THE MERCURIAL AIR PUMP. 381 the oil; so that the vacuum which can be produced by an ordinary air pump is not sufficiently good for incandescent electric lamps. In the Fleuss air pump the passages of the pump are filled with oil which circulates and fills up the clearance, and the oil is freed from air in a duplicate pump alongside. Sometimes mercury is employed to fill up the clearance, as in Kravogl's air pump; and one of the earliest and best methods of exhausting a vessel is to make it into a Torricellian vacuum, as in Torricelli's original method, during which he discovered the barometer (§ 171); but this method requires a large quantity of mercury. In Sprengel's mercurial pump (fig. 84) the exhaustion of the air from a globe C is performed automatically by an intermittent flow of mercury by drops from the reservoir A, which gradually sweep out the air, and discharge it in bubbles in the cistern B; a pinch cock E on a short length of india-rubber tube controlling the flow of the mercury. This is the essential part of the instrument; but a duplicate arrangement FG is now generally placed alongside, the vessel G to serve as an air trap for the bubbles in the mercury (fig. 85). To make a joint perfectly airtight, it is sealed by mercury surrounding it, as shown in the joint above D in fig. 85. If the bubbles at B are discharged into a receiver, partially exhausted of air by a pump, the apparatus can be considerably shortened below its normal height of about 40 ins; three or four fall tubes may be employed, to make the exhaustion more rapidly. 382 THE MERCURIAL AIR PUMP. The barometric column HK measures the rarefaction; this is also measured by the McLeod gauge, consisting of a graduated tube closed at the top which can be filled up with mercury to a given head, as in fig. 66; the compression of the rarefied air imprisoned in the gauge measures the rarefaction, to a millionth of an atmosphere, which would be quite insensible on the barometric column HK. If the drops of mercury occupy equal lengths a of the fall tube, and if c denotes the length of the air bubble when at the level of the cistern B, and therefore at atmospheric pressure, then the lengths of the successive bubbles above the cistern are where h denotes the height of the mercury barometer; these lengths of air increasing in H.P. till the junction D is reached, so that they can be represented by the ordinates of a rectangular hyperbola. An inverted Sprengel tube LMA, driven by compressed air at L, can be employed to raise the mercury again from the cistern B to the reservoir A. (Rev. F. J. Smith, Phil. Mag., 1892; Nature, Aug. 1893; Mercurial Air Pumps, S. P. Thompson: Journal Soc. of Arts, 1887.) Examples. (1) Prove that if the height of the spout of a suction pump above the water supply is the height of the water barometer, and if at the commencement of any stroke the water in the suction pipe is m and n ft below the spout and the fixed valve, the water will rise mm-/n) ft in the next stroke, if there is no clearance and if the pump is of uniform section throughout. air is one (2) Examine the effect of taking alternate strokes of an pump and of a condenser attached to a receiver. Prove that if the barrel of each pump twentieth of the receiver, and the condenser be worked for 20 strokes and then the air pump for 14 strokes, the density of the air will be practically unaltered. (3) Prove that if a bladder occupies one nth of the volume of the receiver of an air pump, and if it bursts when the pressure is reduced to one mth of an atmosphere, the mercurial gauge will fall h(m-1)/mn, when h is the height of the barometer. (4) Prove that if the temperature is constant the work required to increase q fold, or to diminish to oneqth, the density of atmospheric air of pressure P in a receiver of volume V is, respectively, Calculate the work required and the change of temperature in these cases when the compression or rarefaction takes place adiabatically (§ 233). Work out V=1m3, P=101kg/m2, q=100. (5) Examine the change in the indications of the siphon barometer of § 179, placed in the receiver of an air pump or condenser, when the dimensions of the barometer are taken into account; and prove that, in one stroke of the air pump, the barometric column falls a distance, approximately, while, in n strokes of the condenser, it rises, approximately, where A denotes the original volume of atmospheric air in the receiver. Prove also that if v denotes the volume and a the height of the air pump gauge in § 269, the mercury will rise in one stroke (neglecting the square of v), Bh Bhv CHAPTER IX. THE TENSION OF VESSELS. CAPILLARITY. 276. The vessels employed for containing a fluid under great pressure are generally made cylindrical or spherical for strength; and it is important to determine the stress in the material for given fluid pressure, or the maximum pressure allowable for given strength of material, for the purpose of calculating the requisite thickness. The simplest case of a vessel in tension is a circular pipe or cylindrical boiler, exposed to uniform internal pressure, so that there is no tendency to distortion from the circular cross section. With an internal pressure p, a circumferential pull will be set up in the material of magnitude T per unit of length suppose, acting across a longitudinal section or seam of the cylinder; and to determine T we suppose a length l of the cylinder to be divided into two halves by a diametral plane, and consider the equilibrium of either half. Denoting by d or 2r the internal diameter of the tube, the resultant fluid thrust on the curved semicircular surface is equal to the thrust across the plane base, and is therefore pld; and this thrust being balanced by the pull Tl on each side of the diametral plane, therefore G.H. 2Tl=pld, or T=1pd=pr. 2B .(1) 385 |