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Fluids, when compressed, transmit the pressure equally in all directions, and hence any substance immersed in a fluid or floating upon it is buoyed up by a force equal to the weight of the fluid displaced.

Two important consequences of this fact may be noted:

(i) Suppose a body of known mass M floats in a liquid of density A, with the volume V immersed,

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thus, the mass of an hydrometer divided by the volume of the immersed portion gives the density of the liquid in which it floats.

(ii) When substances are weighed in a balance, they are usually immersed in air, and hence they apparently weigh less than they really do by a weight equal to that of the air displaced. The weights are also affected by the

same cause.

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Hence, if V, be the volume of the substance in c. c., V that of the weights, and a the mass of 1 c. c. of air under the conditions of experiment, the real mass of the substance is equal to the mass of the weights

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The total normal pressure on a surface of area A immersed in an incompressible fluid of density ▲ is

P=A.A.g. 2,

where is the depth of the centre of gravity of the surface below the surface of the fluid.

Thus, to find the pressure on a surface of 1 sq. c.m. immersed with its centre of gravity 76 c.m. below the surface of mercury ▲ 13.596,

P=1 × 13.596 × 76 × 981 = 1033.3 × 981 grams.

In the case of gas or vapour the pressure may be measured in a variety of ways, e.g. by the elasticity of a thin sheet of metal as in the aneroid barometer, by a lever and weight as in the safety-valve &c., but in accurate experiments it is preferable to measure the pressure by finding the height of the column of a liquid of known density, generally mercury, which the pressure of the gas will sustain.

(13) THE BAROMETER.

The barometer in its most simple form consists of a tube about 1 c.m. wide, and 80 c.m. long, closed at one end, filled with mercury, and inverted in a vessel of mercury.

Since fluids transmit pressure equally in all directions, the pressure of the air on a portion of the surface of the mercury of area A in the vessel is equal to that of the column of mercury inside the tube the area of which is also A,

P=A.H.A. g.

Taking A as 1 sq. c.m. and omitting g as being constant for the same place,

P=Hx 13.596.

The standard pressure of the air, called an atmosphere, is taken as equal to that of a column of mercury 760 m.m. or 76 c.m. high.

In this case P=76 × 13·596=1033.6 grams on the square centimetre, or 14.7 lbs. on the square

inch.

If two barometers under the same circumstances contain liquids of different densities,

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When the mercury (A 13.596) barometer stands at 720 m.m. how high will one of glycerine (§ 1·27) stand?

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* Since increase of temperature causes the mercury and the scale of the barometer to expand, a correction must be applied for any temperature t° C. If the reading on a brass scale is h m.m. the true reading is H = h (1−0·00016 t).

The higher a barometer is carried from the sea-level the less is the action of gravity upon the mercury, and the shorter is the column of air above the mercury, hence for each metre that the place of observation is above the level of the sea, 083 m.m. must be added to the observed height of the barometer, to reduce it to the true reading at the sea-level.

The difference in height in metres D between two places at the temperatures 7 and t° Centigrade, where the mercury-barometer stands at H and h metres respectively, may be found by the formula,

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(14) THE CHANGE IN VOLUME OF A MASS OF GAS PRODUCED BY A CHANGE IN PRESSURE.

Boyle's Law. The volume of a mass of gas varies inversely as the pressure upon it; or, the volume of a mass of gas multiplied by the pressure at any one time is equal to the volume of the same mass of gas multiplied by the pressure upon it at any other time;

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If the pressure upon 1000 c. c. of gas be increased from 400 m.m. to 800 m.m. what is the new volume ?

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250 c. c. of gas under pressure of 742 m.m. have the pressure increased to 760 m.m.

What is the new volume?

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(15) TEMPERATURE AND THERMOMETERS. The temperature or hotness of a body is the energy with which the heat in that body tends to transfer itself to other bodies. Temperature is usually measured by thermometers, which are generally inclosed volumes of air or mercury from the expansion of which the temperature is determined.

In every case two 'fixed points' are taken, the meltingpoint of ice, and the boiling-point of water under a pressure of 760 m.m. of mercury.

The difference in temperature between these two points is divided into a number of equal degrees and a similar graduation is carried above and below the fixed points.

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Since the difference between the fixed points is the same

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Hence any given number of degrees a on one scale can be expressed on another scale by the following formulæ :

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Thus, to find what temperature Centigrade is equal to

113° F.,

(113° F. - 32) × 5

==

= 45° C.;

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and what temperature Fahrenheit is equal to - 32o R.,

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There are reasons for supposing that 273° C. is the lowest possible temperature; hence it is called the absolute

L. C. A.

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