242 PNEUMATICS where g is the force acting on unit mass at height h. If we put K = <7H, the equation becomes jtf=JV~* /H > where H is obviously the height of a fluid of uniform density p /~K. which would give at its base the pressure p in other words, the height of tlie homogeneous atmosphere, as it is called. Its value is readily found, since it bears to the height of the mercurial baro metric column the same ratio which the density of mercury bears to the density of the atmosphere at the sea-level. For dry air at C. and with g taken as equal to 981 dynes ( = 32 2 poundals nearly), the value of H is 7 9887 x 10 5 centimetres, or 26,210 feet. Hence the formula giving the height above the sea-level in terms of the pressure may be written h = 7 9887 x 10 5 x Nap. log. (p jp) . In practice this formula must be modified to suit regions where g is other than 981, and where the temperature is other than 0. The effect of the water-vapour present must also be taken into account, and the constants involved carefully tested by observation. The subject is treated in detail under BAROMETER. In an appendix to the New Experiments, Physico- Mechanical, &c. y touching the Spring of Air (1660), Robert Boyle states that the density of air is directly as the pressure. His apparatus and method ofiexperiment are as follows. A U-shaped tube is taken, one of whose limbs is considerably longer than the other. The shorter limb is closed at the end ; and the whole apparatus is set vertically with the open end pointing upwards. A small quantity of mercury fills the bend, so that at the beginning of the experiment the two mercury surfaces are at the same level. Hence the air confined in the shorter limb is subjected to a pressure along its lower surface equal to the atmospheric pressure,, or one atmosphere as it is com monly called. As the height of the air column in the closed tube is small, the pressure and density are practic ally the same throughout. Now let mercury be poured into the longer limb. The free mercury surface will be observed to rise in the shorter limb, so that the air con fined there becomes compressed into smaller bulk. Since the mass of air has not altered, the density is obviously inversely as the bulk, and can therefore be easily measured. Again, the pressure to which the confined air is now sub jected is equal to the pressure over that surface in the mercury in the open limb which is at the same level as the free mercury surface in the closed limb. But this pres sure is clearly the sum of the atmospheric pressure and the pressure due to the superincumbent column of mercury, which latter can be readily expressed in atmospheres if the height of the barometer is known. In other words, divide the vertical distance between the two mercury sur faces by the height of the barometer column. The quotient added to unity gives the required pressure in atmospheres. Mariotte s Fourteen years after the date of the publication of experi- Boyle s results, Mariotte, 1 working independently, dis covered the same law, which is still widely known on the Continent as Mariotte s law. He supplemented Boyle s experiments by investigating the effect of pressures less than that of the atmosphere, and proved that the same law held at these diminished pressures. His method was essentially as follows. A barometer tube is filled in the ordinary way with mercury and fixed up as in the Tor ricellian experiment. A little air is then introduced at the lower end of the tube which is dipping in the reservoir of mercury. This air travels up the tube and fills the Torricellian vacuum at the top, thereby depressing to a .slight extent the barometer column. The amount of depression divided by the true height of the barometer gives the pressure in atmospheres which acts upon the air in the tube. The tube, always kept truly vertical, dips in a reservoir of mercury sufficiently deep to admit of its complete immersion. For a certain position of the tube the free surfaces of mercury in the tube and reservoir are 1 Traite de la Nature de I Air, 1676. ments. at the same level. For that position the confined air is at the atmospheric pressure ; and for any higher position of the tube the pressure in the confined mass of air is less than the atmospheric pressure by the pressure due to the column of mercury between the free surfaces. Recent experiments by Kraevitch and Petersen (Journal of the Russian Chemical Society, vol. xvi.) seem to show that very rarefied air is very far from obeying Boyle s law. At such low pressure, the condensation of the gas upon solid surfaces is an important factor. For most ordinary purposes Boyle s law that, at con- Boyle s stant temperature, the density of a gas varies directly as law on l; the pressure may be assumed to be true, at least for a PP roxi moderate ranges of pressure ; but the careful investigations ma e< of later experimenters, such as Oersted, Despretz, Dulong, Regnault, Andrews, Cailletet, and Amagat, have proved that the law is only approximate for every known gas, and that the deviation from correspondence with the law is different for each gas. The most recent investigations are those of Cailletet and Amagat, who have carried the results to much higher pressures than former experimenters employed. Both adopted in the first place a form of apparatus essentially the same as Boyle s, only much longer. The gas was subjected to the pressure of a mercury column enclosed in a strong narrow steel tube ; and, as oxygen acts vigorously upon mercury at high pressures, nitrogen was used. In this way Cailletet 2 attained to a pressure of 182 metres of mercury, and Amagat 3 to a pressure of nearly 330. Having thus determined accurately the corresponding Amagat pressures and densities of nitrogen, Amagat proceeded to ex P eri - determine the relation for other gases by Pouillet s ments differential method. That is, the pressure to which the new gas was subjected was made to act simultaneously upon a given mass of nitrogen, whose volume could be readily measured and pressure estimated. Oxygen, hydro gen, carbonic oxide, dry air, olefiant gas, and marsh gas were investigated ia this way. The general results obtained by Amagat are exhibited in the subjoined chart taken from his paper. For all gases except hydrogen the product pv (pressure into volume), instead of being con stant, as Boyle s law would require, diminishes at first as the pressure is increased. At a certain pressure, however, different for each gas, the diminution ceases, and if the pressure is still further increased the product pv begins to increase also, and continues so to do to the greatest pressure used. In tho case of hydrogen the product increases from the very beginning. On the diagram, abscissae represent pressures in metres of mercury, and the ordinates represent the deviations from the Boylean law. 1 1 will be observed that all the curves pass through the point on the pressure axis which represents a pressure of 24 metres of mercury. If IT represents the product pv for any gas at this pressure, and ir the corresponding product for any other pres sure, then we may write where 8 represents the deviation from Boyle s law. All the curves except that for hydrogen show a well-marked minimum, at and near the pressure corresponding to which the particular gas obeys Boyle s law. For the several gases these positions occur at the pressures as given in the following table : Nitrogen.., 50m. Carbonic acid .., . 50 in. Oxygen 100 m. Air... 65 m. Marsh gas 120 in. Olefiant gas 65 in. For olefiant gas 8 is so great, and varies so rapidly, that only portions of the curve are represented. The value of 5 for its minimum point is - 1 3, while the corresponding value for oxygen is -0 05. In these experiments the temperature of the gases varied between 18 and 22 C. Amagat 4 has extended his researches to higher temperatures up 2 Journal de Physique, vol. viii., 1879. 3 Annales de C himie et de Physique, vol. xix. , 1880.
4 Annales de C himie et de Physique, vol. xxii., 1881.