metal plate. The inside of this box is exhausted by means of a pump, leaving a more or less perfect vacuum, and the pressure of the air, acting on the thin elastic lid, bends it and forces it in to a certain extent. As the pressure of the atmosphere varies, the amount of flexure of the lid varies, and by means of a system of delicate levers, C, D, E, this change in the flexure of the lid is shown by the movement of a pointer, F, over a graduated scale. The great advantage of an aneroid barometer over a mercurial barometer is its extreme portability. The scale of all aneroids, however, has to be set out by comparing them with a mercurial barometer. 135. Corrections to Barometer Reading.-In addition to the corrections to reduce the height of the mercury column to what it would be at o° C., at latitude 45°, and at the sea-level, a correction has to be applied to allow for the expansion of the scale by means of which the height of the column is measured. If this scale is correct at o° C., then at all temperatures above o° C., the length of the divisions will be too great, since all metals increase in length when heated. Let a be the coefficient of linear expansion of the metal of which the scale is composed (§ 184), so that unit length of the scale at o° C. becomes 1+a at 1°C. and 1+ at at t°C. If he is the barometric height as measured with the scale at a temperature, then the height as measured with the scale at o° would be greater, since the length of each division of the scale would be less in the ratio of 1 to 1+at, so that the number of the divisions corresponding to a given length (ie. the length of the mercury column) will be increased in the ratio of 1+ at to I. Hence if he is the barometer reading corrected for the expansion of the scale, h。=ht (1+at). Now he is the height of a column of mercury at a temperature t, and we have to find what would be the height if the temperature of the mercury were o° C. If dt is the density of the mercury at 1o, do the density at o°, 8 the coefficient of cubical expansion of mercury (see § 189), and H the height which the column would have if the mercury were at o° C. ; then I c.c. of mercury at o° becomes 1 +6 c.c. at 1°, and 1+St c.c .at 1°. Hence, since the mass M of the mercury remains the same, I M=Vodo-Vidt, where V and V are the volumes of the mass M at the temperatures o° and to respectively. Therefore Since & is an excessively small quantity, we may neglect the term involving d2 and higher powers of d. Therefore The height of a column of liquid supported by a given pressure being inversely proportional to the density. Hdt = 1-St. Hence H=ho(1-St) = he(1 + at)(1 − dt) if we neglect the term dat2, which is excessively small. For brass a=.c00020, and for mercury d= .000182. Hence, for a mercury barometer with a brass scale, the reduced height corresponding to an observed height ht, at a temperature t, is given by H=h(1-0.0001627). This height H corresponds to a pressure of Hg dynes, where g is the acceleration of gravity at the place of observation. If g is the value of g at latitude 45°, and at the sea-level, where 845 =1-0.0026 cos. 2λ -0.0000002/, is the latitude of the place of observation and / is the height above the sea-level in metres. If H, is the height, under standard conditions, which corresponds to the same pressure as does H at the place of observation, then Hg=Hog45 or Ho= =ht(1 -0.0001621)(1 −0.0026 cos. 2λ −0.0000002). The above-mentioned corrections are practically common to all mercury barometers, since the scale is almost invariably made of brass, and the magnitude of the corrections is the same for all barometers under the same conditions. There is, however, a correction which depends on the fact that the surface of the mercury in the tube (meniscus) is curved and not plane. Hence, on account of capillarity (see § 160), there is a force tending to depress the mercury column, and on this account the height of the column is less than it would be if the atmospheric pressure were counterbalanced by the weight of the column alone. The amount of the correction to be applied to allow for this capillary depression of the column depends on the diameter of the bore of the tube, and for tubes of which the diameter exceeds 2.5 cm. it can be entirely neglected. The corrections to be applied to barometers having smaller bores are given below, but it must be remembered that these corrections are only approximate, and the only satisfactory method of finding the capillary correction for a barometer is to compare its reading with that of a standard barometer of which the bore is more than 2.5 cm. in diameter. In every case the capillary correction must be added to the observed height, since capillarity tends to give too low a value for the barometric height. In the syphon barometer the effects of capillarity in the two limbs tend to neutralise each other; but since in one case the mercury surface is quite clean and exposed to a vacuum, while in the other case it becomes coated with dust and is exposed to air, this compensation is by no means complete. D B 136. Mechanical Air-Pump.-An air-pump is an instrument for withdrawing the air from within a vessel. In its simplest form the airpump consists of a cylinder in which a piston P (Fig. 105) fits air-tight. There is a hole through the piston closed by a flap valve C, which can open outwards. A pipe, the opening to which can be closed by a valve, B, which opens inwards, leads to the vessel D, that is to be exhausted. When the piston is drawn upwards the valve C closes, and the pressure below the piston is reduced so that the air in the receiver, on account of its elasticity, is able to raise the valve B, and flows into the cylinder. When the piston descends the valve B closes, and the air in the cylinder is compressed till it is able to force open the valve C, and escape into the air. By repeating this process the air is gradually pumped out of D. FIG. 105. If the volume of the vessel D and the pipe connecting it to the cylinder is V, and the volume of that part of the cylinder through which the lower surface of the piston moves during a stroke is v. Then, if we start with the piston at the bottom of its stroke, the volume of the mass (m) of air in the instrument is V. At the end of the upward stroke the volume of this mass of air will be V+v. Of this volume 7 c.c. will be expelled at the down-stroke, and V c.c. will be left in the instrument. Hence at the end of the first stroke the mass of air in the receiver is V m. At the end of the second up-stroke the volume of this mass V+V of air expands to V+v, and during the down-stroke v c.c. of air at this density are expelled. Hence the mass of air at the end of the second stroke left in the receiver is + of the mass of air in the receiver V L m. In the same way the mass of air left after three strokes 3 m, and generally the mass of air left after n strokes is n m. Since this mass of gas now occupies Vc.c., it follows that its density is (4) m/V, while the original density was m/ V. Hence (177)*th. the density of the air left in the receiver after n strokes is th, of what it was originally. From this expression it will be seen that we cannot make the density of the air zero unless the number of strokes n is infinite. If the original pressure within the receiver is p, then after n strokes it will be (+). In practice, however, it is not possible to obtain a very low pressure owing FIG. 106. 22 to mechanical defects in the construction of the valves, to leakage round the piston, and to the fact that the piston, when at the bottom of its stroke, does not completely expel all the air in the cylinder. Another difficulty met with in mechanical pumps is that, after the exhaustion has proceeded a certain distance, the elasticity of the air left in the receiver is not great enough to lift up the valve B (Fig. 105), so that the air left in the receiver cannot escape into the cylinder. In order to overcome this difficulty, the valve is often carried at the end of a rod A (Fig. 106), which passes through the piston with a little friction. When the piston starts moving up, it raises the valve A as far as a stop fixed to the top of the rod will allow. When the piston commences to descend it forces the valve down into its seating, and thus closes the connection between the cylinder and the receiver. In this way the valve is opened by the movement of the piston, and not by the elasticity of the air in the receiver. C H G In the Fleuss pump, which is shown diagrammatically in Fig. 107, the difficulty with the valves, and also the defect that in the old form of pump there is always a certain amount of clearance between the bottom of the piston and the cylinder, so that all the air contained within the cylinder is not expelled during the downward stroke, is avoided in another way. The piston P consists of a metal frame with a leather bucket L, A FIG. 107. and has a valve N, which opens upwards. The pressure of the air on the upper side of the piston presses the leather against the wall of the cylinder, and thus ensures a close fit. The valve A only acts when exhaustion commences, and also to allow any oil which may have got below the piston to pass up. The piston-rod passes through the upper valve B, which is held down on the seating c by means of a spring 1. The communication with the vessel to be exhausted is made through the tube G. The tube F is designed to relieve the piston during the first few strokes, when otherwise there would be a vacuum below and atmospheric pressure above. As the piston rises it cuts off communication with G, and then compresses the air till it strikes E the valve B, which it raises, allowing the air to escape. The whole of the air is driven out, some of the oil D, which is above the pi ton, being driven out. The valve does not close till the piston has descended about inch, so that some of the oil above the valve passes down to the top of the piston. 111 137. Mercury Air-Pumps.-Avery good mechanical pump will exhaust a vessel till the pressure of the remaining air will support a column of mercury of about 0.05 millimetre in height. In order to get a better vacuum than this, it is necessary to employ a pump in which the piston is formed by a quantity of mercury. Sprengel's mercury-pump consists of a bent glass tube ABC (Fig. 108), with a side-tube D joined on at the bend. The end A of this tube is connected by means of a thick-walled rubber tube with a reservoir E containing mercury. The vessel to be exhausted is connected to the side-tube D, generally by means of a glass tube fitting by a well-ground neck into the end of the tube D. This ground joint is surrounded by a glass cup, shown on a large scale at F, in which a little mercury is placed to prevent the external air reaching the joint. The flow of mercury from the reservoir E is adjusted by a pinchcock on the rubber tube, so that when the mercury reaches the top of the bent tube (shown on a larger scale at G) it does not pass over in a continuous K C FIG. 108. |