COMBUSTION, Velocity of. It can be shown by direct experiment that the burning of a grain of powder in a fire-arm is progres sive, and that the size of the g.rain exerts a great influence on the velocity of the projectile. For instance if one piece of the press cake were placed in a small mortar and fired, little or no motion would be given to the projectile. If this piece be divided into seven or eight parts, the projectile will be thrown a short dis tance; and by increasing the number of parts or grains, so will the effect of the powder on the projectile also increase. The progressive burning of powder is further confirmed by the fact that burning grains are sometimes pro jected from the gun with sufficient force to perforate screens of paper and wood at con siderable distance. It is even found that they are set on fire in the gun and afterward ex tinguished in the air before they are completely consumed. The velocity of combustion of powder varies with •the purity, proportions, triturative, density and condition of the ingre dients, also with the pressure under which the powder is burned. By varying the proportions and increasing the sulphur there is a tendency to make a more violent explosion and a more quickly kindling mixture. A general formula may be deduced to show the amount of gas developed and the quantity of povrder burned at any instant of the combustion of a grain or charge of powder. For this purpose take a s_pherical grain of powder and consider it in flamed over its entire surface. Let t represent the time of burning, from the instant of igni tion to the moment under consideration; R , the radius of the grain. Since the combustion of the grain passes over the radius R in the time t, the velocity of combustion is equal and for the time, t, it will pass over the space t 7 or R F1 the radius of the decreasing sphere vrill therefore be R (14 ) . The volume of
the grain of powder and that of the decreasing sphere are 1 le and )s respec tively; and their difference ir or the quantity of powder burned, will be equal to 11-R8(1--1.) a).
The first factor of this expression represents the primitive volume of a grain of powder, and the other expresses the relation of the volume burned to the primitive volume.
The same expression will answer for all of the grains of a charge of powder, if they are of the same size and composition; consequently, if we let A represent the volume or weight of the grains composing a charge of powder, the quantity remaining unburned after the time, t, will be represented by A (14)s ; and the tity burned by Al— (1— 1-)1). Although the grains of powder are not spherical, their sharp angles are partially worn away by rubbing against each other in glazing and in transportation; and the mode of fortification and inspection reduces the variation in size within narrow limits; therefore, if we examine the influence which the actual form and size of the grains exercise over the phenomenon of combustion of powder, we shall find that the effect varies but slightly from that due to the spherical form. If we consider the velocity of the projectile on leaving a gun and the time necessary to over come its inertia in the first period of its move ment, we shall see that a very large portion of each grain is burned up before the projectile leaves the gun. If the size of the grain be in creased, the effect will be to diminish the amount of gas evolved in the first instant of time, and to diminish the pressure on the breech. This principle has been made use of to increase the endurance of large cannon.