I the compafs, viz. N. W. W. S. S. W. S. E. by 2. Suppofe the variation is 21° 30' E. it is required to correct the following courfes fteered by the com Correct course N. Variation add 55° 15 E Cor.courfe S. 1° 00'E Courses fet W.S.W.67° 30' (N.W.byW.=56° 15′ 21 30 Var. fub. 21 39 Correct courfe S. 89° 00W Cor. courfe N.34°45'W A GUNNER Y. DEFINITIONS and PRINCIPLES. *T different forces, namely, the impellent force THE path of every projectile depends on two whereby the motion is firft begun, and which, acting alone, would carry the body forward in a straight line; and the force of gravity by which the projectile du « ring the whole time of its flight is urged downwards toward the center of the earth; and because both forces act continually whilft the body is in motion, its path is a curve line lying between the directions of both. It has been proved by many authors, that the path of a projectile in vacuo is a curve line called a parabola; but in air, the refiftance it meets with changes the form of its path. Moft writers on this fubject have thought that the action of the air on such projectiles as cannon balls, was too fmall to be taken notice of; and therefore have fuppofed that the path of a ball in the air was truly, or very nearly, the fame, as in vacuo. But, although it is now known, that the refiftance of the air to the motions of large and heavy bodies, fuch fuch as bombs and cannon-balls, is much greater than has been commonly reprefented, and therefore muft affect both the magnitude and figure of their path: Yet, if the amplitude of the projection answering to any given elevation be firft found by experiment (which is always supposed in gunnery), the amplitudes in all other cafes, where the elevations and velocities do not differ very much from the firft, may be determined to a fufficient degree of exactness, by the rules ar fing from the parabolic hypothesis; because, in all fuch cases, the effects of the air's resistance will be nearly as the amplitudes; and, were they accurately fo, the proportions of the amplitudes at different elevations would then be the same as in vacuo. Hence, the common rules given by the writers on gunnery, although not mathematically true, may be fafely admitted in practice. 2. The point where the projectile begins to move, is called the point of projection. 3. The impetus of a piece is the height to which, with its proper charge of powder, it could make the bali afcend, when fired off in a direction perpendicu lar to the horizon; or the perpendicular height from which the ball must fall, to acquire the velocity it hath at the point of projection. 4. The elevation is the angle contained between the axis of the gun and a right line drawn from the point of projection in the horizontal level. 5. The amplitude, random, or range of a projectile, is the distance between the point of projection and the place where it impinges on the ground: Or, it is the horizontal distance which the projectile paffeth over in its flight.: 6. Different elevations of the fame piece give different amplitudes; for if, when a piece is fired off, its axis be either in the plane of the horizon, or perpendicular to it, there will be no amplitude; because, in the first case, the ball, by the action of gravity, will meet the ground immediately on leaving the mouth of the gun; and, in the laft, it will fall down on the point of projection. At equal distances from either of these directions, fuch as, at an elevation of 25 or 65 degrees, the amplitudes will be equal. And, When the elevation is 45 degrees, the amplitude will be the greatest poffible. 7. The greatest amplitude is double to the impetus of the piece; and, when the elevation is 45 degrees, the greatest altitude of the ball is one fourth part of the amplitude. 8. If a body be projected oblique to the horizon, it will fall there again in the fame oblique direction, and with the fame velocity with which it was projec ted. 9. The time which a heavy body, projected at an elevation of 45°, will continue in the air, before it arrives at the horizon, will be equal to the time that the fame body would take to defcend by the force of gravity, through a space equal to its amplitude, or ho rizontal range. 10. In most problems in gunnery, it is supposed that the gunner makes an experiment on every gun he has the the care of, with its ordinary charge of powder, at an elevation of 45°, in order to find the greatest amplitude of the piece, and then half of this is the impe tus. The rules made ufe of in folving the following problems, are demonftrated by the writers on projec tiles. Of PROJECTIONS made on the Plane of the Horizon. PROB. I. The impetus of the piece and the distance of the object aimed at being known, to find the ele vation, fo as to strike the object. RULE. The horizontal ranges of equal bodies pro jected with the fame velocity at different elevations, are to one another as the fines of twice the angles of elevation. EXAM. Required the elevation necessary to strike an object on the horizon at the diftance of 5170 yards, the impetus of the piece being 3375 yards. As twice the impetus, or greatest amplitude 6750, To the fine of twice the elevation=50°. Hence, the lower elevation is 25o, and the higher 65°; For thefe are equally distant from 45°. PROB. 2. The angle of elevation, and the amplitude being given, to find the greatest altitude of the ball. |