In this paper, the author first considers the theory of rifles, with which the subject of it is intimately connected; and regarding it as an admitted principle, that irregularities in the flight of shot arise from irregularities either in their surface or substance, shows how the rotatory motion of a rifle ball, by presenting every part uniformly to the action of the resisting medium, obviates the effect of these irregularities. The spiral or rotatory motion of the ball in rifles, is generally supposed to arise wholly from the re-action of the grooves in the barrel, or from the indentations made by them in the surface of the ball; but the author, taking into consideration the powerful action of the air on projectiles, is led to conclude that the rotation of a grooved ball may be sustained during its flight, or even produced originally by the resistance of the air acting on the inclined planes formed by the grooves, on the same principle as the rotation of the sails of a windmill. These considerations led the author to conceive the possibility of giving the spiral motion to grooved shot fired from a plain barrel; an idea which, he remarks, seems to have also occurred to Mr. Robins, who left, however, no clue to enable us to discover the nature of his plan. He accordingly commenced a series of experiments for the purpose, and, abandoning all idea of success with spherical shot, adopted the cylindrical form. His first trials were made in the summer of 1821. Hemispherical ends were adapted to cylindrical shot, but abandoned, it being found desirable so to dispose the weight as to give the greatest possible length to the shot; grooves of various dimensions were tried, and were found not to answer when narrow, but required to be wide enough to allow their sides to be exposed, from one end to the other, to a current of air blowing straight between them. In 1822, some further experiments were made at Woolwich, with grooved leaden shot fired from musket barrels, and with wooden shot from a 5^-inch howitzer, in which the shot, being received on targets, or in banks of earth, were in numerous instances found to have flown in the manner expected, i. e. point foremost. Similar trials with grooved leaden bullets from a plain barrel, were made in 1823, to the extent of several hundreds; and the balls, when well made, were always found to fly end foremost. Large wooden grooved shot were also fired from a 24-pounder, at Kinsale Fort, and on some occasions by night with lighted fusees in their sides, by which contrivance it was distinctly seen that the spiral motion was acquired and maintained steadily throughout their flight.