces, and also that the column should revolve once in a year, to present all the variations of space to the index. This annual motion of the column is said to be effected by wheel-work in the following manner:¾on the arbor of the water-wheel, K, is fixed the pinion, N, of six leaves, which impels the contrate-wheel I, of 60 teeth in 6 x 60/6 = 60 days, then on the perpendicular arbor of I is another pinion, H, of ten leaves, which drives the wheel, G, of 61 teeth round in 60 x 61/6 = 366 days, and along with it the horary column, into which its arbor is inserted at L. On the bottom of the column is marked an ecliptic circle ; and 12 perpendicular lines drawn lengthwise down the column divide it it into the respective signs, which are serviceable for ascertaining the requisite slope of the hour lines in any month. The writer of this article, however, suspects, that the above train of wheel-work is only what Perrault, the translator of Vitruvius, supposed to be that of Ctesibius; for, on referring to the original account of Vitruvius, the year in which the column revolved is stated to be 365 days, a period which might be effected thus : Let the water-wheel have only five compartments instead of six, and let an endless screw be cut on its arbor to impel a wheel of 73 teeth, with a perpendicular arbor, to be inserted into the column of hours, which will, by such a simple construction, revolve in 5 x 73/1 = 365 days, agreeably to the original account. The clepsydra, in one of its earlier forms, was used as an astronomical instrument, by the help of which the equator was divided into twelve equal parts, before the mathematical division of a circle was understood ; it was deemed of more value than a sun-dial, on account of its dividing the hours of the night as well as of the day. It was introduced into Greece by Plato, and into Rome by P. Cornelius Scipio Nasica, about 157 years before Christ. Pliny says (lib. xxxvii.) that Pompey brought a valuable one among his spoils from the Eastern nations ; and Caesar is said to have met with an instrument of this kind in England, by the help of which he observed that the summer nights his of this climate are shorter than they are in Italy. The life which Pompey made of his instrument was to limit the speeches of the Roman orators ; which Cicero alludes to when he says "latrare ad clepsydram."
Besides the ancient clepsydra, above described, F. Berthoud mentions
another (Histoire de la Mesure du Temps, tom. I. p. 20.), which was called
the anaphoric, on the dial-plate of which were projected the circles of
the sphere, including the parallels of the sun's altitude, with the
semi-diurnal and semi-nocturnal arcs, to which an adjustable bead, as the
sun's representative, pointed as an index to shew the hours, parallels,
&c. as the dial-plate revolved daily by means of wheel-work, which was
impelled by water. It does not seem certain at what period this instrument
was invented and used ; but Berthoud thinks that tables of the sun's
motion must have existed previously to its invention, and also a knowledge
of projections of the sphere on a plane surface, whence he fixes the date
posterior, to the time of Hipparchus, who, according to Pliny, died about
125 years B.C. The name anaphoric derived from anaphora, which was the
second house in the heavens, according to the doctrine of astrology, which
prevailed about the time here specified. The anecdote in Athenaeus concerning the mechanical amusements of the great ideal philosopher, is curious. What a condescenslon in the divine Plato to stoop to the invention of any thing useful ! This musical clock must have been wholly played by mechanism. In describing it, Athenaeus says, it resembled in appearance a round altar ; but was not to be ranked with stringed but wind instruments, composed of pipes ; the orifices of which being towards the water, when it was agitated, produced from the pipes, by its fall, a soft and pleasing sound. Modern Clepsydra.--The modern method of dividing the natural day into 24 solar hours of equal length, has rendered the preceding constructions of the clepsydra useless for some centuries back ; and, notwithstanding the science of hydrostatics is much better understood by the modern than it was by the ancient philosopher, to that a scale of altitudes corresponding to the variable velocities of the efflux of a fluid out of a given aperture can be ascertained by calculation for a containing vessel of any capacity or figure, yet, since the happy inventions of the balance and pendulum, as regulators of watches and clocks, horological machines, actuated by the motion of water, have become so rare, as to be considered as objects only of curiosity. Beckmann, in his "History of Inventions," vol. i p. 136, attributes the contrivance and introduction of a water-clock to some time between 1643 and 1663, and gives nearly the same brief account of one as we meet with in " Bion, or Mathematical Instruments," and also in "Ozanam's Recreations," edited by Dr. Hutton, the last of which authors said, in the year 1693, that the first water-clock brought to Paris about that time was from Burgundy. He also says, that father Timothy, a Barnabite, had given the machine all the excellence it was capable of, by constructing it so as to make it go a month at one winding up, and to exhibit not only the hours on a dial-plate, but also the sun's place, day of the month, and festivals throughout the year.
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In fig. 1, of Plate I I. of Horology, A B C D is an oblong frame of wood, to the upper part of which two cords, A a and B b, are fixed at their superior extremities, and at their inferior, to the metallic arbor, a b, of the drum, E, which contains distilled water ; this water is confined in cells so peculiarly constructed, that they regulate the velocity with which the drum shall descend by the force of gravity from the top to tile bottom of the frame, and the ends of the arbor indicate the hours marked on the vertical plane of the frame during the time of descent. An observer, who knows not the nature of the interior cells of the drum, is surprised to see that its weight does not make it run down rapidly, when mounted to the top of the frame by merely folding the strings round the arbor, there being, apparently no mechanical impediment to the natural action of gravity.
To explain how this phenomenon is produced, we must refer to fig. 2, which is a section of the drum at right angles to its arbor ; this circular plane we will suppose to be six inches, which is about the usual size, in diameter, and to represent the inner surface of either of the two ends of the drum, which may be made of any of the unoxidable metals ; then, if we conceive seven metallic partitions, F f, G g, H h, I i, K k, L l, and M m, to be closely soldered to both ends of the drum, in the sloping direction indicated by the figure, where the black lines are equidistant tangents to the small dotted circle of an inch and half diameter at the points f, g, h, &c. ; it is evident, that any small quantity of water introduced into the drum would fall into two, or at most three, of the lower compartments, and would remain there until some external force should alter the position of the drum, supposing in this case the cords tied fast to the arbor ; but we have said that they are wound round the circumference of an arbor, that has a sensible diameter, suppose one-eighth of an inch ; therefore, they are removed one-sixteenth of an inch, or upwards if we take their thickness into the account, from the centre of the drum, which would also be 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 N O ; 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 this drum, in which situation all motion would cease, and the drum would remain, suspended, indeed, by the cords, but in 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, F G H, 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 counterpoise in aid of the water, if the fall be too rapid, or vice versa. It is absolutely 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 Ionger afford a true indication of time. Sometimes a cord, c d, 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 a, 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 12 or 24 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 supposed, would make any difference. The minute hand and also the striking part of a common clock might easily be superadded to this clepsydra. 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. (See page 335.) CLEPSYDRA is also used for an hour-glass of sand. CLEPSYDRA is also applied to a chemical vessel perforated in the same manner.
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