surface of the mercury stood at the mark D in the closed tube, and at the same level in the open tube. The gas was therefore at atmospheric pressure. Water was then pumped into F till the surface of the mercury stood at E, and the position of the top of the mercury column in AB, measured from E, was read, and thus the new pressure was obtained. Then, the pressure being kept constant, gas was pumped in through K till the surface of the mercury was at D. More water was then pumped into F, till the gas was compressed to the volume CE, and the pressure noted as before. More gas was then pumped in, and the series of operations repeated till the greatest available pressure was reached.

From the readings thus taken it could be seen what increase of pressure was necessary to compress the gas from the volume CD to the volume CE, starting at different initial pressures; the great improvement on the previous methods being that the initial and final volumes were the same at the high pressures as at the low, and hence the inevitable small uncertainties made in measuring the volume did not produce a greater percentage error at the high pressures than at the low.

In deducing the pressure from the height of the mercury column, Regnault allowed for the change in density of the mercury with temperature, the temperature of the column being measured by a series of thermometers T3, T4, &c., placed alongside the column. He also allowed for the increase in density of the mercury at the lower parts of the column produced by the pressure of the superincumbent mercury. Finally, since to obtain the total pressure to which the gas is subjected we must add the pressure of the atmosphere (§ 133) on the top of the mercury column in the open tube, he read the height of a barometer placed on a level with the surface of the mercury in AB for each position.

In the following table some of Regnault's results are given. The first column contains the initial pressure (P) in centimetres of mercury under which the gas occupied the volume CD, which may be called Vo If then P1 is the pressure when the volume is reduced to CE, say 1, then, if VoPo 0 Boyle's law is exactly true, VP would be equal to V11, or the ratio would be unity; the actual values found for this ratio are given in the second column of the table :—

From this table it will be seen that in the case of air and carbon dioxide VP is always slightly greater than VIP1, and that as the pressure increases this excess becomes greater and greater. Hence these gases are slightly more compressible, particularly at high pressures, than they would be if they obeyed Boyle's law exactly. Hydrogen, however, deviates from Boyle's law in the opposite direction, VP, being less than VIP, so that this gas is less compressible than a gas which obeys Boyle's law exactly.

Regnault in his experiments was only able to go up to a pressure of 27 atmospheres (§ 133). Amagat has, however, investigated the

elasticity of gases up to pressures of about 300 atmospheres, and his results for hydrogen, nitrogen, and carbon dioxide (at two temperatures) are shown in Fig. 100. In this figure a curve has been drawn representing for each gas the values of the product PV at different pressures. Since, if a gas obeys Boyle's law exactly, PV is constant, the curve

corresponding to such a gas would be a horizontal straight line parallel to the axis pressures.

It will be noticed that the curve for hydrogen slopes upwards for increasing pressures, indicating that the gas is less compressible, i.e. more elastic, than if it obeyed Boyle's law. In the case of nitrogen at pressures below 40 metres of mercury the curve slopes downwards, and the gas is less elastic than if it obeyed Boyle's law; while for higher pressures it resembles hydrogen, in that its elasticity is greater than that given by Boyle's law. Carbon dioxide at a temperature of 100° C. gives a curve which is an exaggeration of the nitrogen curve. At a temperature of 35.1 the curve for carbon dioxide has a very distinctive form, there being a pressure (70 metres of mercury), for which the product VP has a sharply marked minimum value.

A consideration of these curves shows that gases, which at low pressures deviate from Boyle's law in that they are too compressible, at high pressures and temperatures resemble hydrogen at ordinary pressures, and deviate from Boyle's law in the opposite sense to that at low pressures.

C

A

D

131. The Air Manometer.-The elasticity of a gas can be made use of to measure pressures. An instrument for this purpose consists of a curved tube ABC (Fig. 101) closed at one end, A, with some mercury in the bend enclosing some air in the closed limb, the volume of which can be read off on a scale attached to the side of the tube. The open end c being connected with the vessel in which the pressure has to be measured, suppose the volume of the air to be reduced from Vo, at atmospheric pressure, to , the mercury in the tube standing at E and D in the two branches of the tube. Then the ‣ pressure acting through c is balanced by the elasticity of the air, together with the weight of a mercury column of height DE. The pressure due to the elasticity of the air is by Boyle's law equal to atmospheres, and hence the pressure to be measured is equal to

Vo

E

B

FIG. 101.

atmospheres together with the weight of the column of mercury DE. Of course for high pressures a correction would have to be applied, to allow for the deviation of air from Boyle's law.

132. Torricelli's Experiment.-In the year 1643, an Italian named Torricelli having filled a glass tube, about a metre long and closed at one end, with mercury, inverted it and dipped the open end below the surface of some mercury in a trough. He then found that, instead of continuing to completely fill the tube, the mercury forsook the upper part of the tube, the height of the column being about 76 centimetres. Torricelli gave the true explanation of this phenomenon, namely, that the mercury column was supported by the pressure of the atmosphere

acting on the free surface of the mercury in the trough, so that this pressure was equal to the weight of a column of mercury about 76 cm. high. This explanation also accounted for the elevation of water in suction-pumps, which had previously been explained by saying that nature abhorred a vacuum, and that as the plunger of the pump rose, it tended to produce a vacuum, and therefore the water rushed in. Torricelli's experiment was further extended by Pascal, who tried the experiment with tubes filled with oil, water, and wine, the height of the column being in each case inversely proportional to the density of the liquid employed. Pascal also suggested that if Torricelli's explanation were the correct one, then the maximum height of the mercury column, or the height of the barometer, as it is called, would be less at the top of a mountain than at the foot, since the air is a heavy fluid, and therefore the pressure increases with the depth. This experiment was carried out, and the results completely confirmed his prediction.

In

133. Pressure of the Atmosphere. Since the volume of a gas is so very largely affected by the pressure to which it is subjected, it is necessary to state the pressure at which the measurement is made. To simply state that the measurement was made at "atmospheric pressure" is, in many cases, not accurate enough, for it is found that the barometric height, and therefore the pressure of the atmosphere, varies by a considerable amount from time to time. A standard pressure has therefore been adopted, which is called an atmosphere, or simply the standard pressure. This pressure is such that it would support a column of mercury 76 cm. high. Since the density of mercury varies with the temperature, and the pressure necessary to support a given height depends on the density of the mercury, it is necessary to state the temperature of the mercury when defining the standard pressure. addition, since the pressure necessary to support the column of mercury depends on the weight of the mercury, and the weight of a column of mercury of given height depends on the value of g, or the acceleration due to gravity, it is necessary to state the value of g for which 76 cm. of mercury are equal to the standard atmosphere. The temperature chosen has been that of melting ice (o° C.), and the value of g, since g varies both with the latitude (§ 116) and with the altitude, is taken as that at latitude 45° and at the sea-level. Hence the standard pressure is defined as such that it will support a column of mercury 76 cm. high, at latitude 45° and at the sea-level, the temperature of the mercury being o° C. The density of mercury at o° C. is 13.596, and the value of g at the sea-level and at latitude 45° is 980.60 cm. per sec. per sec. Hence the value of the standard pressure is

76 × 13.596 × 980.60 dynes per sq. cm.

= 1013250 dynes per sq. cm.

This number is very nearly one million dynes per square centimetre,

and it has been proposed to take a pressure of exactly one million or 16° dynes, or a mega-dyne, per square centimetre as the standard pressure. This would correspond to a column of mercury at o° C., at Latitude 45° and the sea-level, of a height of

134. The Barometer.-A knowledge of the pressure exerted by the atmosphere, or the height of the barometer, is of great importance not only in meteorology, but also, as we shall see in the later sections of this volume, in many branches of physics. An instrument designed for measuring the pressure of the atmosphere is called a barometer, and we shall now proceed to describe one or two of the more important kinds of barometers.

Barometers may be divided into two classes: (1) Liquid barometers, in which the pressure is measured in terms of the height of a column of a liquid, and (2) aneroid barometers, in which the pressure is measured by the deformation of the lid of a metal box.

Practically the only liquid that is used in liquid barometers is mercury, since, on account of its great density, the height of the column which the pressure of the atmosphere can support is of a manageable magnitude. Another advantage possessed by mercury is that it does not absorb moisture from the air, as does glycerine, the only other liquid that has been used to any extent.

B

D

The simplest form of mercury barometer is the syphon barometer. It consists of a U-shaped tube, the longer limb (AB, Fig. 102) of which is closed at A, and is about 86 cm. long, while the shorter limb is open at C. This tube is filled with pure mercury, and by boiling the mercury any air or moisture adhering to the mercury or the bore of the tube is expelled. The distance DE is equal to the barometric height. When the barometric pressure increases, the mercury rises in the closed limb and falls in the open limb; and if the bore of the two limbs is the same, the movement of the mercury surface (meniscus) is the same in the two limbs but in opposite directions. Hence, if the mercury rises in the closed limb by 1 cm. it will also fall in the open limb by 1 cm., and therefore the distance DE will increase by 2 cm., that is, the Eatmospheric pressure will have increased by two centimetres of mercury.

FIG. 102.

If a scale is attached to either of the tubes, and each half-centimetre is marked a centimetre, then the reading at once gives the height of the barometer. Since, however, the bore of a glass tube is never quite uniform, two scales are fixed, one alongside each limb, having their zeros on the same horizontal plane, that alongside the closed limb reading upwards, and