full of fluid, and have over every part of the sides and bottom a perpendicular column of the fluid reaching to the surface, the whole vertical pressure of the fluid upon the bottom and sides of that vessel will be equal to the weight of the whole fluid.

II. That if a body, as AEDBM, (fig. 7. pl. 88.) of which AIBF is the greatest horizontal section, is immersed in a fluid to any depth whatever, and if we drop the consideration of the pressure sustained by the upper part AMB, the vertical effort of the fluid to raise the body is equal to the weight of the volume of fluid which is comprised between the surface A' D', the surface AIBFE, and the convex surface formed by perpendiculars let fall from all the points of the perimeter AIBF upon the plane A' D'; that is equal to the sum of the weights of fluid in the prism a i bƒ AIBF, and the space AIBFCE.

III. If we would now estimate the pressure sustained by the superior surface AMBFI of the body, we shall see, by the same kind of reasoning, that the result in the vertical direction, tending to force the body down wards, is an effort equal to the weight of the volume comprised between the horizontal projection aibf, and the upper surface AMBFI of the body. If, then, from the first of these efforts we deduct the second, it will appear that the body is pushed vertically upwards, with an effort equal to the weight of a volume of the fluid equal to that of the body immersed. We conclude therefore, that if a body is immersed in any fluid whatever, it will lose (relatively) as much of its weight as is equal to the weight of the quantity of fluid it displaces.

IV. With regard to the resultant of all the vertical forces whose magnitude we have just determined, it is easy to see that it must pass through the centre of gravity of the volume of fluid displaced. For, if we conceive this volume decomposed into an infinite number of evanescent vertical filaments, the effort made by the fluid to push each filament vertically will be expressed by the weight of a quantity of fluid equal to that filament. Therefore, to obtain the distance of the resultant from any vertical plane whatever, we must multiply the mass of each filament (considered as of the same nature with the fluid) by its distance from this plane, and divide the sum of the products by the sum of the filaments; which is precisely the rule that must be followed to find the centre of gravity of the volume displaced. Therefore, universally, a body immersed either wholly or in part in a heavy fluid, and at rest, receives from the fluid pressares which are together equivalent to a vertical force directed upwards through the centre of gravity of the fluid displaced by the body, and equal to the weight of a quantity of the fluid so displaced by the immersed part of the body.

Indeed, we may readily assign a reason, à

priori, of this; for, supposing a force acting on a body without heaviness retains it in equilibrio when immersed either wholly or partly in a heavy fluid: if we substitute for the immersed part of the body, that is, for the fluid it displaces, an equal and similar portion of the same fluid become solid (as ice, and the density unchanged), the equilibrium will still obviously subsist; consequently, the pressure of the fluid upon the immersed body will be altogether equal, and directly opposed to the weight of this solid; and must, therefore, pass through its centre of gravity, in order to sustain it in equilibrium.

V. It now remains for us to consider how the horizontal forces are disposed of. If we take any one of the horizontal laminæ into which either the fluid, or the solid immersed in the fluid, may be imagined to be divided, and through the sides a b, bc, cd, &c. (fig. 6. pl. 88.) of the inferior section conceive vertical planes to pass, and to be terminated by the superior section; these planes will form the contour of a prism whose height is that of the lamina, and each face of the prism will have (1) the measure of its surface proportional to the value of the hori zontal force to which it is perpendicular. But, as all these faces are of the same altitude, their surfaces are proportional to their bases a b, bc, &c. and consequently, the horizontal forces are respectively in the ratio of the sides a b, bc, &c. And as the altitudes of these faces are evanescent, we may regard all these forces as applied in the same horizontal plane a be def, and to be each respectively proportional to the length of the side, on the middle of which it acts perpendicularly. Now it has been shown, that if any number of forces represented in magnitude and direction by the sides of a polygon taken in order, act simultaneously upon the same point, they will be mutually destroyed, and the point continue at rest: also, that when any number of forces are in equilibrio, when applied to different points of a body, they are the same as would be in equilibrio about a single point; and, since the directions of the several forces P, P' P", &c. in the present case would, if produced, form a polygon similar to a bed ef, the consequences just referred to will apply to them likewise: and, in like manner, to the pressures upon any other horizontal lamina. Consequently, the efforts which result in the horizontal direction, from the pressure of a heavy fluid upon the surface of any body immersed in it, are mutually destroyed.

Scholium. From the preceding doctrine of the pressure of fluids, an important practical maxim may be deduced. We have seen that in any vessel containing a heavy fluid, the parts that are deepest below the surface sustain a proportionally greater pressure. If, therefore, we have, to construct an assemblage of vertical pipes or

tubes, to elevate water or any other fluid, we may run into a superfluous expense, by giving the same thickness to the material in every part. For, if the substance be uniformly thick, and the lower parts are sufficiently strong, the upper parts are, of consequence, much thicker than necessary. The method suggested by theory is, while we give to the whole assemblage the same interior diameter, to give a safe and sufficient thickness to the material at the lowest part, and let it gradually diminish to the top, in the same ratio nearly as the diminution in the depth of the fluid. The same maxim may also find an application in the construction of sluice-gates, dams, banks, &c. And in all such cases it is advisable to determine, first, the adequate strength to resist the pressure at the greatest depth; as, by this means, safety may always be insured without any waste of materials.

A few more general observations will conclude this article.

There exist two states of equilibrium perfectly distinct. In one, if the equilibrium be ever so little deranged, the bodies which compose the system only oscillate about their primitive position; and then the equilibrium is stable. This stability is absolute, if it obtains whatever be the oscillations of the system; it is relative, if it obtain only with respect to oscillations of a certain kind. In the other state of equilibrium, bodies deviate more and more from their primitive position when once they have removed from it. We may derive a correct idea of these two states, by contemplating an ellipse placed vertically on a horizontal plane. When the ellipse is equilibrated upon its minor axis, it is obvious, that if it be drawn a little from that situation, it will tend to return to it, making oscillations which friction and the resistance of the air will soon annihilate but if the ellipse be in equilibrium upon its major axis, when once drawn from that situation, it will tend to deviate still farther, and terminate by adjusting itself upon its minor axis. The stability of equilibrium depends, therefore, on the nature of the minute oscillations which the system, any way disturbed, will make about that state. Frequently, this kind of inquiry presents many difficulties; but in several cases, and especially in that of floating bodies, to judge of the stability of the equilibrium, it will suffice to know, whether the force which solicits the system a little deranged from that state, tends to bring it back thither again. We shall attain this with regard to bodies floating on water, by the following rule.

If, through the centre of gravity of the plane of floatation (or section level with the water) of a floating body, we imagine a horizontal axis, drawn so that the sum of the products of each element of the section, into the square of its distance from that axis,

shall be less than relatively to any other horizontal axis drawn through the same centre; the equilibrium is stable in every direc tion when that sum exceeds the product of the volume of fluid displaced into the height of the centre of gravity of the body, above the centre of gravity of that volume. This rule is especially useful in the construction of vessels, to which it is proper to give a stability sufficient to furnish resistance to the efforts of tempestuous winds and swells. In a vessel, the axis drawn from the poop to the prow, is that with respect to which the sum in question is a minimum; it is therefore easy to know, and even to measure, the stability, by the preceding rule.

Two fluids contained in a vessel, dispose themselves in such a manner that the heaviest occupies the bottom of the vessel, and that the surface which separates them is hori

zontal.

If two fluids communicate by means of curved tube, the surface which separates them in the state of equilibrium is horizontal, and their heights above that surface are reciprocally as their respective densities. Supposing, therefore, the density of the whole atmosphere to be the same as it is near the earth at the temperature of freezing water, the height of such atmosphere would be about 54 miles; but since the densities of the atmospheric strata diminish as they are elevated farther above the earth's surface, the height of the real atmosphere is considerably greater.

To sketch the general laws of the equilibrium of a fluid mass solicited by any forces whatever, we shall observe that each point of the interior of that mass experiences a pressure which, in the atmosphere, would be measured by the barometer, and which may be ascertained in a similar manner for any other fluid. Considering each molecule as an indefinitely small rectangular parallelopiped, the pressure of the surrounding fluid will be perpendicular to the faces of that parallelopiped which tends to move itself perpendicularly to each face, in virtue of the difference of the pressures which the fluid exerts upon the two opposite faces. From these differences of pressures result three forces respectively perpendicular, which must be combined with the other forces that solicit the fluid molecule. Thus, that molecule will come to be in equilibrium in virtue of all the forces; the principle of virtual velocities will give the general equa tions of its equilibrium, whatever be its position in the entire mass. The conditions of integral ability of these differential equations will make known the relations which ought to subsist between the forces by which the fluid is actuated, to render the equilibrium possible: their integration will give the pressure that each fluid molecule experiences; and, if the fluid be compress ible, that pressure will determine its elasti

crystallised form by Vanquelin. The crys tals are transparent and colourless, having the figure of four-sided prisms terminated by quadrangular pyramids, and sometimes of octahedrons. The taste of this hydrosul phuret is extremely bitter: it is very soluble in water and alcohol, producing cold; it deliquesces on exposure to the air, and is decomposed by acids.

Hydrosulphuret of Zinc may be formed by treating the white oxyd of that metal with hydrosulphuret of aminonia; or by the precipitation of zinc from its solution in an acid, by means of the hydrosulphuret of potash or ammonia.

The other hydrosulphurets either have not been much examined, or have been found to differ very little from the common properties of the preceding.

In the composition of the articles which relate to hydrogen and its combinations, recourse has been had to the writings of Thomson, Davy, Lavoisier, Fourcroy, Kirwan, Accum, Parkes, the Journals of Nicholson and Tilloch, &c.

HYDROSULPHURETUM STIBI RUBRUM. Kermes mineralis. This sulphuret of antimony was formerly in high estimation as an expectorant, sudorific, and antispasmodic, in difficult respiration, rheumatism, diseases of the skin and glands.

HYDROTHO'RAX, (hydrothorax, acis, m., from dug, water, and wea, the chest.) Hydrops thoracis. Hydrops pectoris. A genus of disease in the class cachexia, and order intumescentiae of Cullen, known by dyspnea, paleness of face, oedematous swelling of the legs, scarcity of urine, impatience of a horizontal situation, a sense of weight and tightness across the chest, sudden startings from sleep, and palpitations of

the heart.

HYDROTIC, phlegm.

HYDRU'NTUM, in ancient geography, a noble and commodious port of Calabria, from which there was a shorter passage to Apollonia (Pliny). Famous for its antiquity, and for the fidelity and bravery of its inhabitants. Now Otranto, a city of Naples.

HYDRUS, in astronomy, the male hydra, a small southern consteliation, containing 10 stars, viz. 0. 0. 1. 1. 4. 4.

HYE/MANTES, in the primitive church, offenders who had been guilty of such enormities, that they were not allowed to enter the porch of the churches with the other penitents, but were obliged to stand without, exposed to all the inclemency of the weather.

HYE'NA. See HYENA. HYGEIA, (vyuα, from vymns, sound.) Sound health of body and mind.

HYGEIA, the goddess of health, daughter of Esculapius, held in great veneration among the ancients. According to some authors, Hygeia is the same as Minerva.

HYGIE/NE (Hygiene, es, f.

from

vy, to be well). Modern physicians have applied this term to that division of therapia which treats of the diet of the sick, and the non-naturals.

HYGRO'LOG (Hydrologia, æ, f. vyoɔdoyle, from ʊy, a humour or fluid, and Aoyos, a dis. course). The doctrine of the fluids.

HYGRO'MA (Hygroma, atis, n. vygwμa, from vypos, a liquid). An encysted tumour, whose contents are either serum or a fluid like lymph. It sometimes happens that these tumours are filled with hydatids. Hy. gromatous tumours require the removal of the cyst, or the destruction of its secreting surface.

HYGROMETER (from bygos, a liquid, and law), an instrument used to measure the degrees of dryness or moisture of the atmosphere, in like manner as the barometer and thermometer measure the dif ferent degrees of its heaviness and its warmth.

There are various kinds of hygrometers; for whatever body either swells or shrinks, by dryness or moisture, is capable of being formed into an hygrometer. Such are woods of most kinds, particularly ash, deal, poplar, &c. Such also is catgut, the beard of a wild oat, &c.

All bodies that are susceptible of imbibing water, have a greater or less disposition to unite themselves with that fluid by the effect of an attraction similar to chynical affinity. If we plunge into water several of these bodies, such as wood, a sponge, paper, &c. they will appropriate to themselves a quantity of that liquid, which will vary with the bodies respectively; and, as in proportion as they tend towards the point of saturation, their affinity for the water continues to diminish, when those which have most powerfully attracted the water, have arrived at the point, where their at tractive force is found solely equal to that of the body, which acted most feebly upon the same liquid, there will be established a species of equilibrium between all those bodies, in such manner, that at this term the imbibing will be stopped. If there be brought into contact two wetted or soaked bodies, whose affinities for water are not in equilibrio, that whose affinity is the weakest, will yield of its fluid to the other, until the equilibrium is established; and it is in this disposition of a body to moisten another body that touches it, that what is called humidity properly consists. Of all bodies, the air is that of which we are most interested to know the different degrees of hu midity, and it is also towards the means of procuring this knowledge, that philosophers have principally directed their researches; hence the various kinds of instruments that have been contrived to measure the humidity of the air. A multitude of bodies are known in which the humidity, in propor