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long a time are now being remedied to a great extent, and as it becomes known, and its resources are developed, there is every reason to anticipate that the wisdom shown in the acquisition of Alaska will be fully demonstrated.*
*A more extended account of the climate, resources, and population of Alaska may be found in the valuable report of Mr. Ivan Fetrof, published in Report of the 10th Census of the United States.
U. S. NAVAL INSTITUTE, ANNAPOLIS, MD.
POWDER IN GUNS.
[A continuation of " Velocities and Pressures in Guns," Vol. XIV, No. 2.]
By Lieutenant J. H. Glennon, U. S. N.
In a paper entitled " Velocities and Pressures in Guns," Vol. XIV, No. 2, the action of powder in guns was treated mathematically, with the tacit assumption of a certain premise which, though not new, being in fact the very foundation of Messrs. Noble and Abel's treatment of the work done by powder in guns, at first appears doubtful. The question is whether or not a progressive powder, if all burnt in a gun, and the gases produced have gained mechanical and thermal equilibrium by the time the projectile reaches the muzzle, will give as great a muzzle velocity, weight for weight, as a powder all of which is burnt before the projectile begins to move. This point can be elucidated in several ways, assuming, as in that paper, no radiation or conduction of heat to the gun or between the portions of the gas. In other words, the portions of gas are assumed to expand adiabatically.
One comment has been made and may be noticed here, namely: if, immediately around the surface of the burning powder grains, gas at high temperature and pressure exists, and the rest of the gas is, or may be considered, in thermal and mechanical equilibrium at a lower temperature and pressure, then the lower pressure, being that of the gas directly in rear of the projectile, would be the force accelerating it. Looking into the subject, however, we see that if only the low pressure exists at the base of the projectile, the high pressure must be somewhere else, as at the face of the breech-block ; and if the low pressure may be considered by itself as accelerating the projectile in one direction, so may the high as accelerating the gun in the opposite direction. Newton's law on the equality of action and reaction would then not apply, remembering, of course, that the mean forward motion of the powder gas (a motion partly action and partly reaction) is limited by the relative motion of the projectile and gun.
To proceed, suppose that we have a quantity of gas occupying a non-conducting cylinder OMCD, Fig. 1, that the pressure of this gas is represented in Fig. 2 by LB and the volume by OD. Interpose a non-conducting piston AB between the two halves of the volume of gas.
Now suppose that we push the piston AB to the position AlB1 (Fig. 1). The pressure of the gas to the left of the piston will increase from LB (Fig. 2) to NBU following the pressure-volume lawpv" =
pvV*, where n equals —, the ratio of the specific heats of the gas, or
approximately 1.4. The work done in compressing the left half will then be represented (in proper units) by an area NBXBL (supposing no friction). Part of this work, LBBXK, will be done by the other half of the gas. The external work necessary to push AB to the position AXBX will therefore be represented by NKL. If now the piston at AXBX is released it will start towards AB, and when it reaches that position it will have a vis viva represented by NKL, will pass the position AB, and will then encounter retarding pressures equal to those formerly accelerating it. It will be brought to rest at the position A,B„ determined by BBV = BB„ will then return to AXBX, then back again, and so on, as long as there is no external work done.
Now connect the piston by means of a piston-rod, or otherwise, with the outside, so that it may do external work. It will come to rest when it has done the external work represented by NKL, and not until then. It will then be in its original position AB. and the pressure on each side of it will be the same as originally, so that if it were removed the gas would be in thermal and mechanical equilibrium.
Evidently, while the piston is in motion from B, to B„ the cylinder head CD will be subject in succession to all the pressures represented by the ordinates of the curve KLNU and not alone to the pressure BXK, with which the pressure to the right of the piston begins.
If now the mass of the piston is made smaller, its velocity at B will be increased, its mechanical energy or vis viva still remaining KLN. In the limiting case, where the mass of the piston is infinitesimal, its velocity will be infinite, the mean velocity for the travel of the piston will be infinite, and the distance BXB7 will be traversed in an infinitesimal time. Suppose that we take this limiting mass for the piston, and suppose, simultaneously with its release, that we release the cylinder head CD, allowing it free motion along OD, the mass of CD being supposed appreciable. Evidently CD will start under an accelerating force KBU and in an infinitesimal time will be subject to all the pressures KBX to NBr The piston AB will make an infinite number of vibrations in a short finite time, and will finally take up a mean position between O and D. The piston AB might then be removed, as, its velocity being finite, it will have no finite vis viva, the gas will be in equilibrium, and all the energy represented by NKL will have been transmitted to CD. The piston of infinitesimal mass of course does not exist; more properly a piston should be supposed which by its mass and motion would represent the mass and motion of the gas itself. In this case equilibrium would be gained, though not so quickly as with the infinitesimal piston. A little explanation possibly will be necessary to connect the assumed case with the case of fired gunpowder.
A charge of gunpowder is not all ignited at once. The particles of gas have a certain temperature and definite tension at the instant of combustion. Suppose a small quantity of the powder ignited