HYDROSTATIC*. 



HVDROTHORAX. 



expre** the weight in avoirdupois ounce* : thtu the weight o{ a cubic 

 foot of rain water being 1000 ounce*, and that of a cubic foot of ca*t- 

 iroo being 7207 ounce*, those number* are used to denote the specific 

 gravities of the bodies. From thi* definition it follow* that, wlu-n flu- 

 volume* of two bodie* are equal, their specific graTitie* will be pro- 

 portional to their weight* : when the weight* are equal, the specific 

 graritie* are invenely proportional to the volume* ; and, in general, 

 the weight* of bodie* vary in a ratio compounded of their volume* and 

 pacific graTitie*. 



It may hence be cosily ahown that when two fluids uf different 

 specific gravitie*, a* water and mercury, are in equilibrio jn a bent 

 tube, the vertical altitude* of the columns above the horizontal plane 

 <>f junction will be invenely proportional to their specific gravitie*. 

 For, let M (Jig. 3) be a line in the plane of junction ; then the area of 

 the section at in being common to both fluids, the baae* of the columns 

 in the two branches may be considered a* equal to one another. Now, 

 if the vertical altitude of the column m p be represented by a, and 

 that of 7 by A, the specific gravity of the fluid in m p by 8, and that 

 in 9 by ; then the weights of the columns, or rather the pressures 

 on every point of their base*, at and n may be expressed by a 8 and 

 A i ; and in the case of equilibrium these terms ore equal to one 

 another : therefore we have A : a : : s : t. 



The specific gravity of a solid body is readily found by means of the 

 hydroctatical balance, an instrument which differs in no respect from a 

 common balance, except in being made with greater delicacy. It is 

 customary to weigh the body both in air and in vacua ; from whence 

 may be obtained the ratio between the density of the body and that of 

 the fluid in which it is weighed. [SPECIFIC GRAVITY.] 



The specific gravity of a fluid may be found from the following 

 proposition : let a + 4 be the volume of a body which will float in the 

 fluid, b being that of the immersed part ; let also the specific gravities 

 of the body and fluid be represented by < and ' respectively. We 

 have then the weight of the body = (o+o) >, and that of the displaced 

 fluid = 61'; but these weights ore equal to one another: therefore, 

 A : (a + 6) :::'. Consequently, the specific gravity of the solid 

 body being supposed to be known, we have that of the fluid, after 

 making a correction on account of the loss of weight in air. On the 

 principle explained in this proposition is founded the construction of 

 the HYDROMETER, by which the qualities of liquors are usually deter- 

 mined. 



By mean* of the specific gravity of bodies may be ascertained the 

 quantities of the different materials which enter into any compound 

 body. Thus, let a and vt represent the weight* of a mixed metal in 

 air, or vacuo, and water respectively, * and ' the known specific 

 gravitie* of the two metal* in the mixture, and let x be the weight 



in air or vacuo of the heavier metal. Then - - the weight of water 



which would be displaced by x 



the weight which would 





 be displaced by the lighter metal ; and we shall have / = - + j- ; 



- p ', and tc x ( = the weight of the lighter 



whence * 



It ha* been shown that the pressure of a fluid against any point in 

 an upright wall, or in the side of a vessel containing it, is proportional 

 to the depth of that point below the upper surface of the fluid ; but, 

 in determining the form and dimensions of a retaining wall which shall 

 be equally strong in every part of it* height, it will be necessary to 

 consider that the horizontal pressure of the fluid at any point, as a 

 (At- 4) (B A E representing a vertical section through such a wall), tends 



Fl. 4. 



to overturn or fracture the wall at every other jioiiit, M . . Now, let 

 Bo=x, and let the depth of an elementary portion of the wall t a be 

 represented by rfj; then, if BC be represented by 6, we shall have 

 c = o x, and (6 f) xdx will expre** the force of the water on an 

 deoMOUry area at a to turn the wall about c : consequently, /(6-x) 



f <l -r, between x= o and x= 6, will express the sum of all the force* of 

 the water above c to turn the wall about the latter point. But the 

 integral between those limits is equal to > 6* : therefore the tendency 

 of the fluid to fracture the wall at any point, as c, is proportional to 

 the cube of the distance of that point from the upper surface of the 

 fluid. The strength of the wall to resist transverse pressure in the 

 direction of it* thickness is, by mechanics, proportional to the square 

 of that thickness ; that is, proportional to c n*. Therefore, in order 

 that the wall may be equally strong in every part, the form of a vertical 

 section should be such that the squares of the horizontal ordinates, as 

 c D, are proportional to the cubes of their vertical depths from the top. 

 This is a property of the semi-cubical parabola, and the exterior or 

 interior surface of the wall should have that figure. Agreeably to this 

 principle also the thickness of tube* containing columns of fluid in 

 vertical positions should increase from top to bottom, according to the 

 same law. 



This article may be concluded by an indication of the principles on 

 which the stability of ships or other vessels on the water may be 

 determined. 



Let ABC (fy. 5) represent a vertical section through the centre of 



Fig. S. 



gravity G of a ship, and let M i > 1 n- the surface of the water ; let also g 

 be the centre of gravity of the immersed part, while the plane of the 

 masts is vertical. Now, by the action of the wind or otherwise, let the 

 ship be inclined so as to take the position a 6 c ; the centre of gravity 

 of the immersed part and of the displaced water will then be removed 

 to h, and that of the ship to o'. Draw a vertical line through h, and 

 let fall upon it the perpendicular o'k; then the stability of the vessel, 

 or the force by which it resist* the effort of the wind to overturn it, 

 is expressed by the product of the upward pressure of the wat 

 the weight of the vessel) acting in the vertical line k h into the length 

 c'i of the lever, whose fulcrum is c;'. And, that an equilibrium may 

 subsist, this expression must be at least equal to the product of the 

 force of the wind acting against the sails or hull into the distance of 

 the centre of pressure, or melactntrt, from the centre of gravity of the 

 ship. 



Hence it is, that the keel and bottom of a vessel must be made so 

 much stronger, the deeper the vessel sinks. Suppose a vessel sink* 

 16J feet when loaded ; then the bottom must be able to resist a pres- 

 sure of 74 Ibs. on the square inch, that is, the weight of a cylinder of 

 water 16) feet long, and 1 inch in section. Hence, if a leak should 

 spring in such a vessel, a weight of TJ Iba. per square inch would l>c 

 required, to keep a plank, thrown across the hole, from being forced 

 upwards. 



IIVDHOSULPHOCYANICACID. [CTAKO<;I.N.| 

 IIYimoSI'Ll'HriiK' \< IH. S. i i iii i: : >. ./,./,,. ,*,,/ //,/,/, ,,/,,.. I 

 HYDROTHIONIC ACID. Synonymous with Sulphuretted //./ 

 ilroyen. |Sri.rnrn.l 



HVIilliiTHO'RAX (from CSttp, water, and Mfa(, the chest), dropsy 

 of the chest, is a term applied to express the existence of a collection 

 of serous fluid in the cavity of the pleura. 



Thin collection may take place in consequence of inflammation of the 

 pleura, which, like inflammation of other serous membranes, terminates 

 in effusion ; or it may result from the causes of general dropsy, 

 namely, some obstacle to the circulation through the heart, or organic 

 disease of the kidney. When it, arises from the former cause it is 

 merely a symptom of pleurisy. Iii some cases of pleurisy, however, in 

 which pain is absent, and in which fever does not exist, or in xlight, 

 this effusion and the difficulty of breathing to which it gives rise con- 

 stitute almost the only symptoms of the disease. Abundant effusions 

 of this kind, unattended by pain or fever, sometimes take place very 

 rapidly, especially in old perrons and in adults in a cachectic condition. 



