AMIDE  17- 16-!1 , , 15- :

steam-engine, representing graphically by a curve CPD the relation between the volume and pressure of the powder-gas; and in addition the curves AQE of energy e, AvV of velocity v, and MT of time t can be plotted or derived, the velocity and energy at the muzzle B being denoted by V and E . After a certain discount for friction and the recoil of the gun, the net work realized by the powder-gas as the shot advances AM is represented by the area ACPM, and this is equated to the kinetic energy e of the shot, in foot-tons, (I) e=224- (1-I d22tan2S) 2a, in which the factor 4(k2/d2)tan2S represents the fraction due to the rotation of the shot, of diameter d and axial radius of gyration k, and S represents the angle of the rifling; this factor may be ignored in the subsequent calculations as small, less than 1 % . The mean effective pressure (M.E.P.) in tons per sq. in. is represented in fig . 3 by the height AH, such that the rectangle AHKB is equal to the area APDB; and the M.E.P. multiplied by ;,rd2, the cross-section of the bore in square inches, gives in tons the mean effective thrust of the powder on the base of the shot; and multi-plied again by 1, the length in inches of the travel AB of the shot up the bore, gives the work realized in inch-tons; which work is thus equal to the M.E.P. multiplied by ird2l=B—C, the volume in cubic inches of the rifled part AB of the bore, the difference between B the total volume of the bore and C the volume of the powder-chamber . Equating the muzzle-energy and the work in foot-tons w V2 B --C (2) E=2240 . 2g — I2 XM.E.P . V2 w (3) M.E.P . = 2240 2g B?2C . Working this out for the 6-in. gun of the range table, taking L=216 in., we find B—C=61oo cub. in., and the M.E.P. is about 6.4 tons per sq. in . But the maximum pressure may exceed the mean in the ratio 012 or 3 to I, as shown in fig . 4, representing graphically the result of Sir Andrew Noble's experiments with a 6-in. gun, capable of being lengthened to 100 calibres or 50 ft . (Proc .

R.S.,

June 1894) . On the assumption of uniform pressure up the bore, practically realizable in a Zalinski pneumatic dynamite gun, the pressure-curve would be the straight line HK of fig . 3 parallel to AM; the energy-curve AQE would be another straight line through A; the velocity-curve AvV, of which the ordinate v is as the square root of the energy, would be a parabola; and the acceleration of the shot being constant, the time-curve MT will also be a similar parabola . If the pressure falls off uniformly, so that the pressure-curve is a straight line PDF sloping downwards and cutting AM in F, then the energy-curve will be a parabola curving downwards, and the velocity-curve can be represented by an ellipse, or circle with centre F and radius FA; while the time-curve will be a sinusoid . 300 250 200 1500 100 0.4 CORDITE 3000 - CORDITE r-r_ 2800 03~ -_ORDITE _~;36 CORDITE ~ . _ . _ • —_ c . 2800 -~ - ~— p.2 CORDITE ~ _ . --- 2400 4 -CORDITE 2200 ----- --------- ~_ -16—00 - . 0.05 E CCORDITE ~~ '' ' RIFLORDITE W 0.4 Cordite l 36 3 0.2 (0 r (0 a J 1 CO a 006 „ 86 a Plugs 7 B 0 10 11 12 3 14 h Rifle „ 9 „ -I 15 to 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 Velocity Curves, from Chronoscope experiments in 6 inch gun of soo calibres, with Cordite . employed the steel spheres of bicycle ball-bearings as safety-valves, loaded to register the pressure at which the powder-gas will blow off, and thereby check the indications of the crusher-gauge (Proc . R.S., March 1895) .

Chevalier d'Arcy, 176o. also experimented on the pressure of powder and the velocity of the bullet in a musket barrel; this he accomplished by shortening the barrel successively, and measuring the velocity obtained by the ballistic pendulum; thus reversing Noble's procedure of gradually lengthening the gun . But the most modern results employed with gunpowder are based on the experiments of Noble and Abel (Phil . Trans., 1875—1880—1892—1894 and following years) . A charge of powder, or other explosive, of varying weight P Ib, is fired in an explosion-chamber (fig . 7, scale about g) of which the 0234 e 2 4 Travel in feet . But if the pressure-curve is a straight line F'CP sloping upwards, cutting AM behind A in F', the energy-curve will be a parabola curving upwards, and the velocity-curve a hyperbola with center at F' . These theorems may prove useful in preliminary calculations where the pressure-curve is nearly straight; but, in the absence of any observable law, the area of the pressure-curve must be read off by a planimeter, or calculated by Simpson's rule, as an indicator diagram . To measure the pressure experimentally in the bore of a gun, the crusher-gauge is used as shown in fig . 6, nearly full size; it records the maximum pressure by the compression of a copper cylinder in its interior; it may be placed in the powder-chamber, or fastened in the base of the shot . In Sir Andrew Noble's researches a number of plugs were inserted in the side of the experimental gun, reaching to the bore and carrying crusher-gauges, and also chronographic appliances which registered the passage of the shot in the same manner as the electric screens in Bashforth's experiments; thence the velocity and energy of the shot was inferred, to serve as an independent control of the crusher-gauge records (figs . 4 and 5) . As a preliminary step to the determination of the pressure in the bore of a gun, it is desirable to measure the pressure obtained by exploding a charge of powder in a closed vessel, varying the weight of the charge and thereby the density of the powder-gas .

The earliest experiments of this nature are due to

Benjamin Robins in 1743 and Count Rumford in 1792; and their method volume C, cub. in., is known accurately, and the pressure ', tons per has been revived by Dr Kellner, War Department chemist, who ~ sq. in., was recorded by a crusher-gauge (fig . 6) . 278 The result is plotted in figs .