out to a height which depends on the difference between the levels of the outcrop and of the point at which the perforation is made. The waters which feed Artesian wells often come from a distance of sixty or seventy miles. The depth varies in different places. The well at Grenelle is 1,800 feet deep; it gives 656 gallons of water in a minute, and is one of the deepest and most abundant which has been made. The temperature of the water is 27° C. It follows from the law of the increase of temperature with the increasing depth below the surface of the ground, that, if this well were 210 feet deeper, the water would have all the year round a temperature of 32° C., that is, the ordinary temperature of warm baths.

CHAPTER III.

PRESSURES SUPPORTED BY BODIES IMMERSED IN LIQUIDS. SPECIFIC GRAVITIES. AREOMETERS.

94. Pressure supported by a body immersed in a liquid.When a solid is immersed in a liquid, it is obvious that the pressures which the sides of the vessel support are also exerted against the surface of the body immersed, since liquids transmit pressure in all directions (75). But it is readily seen that the pressures which the

Fig. 74.

immersed body supports do not neutralise themselves, but have a resultant, the tendency of which is to move the body upwards.

Let us imagine a cube immersed in a mass of water (fig. 74), and that four of its edges are vertical. The horizontal pressures upon the two opposite faces, a and b, are clearly of the same intensity, for they are exerted at the same depth (77); and as they are in opposite directions they will balance one another, and the only effect will be to compress the body without displacing it.

But the vertical pressures on the faces d and c are obviously unequal. The first is pressed downwards by a column of water whose

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Hydrostatic Balance.

83

base is the face d, and whose height is dn, the lower face c is pressed upwards by the weight of a column of water whose base is the face itself, and whose height is cn. The cube, therefore, is urged upwards by a force equal to the difference between these two pressures, which latter is manifestly equal to the weight of a column of water having the same base and the same height as this cube. By this reasoning, therefore, we arrive at the remarkable principle, that any body immersed in a liquid is pressed upwards by a pressure equal to the weight of the volume of liquid which it displaces. We shall see how this principle can be experimentally verified.

95. Principle of Archimedes. Hydrostatic balance.-We have thus seen that any body immersed in a liquid is submitted to the action of two forces-gravity which tends to make it sink, and

the buoyancy of the liquid which tends to raise it with a force equal to the weight of the liquid displaced. The body weighs less therefore than in air, and the diminution of its weight is exactly equal to the weight of the displaced liquid. The above principle may be

thus enunciated: that a body immersed in a liquid loses a part of its weight equal to the weight of the displaced liquid. For instance, suppose that a body which in air weighs 1,000 grains, when immersed in water displaces a cubic inch of water; it will now only weigh 1,000-252 = 748 grains (a cubic inch of water = 252 grains). This principle, which is remarkable for its numerous applications, is called the 'principle of Archimedes,' after the discoverer. It is shown experimentally by means of the hydrostatic balance (fig. 75). This is an ordinary balance, each pan of which is provided with a hook; the rod, c, slides in the hollow cylinder, d. The beam is supported on the rod, c, which can be fixed in any position by means of a screw, n. The beam being raised, a hollow brass cylinder, b, is suspended to one of the pans, and below this a solid cylinder, a, whose volume is exactly equal to the capacity of the first cylinder ; lastly, an equipoise is placed in the other pan. If now the hollow cylinder, a, be filled with water, the equilibrium is disturbed, but if at the same time the beam is lowered so that the solid cylinder becomes immersed in a vessel of water placed beneath it, the equilibrium will be restored. By being immersed in water, the cylinder a loses a part of its weight equal to that of the water in the cylinder b. Now as the capacity of the cylinder a is exactly the same as that of the cylinder b, the principle which has been laid down is proved.

It is stated that Archimedes discovered this principle on the occasion of a problem which had been propounded to him by Hiero, tyrant of Syracuse. This prince, desiring to offer to Jupiter a gold crown, had furnished a goldsmith with ten pounds of gold as the material for this purpose. The crown when finished was found to weigh ten pounds, but Hiero, suspecting that some of the gold had been replaced by silver, demanded from Archimedes a means of detecting the supposed fraud without destroying the crown, owing to the beauty of its workmanship.

Archimedes, pondering over the solution of the problem, was in the bath, when he observed that he could raise his limbs in water more easily than in air. This simple observation was a gleam of light for him; he discovered the above principle, and this led him to a simple means of calculating the quantity of gold and silver in the crown. It is said that Archimedes was so transported with joy at his discovery that he ran home from the bath, crying in the streets, Εὔρηκα, εὔρηκα (I have found it).

We have all had occasion to make the observation of Archimedes,

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Equilibrium of Floating Bodies.

85

on observing how much lighter our limbs appear in water, and on the contrary, how much heavier they seem when lifted out. In like manner, if the body is almost entirely immersed in water, we can walk barefoot on the stones without injuring the feet; but this is not possible when we are out of the water. For in the former case part of the weight of the body is raised by the liquid, while in the latter the whole weight of the body presses the feet against the sharp projections.

96. Equilibrium of immersed and floating bodies.-When a body is placed in a liquid, three cases are possible: the body may have the same specific gravity as the liquid, in which case it weighs as much as the liquid for an equal volume; or it may be denser, in which case it weighs more; or it is lighter, and in this case it weighs less.

I. If the body immersed is of the same density as the liquid, the weight of the liquid displaced being the same as that of the body, it follows from Archimedes' principle, that the buoyancy which tends to raise it is exactly equal to the force with which gravity tends to sink it. The two forces are thus in equilibrium, and the body remains in suspension in any position in the liquid.

II. If the body immersed is denser than the liquid, it sinks, for then its weight preponderates over the buoyancy. This is the case when a stone or a mass of metal is thrown into water.

III. Lastly, if the immersed body is lighter than the liquid, the buoyancy prevails, and the body rises until it only displaces a weight of liquid equal to its own. It is then said to float. Cork, wax, wood, and all substances lighter than water, float on its surface.

A body which floats on one liquid may sink in another; the body for this purpose must be lighter than the one liquid, but heavier than the other. An egg sinks at once if placed in ordinary water, since it is heavier than an equal volume of water; but it swims if placed in strong brine, which is denser than water. A piece of oak floats on water, but sinks in oil, which is lighter than water. Iron floats on mercury. but sinks at once in water.

Yet a body, though denser than a liquid, may float on its surface. For this purpose it must have such a shape as to displace a volume of liquid, the weight of which is greater than its own. Porcelain is much heavier than water, yet a porcelain saucer placed on water floats on the surface; this arises from its concave shape, owing to which it displaces a weight of water equal to its own, though it is

only partially immersed. It is for the same reason that iron ships, even with very thick sides, float freely on water.

97. Cartesian diver.-The different effects of suspension, immersion, and floating are reproduced by means of a well-known hydrostatic toy, the Cartesian diver (fig. 76). It consists of a glass cylinder, nearly full of water, on the top of which a brass cap, A, provided with a piston, is hermetically fitted. In the liquid there is a little porcelain figure, a fish, o, for example, attached to a hollow glass ball, m, which contains air and water, and floats on the surface. In the lower part of this figure there is a little hole by which water can enter or escape, according as the air in the interior is more or less compressed. The quantity of water in the globe is such, that very little more is required to make it sink. If the piston be slightly lowered the air is compressed, and this pressure is

m

Fig. 76.

is lighter, on the whole, than

transmitted to the water of the vessel

and to the air in the bulb. The consequence is, that a small quantity of water penetrates into the bulb, which therefore becomes heavier and sinks. If the pressure is relieved, the air in the bulb expands, expels the excess of water which had entered it, and the apparatus being now lighter, rises to the surface. The experiment may also be made, by replacing the brass cap and piston by a cover of sheet india rubber, which is tightly tied over the mouth. When this is pressed by the hand the same effects are produced.

98. Swimming bladder of fishes.

Most fishes have an air-bladder below the spine, which is called the swimming bladder. The fish can compress or dilate this at pleasure by means of a muscular effort, and produce the same effects as those just described—that is, it can either rise or sink in water.

99. Swimming.—The human body an equal volume of water; it consequently floats on the surface and still better in sea water, which is