**Constant Projectile Motion**

Projectile motion refers to the motion of an object in a curved trajectory under the influence of gravity alone. In projectile motion, the object is launched at an angle to the horizontal and follows a parabolic path. The object continues to move horizontally at a constant velocity while experiencing a vertical acceleration due to gravity.

In this context, the constant projectile motion refers to the motion of an object where certain quantities remain constant throughout the trajectory. Let's analyze the given options to determine which one of them represents a constant quantity in projectile motion.

**a) Resultant of the velocity of projection:**
The resultant of the velocity of projection is the vector sum of the horizontal and vertical components of the velocity. As the object moves along the parabolic path, both the horizontal and vertical components of velocity change continuously. Therefore, the resultant of the velocity of projection is not constant.

**b) Vertical component of the velocity:**
The vertical component of the velocity represents the rate of change of displacement in the vertical direction. In projectile motion, the vertical component of velocity changes continuously due to the effect of gravity. As the object moves upward, the vertical component decreases until it reaches zero at the peak of the trajectory. Then, it increases in the downward direction. Therefore, the vertical component of the velocity is not constant.

**c) Horizontal component of the velocity:**
The horizontal component of the velocity represents the rate of change of displacement in the horizontal direction. In projectile motion, the horizontal component of velocity remains constant throughout the entire trajectory. This is because there is no horizontal acceleration acting on the object, and only the vertical component experiences acceleration due to gravity. Therefore, the horizontal component of the velocity is constant.

**d) Velocity of projection:**
The velocity of projection is the initial velocity with which the object is launched. In projectile motion, the magnitude of the velocity of projection remains constant, but its direction changes continuously as the object moves along the curved path. Therefore, the velocity of projection is not constant.

Therefore, the correct answer is option 'C' - the horizontal component of the velocity is constant in projectile motion.