in which the weight of the displaced air is transferred to the first member of the equation. As the density of the air is very slight compared to that of lead or iron, the materials of which projectiles are made, dD may be neglected. Making this change, and substituting for P, 43pR3D, the expression for the final velocity reduces to
v2 (1 + vr) = 43 RDA. (16)
The resistance on the entire projectile for a velocity of 1 foot, is ApR2; dividing this by Pg, or the mass, we get the resistance on a unit of mass. Calling this 12c we have,
12c = ApR2 Pg, or 2gc = PApR2.
Substituting for P its value in the equation of vertical descent, we have,
2gc = v2 (1 + vr);
from which we see that v depends only on c; but
c = 23 RDgA (17)
hence, the final velocity of a projectile falling through the air is directly proportional to the product of its diameter and density, and inversely proportional to the density of the air, which is a factor of A. The expression for the value of c shows that the retarding effect of the air is less on the larger and denser projectiles. To adapt it to an oblong projectile of the pointed form, the value of D should be increased (inasmuch as its weight is increased in proportion to its cross-section), while that of A should be diminished. It follows, therefore, that for the same caliber an oblong projectile will be less retarded by the air than one of spherical form, and consequently with an equal and perhaps less initial velocity, its range will be greater.
Velocity of Light. See [Light, Velocity of].