32'2

MISCELLANEOUS

TRACT oS.

will be, as 398*28 :298*28 : : 10 feet or 120 inches : 90 inchesnearly, the space occupied by the air; there!. 120 — 90=30inches, is the distance sought.

PROBLEM IV.

To assign the Cause of the Deflection of Military Projectiles.

It having been surmized that, in the practice of artillery,the deflection of the shot in its flight, to the right or left,from the line or direction the gun is laid in, chiefly arisesfrom the motion of the gun during the time the shot is pass-ing out of the piece: it is required then to determine whatspace an 18-pounder will recoil or fly back, while the shot ispassing out of the gun ; supposing its weight to be 4800lb,that of the carriage 24'00lb, the quantity of powder alb, thelength of the cylinder 108 inches, that of the charge 13 inches,and the diameter of the bore 5*13 inches ; supposing also thatthe resistance from the friction between the platform and car-riage is equal to 3600lb ?

It is well known that confined gunpowder, when fired,immediately changes in a great measure into an elastic air,which endeavours to expand in all directions. Now, in thequestion, the action of this fluid is exerted equally or thebottom of the bore of the gun and on the ball, during thepassage of the latter through the cylinder; the two bodiestherefore move in opposite directions, with velocities whichare at all times in the inverse ratio of the quantities of mattermoved. Now let x be the space through which thejgun re-coils; then, as the charge occupies 13 inches of the barrel,and the semidiameter of the barrel is 2*565, the space movedthrough by the ball when it quits the piece, is 108 — 13 —2*565 — x = 92*435 — x : and as the elastic fluid expandsin both directions, the quantity which advances towards themuzzle, is to that which retreats from it, as 92*435 —x to x :consequently — — and ^ - x 8 are the quantities of the

powder which move, the former with the gun, and the latter