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Art. 28. The pressure of the atmosphere. 29. Correction for
temperature. 30. Relation between the pressure and volume of air.
31. Ratio of the pressure to the density at 0°. 32. Ratio of the
pressure to the density at any temperature. 33. Heat developed
by compression. 34. Surface of equal pressure a horizontal plane.
35. The difference of the altitudes of two stations determined by
the barometer. 36. The same, taking into account the variation of
gravity. 37. Relation between the pressure and volume of vapour
and gases.

52. The

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the waste is not supplied. 62. The motion of a fluid in a tube. 63. The
motion of a small disturbance. 64. Integration of day a2 d2y.
65. The velocity of a small disturbance. 66. The velocity of sound.

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Art. 67. Definition of resistance. 68. The resistance on a plane
perpendicular to the stream. 69. The resistance on a plane exposed
obliquely to the stream. 70. The resistance on a cylindrical surface.
71. On a solid of revolution. 72. On a sphere.

Art. 73. Expansion by heat. 74. The thermometer.

graduation of a thermometer. 76. The standard points.

comparison of different scales. 78. The apparent expansion of

mercury in glass. 79. The cubic expansion of a solid is equal to

three times its linear expansion. 80. Bramah's press. 81. The

diving bell. 82. Space occupied by the air in it. 83. The syphon.

84. The common pump. 85. The height through which the water

rises at each stroke. 86. The range of the piston. 87. The range

in a pump of uniform diameter. 88. The forcing pump. 89. The

fire engine. 90. The condenser. 91. The density of the air in it.

92. The gauge. 93. Hawksbee's air pump. 94. The density of the

air in it. 95. Smeaton's air pump. 96. The receiver. Valves. 97. The

barometer gauge. 98. The syphon gauge. 99. The common ba-

rometer. 100. The comparison of the specific gravities of air and

water. 101. The weight of a given volume of water. 102. The

comparison of the specific gravities of a solid and of a fluid by

weighing the solid in air and in fluid. 103. When the weight of the

solid is less than the weight of the fluid displaced. 104. To compare

the specific gravities of two fluids by weighing the same solid in each.

105. By weighing equal volumes of each. 106. To compare the

specific gravity of a solid in fragments with that of a fluid. 107. The

common Hydrometer. 108. Sikes' Hydrometer. 109. Nicholson's

Hydrometer. 110. Meikle's Hydrometer. 111. Say's instrument

for measuring the volumes of small solids. 112. The Piezometer.

113. The Hydraulic Ram. 114. The Atmospheric Steam Engine.

115. Watts' double acting Steam Engine.

APPENDIX

P. 74.

Art. 116. Experimental proof that fluids press equally in all
directions. 117. Pressure on any surface. 118-140. Examples.
141. Daniell's barometric formula. 142. Pressure of steam. 143. Ex-
pansion of water by heat. 144. Table of densities.

ELEMENTS OF HYDROSTATICS.

SECTION I.

GENERAL PROPERTIES OF FLUIDS.

ART. 1. A FLUID is a body which can be divided in any direction, and whose parts can be moved among one another by any assignable force.

Elastic fluids are those whose dimensions are increased or diminished when the pressure upon them is diminished or increased. Non-elastic fluids are those whose dimensions are independent of the pressure.

Water, mercury, and probably all other liquids, are in a small degree compressible. Their resistance however to compression is so great, that the conclusions obtained on the supposition of their being, incompressible, are in most cases free from any sensible error.

2. Let DEF (fig. 1.) be a piston without weight exactly fitting an orifice in the plane ABC, which forms the side of a vessel containing fluid. It is manifest that the fluid can make no effort to move the piston in any other direction than that of a normal to its surface, the piston may therefore be kept at rest by a force applied at some point G in it, and acting in a direction HG perpendicular to DEF. A force equal and opposite to this is called the pressure of the fluid on DEF.

3. The pressure of a fluid at a given point is measured by the quantity p, pk being the pressure of the fluid on an indefinitely small area κ contiguous to the given point.

When the pressure of a fluid on a given surface is the same, wherever that surface is placed, p is the pressure on an unit of surface. When the pressure on a given surface, varies with the situation of the surface, p is the pressure which would be exerted on an unit of surface, if the pressure at each part of the unit of surface were equal to the pressure at the given point.

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4.

AXIOM. When a fluid is at rest, any portion of it may become solid without disturbing either its own equilibrium, or that of the surrounding fluid.

For as long as the fluid remains at rest, it makes no difference whether the parts of which it is composed, are moveable among one another, and capable of being divided in any direction, or not.

5. Fluids press equally in all directions.

Let Abc (fig. 2.) be a very small prism of fluid in the interior of a fluid at rest; then (Art. 4.) the equilibrium of A b c will not be disturbed, if we suppose it to become solid. Now if R be the accelerating force at A, Abc is kept at rest by the pressure of the surrounding fluid on its ends and sides, together with R. (mass prism) acting in the direction of the force at A. But if the prism remain similar to itself while its magnitude is diminished indefinitely, R. (mass prism) vanishes compared with the pressure on either of its sides; (for the former is proportional to 4 a3, the latter to A a;) and we may consider the prism to be kept at rest solely by the pressures on its ends and sides: and these pressures are respectively perpendicular and parallel to ABC, therefore they must be separately in equilibrium. And since the pressures on Ab, Ac, Cb are in equilibrium, and perpendicular to the sides AB, AC, CB of the triangle ABC, they are proportional to those sides; hence if p. Ab, q. Ac be the pressures on Ab, Ac respectively, p. Ab: q. Ac=AB: AC, therefore p=q. But p, q measure the pressures of the fluid at A perpendicular to Ab, Ac respectively, and Ab, Ac may taken perpendicular to any two given lines, therefore fluids press equally in all directions.

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COR. 1. Suppose the sides of the base of the prism to be indefinitely small compared with its length; then if the pressure on ABC be increased or diminished in any degree without disturbing the equilibrium of Abc, the pressure on abc must be equally increased or diminished. Hence if F, G, H...... M, N, P (fig. 3.) be any series of points in a fluid at rest, so taken that the straight lines FG, GH......MN, NP may be wholly within the fluid, and the pressure at F be increased or

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