259 
PRINCIPLES OP GUNNERY. 
RIFLED ORDNANCE. 
BY 
CAPTAIN J. SLADEN, R.A. 
PROFESSOR OF ARTILLERY, R.H. ACADEMY, WOOLWICH. 
('Continued from p. 253.) 
$ 
CHAPTER VI. 
Trajectories. 
Unresisted Projectile.—Symbols used.—Equations of Motion of an Unresisted Projectile.—Equa¬ 
tion of the Trajectory.—Elementary Discussion of the Conditions of Motion.—The Range on 
Horizontal Plane in terms of Muzzle Velocity and Angle of Departure.—The Time of Plight 
on a Horizontal Plane in terms of Muzzle Velocity and Angle of Departure.—The Projectile 
reaches its Highest Point at one-half of its Range on the Horizontal Plane, and in one-half of 
its total Time of Plight.—The Height of the Trajectory at any given time.—The Maximum 
Height of Trajectory.—The Inclination of the Projectile to the Horizontal Line in the Plane 
of the Trajectory.—Approximate Solution of Low-Angle Trajectories.—Angle of Descent.— 
Maximum Height of Trajectory.—Method of Finding the “Dangerous Distance,” or the 
Distance in which an Object of given height would be struck, under given conditions.— 
Method of Pinding Height of Trajectory at given Distances.—Motion of a Projectile in the Air. 
—Equations of Motion.—The Velocity at the Vertex of the Trajectory.—Bashforth’s Method 
of Solution.—Niven’s Method of Solution.—Practical Examples. 
Before discussing the motion of a projectile in the air, it will be Unresisted 
necessary first to consider the simpler case in which the resistance of pr0 '’ ectile ’ 
the air is neglected, and the projectile is supposed to move without 
any resistance. 
The following symbols will be used in this branch of the subject:—- Symbols 
v for the velocity of the projectile at any point of the trajectory, 
V , n muzzle velocity, 
<£ n inclination of the direction of motion to the horizontal 
line in the plane of the trajectory, 
a // angle of departure, 
t „ time, 
x n horizontal distance from some fixed point, 
y n vertical distance, 
g a acceleration due to gravity. 
The equations of motion, then, in a horizontal and vertical direction Equations 
will "ho of motion 
Wlii De ofanunre- 
<$X n , dh/ sisted pro- 
°’ and ^ = -^ 
Integrating,, 
d& 
jectile. 
dx 
dt 
dy 
= const. = /^ cos a, 
and =2 const. — gt == V sin a —* gt. 
U/t 
