regarding the accelerated velocity of fall. Such velocities were
found to bear a simple relation to the period of time from the
beginning of the fall. Other experiments, in which balls were
allowed to roll down inclined planes, corroborated the
observation that the pull of gravitation gave a velocity
proportionate to the length of fall, whether such fall were
direct or in a slanting direction.

These studies were associated with observations on projectiles,
regarding which Galileo was the first to entertain correct
notions. According to the current idea, a projectile fired, for
example, from a cannon, moved in a straight horizontal line until
the propulsive force was exhausted, and then fell to the ground
in a perpendicular line. Galileo taught that the projectile
begins to fall at once on leaving the mouth of the cannon and
traverses a parabolic course. According to his idea, which is now
familiar to every one, a cannon-ball dropped from the level of
the cannon's muzzle will strike the ground simultaneously with a
ball fired horizontally from the cannon. As to the paraboloid
course pursued by the projectile, the resistance of the air is a
factor which Galileo could not accurately compute, and which
interferes with the practical realization of his theory. But this
is a minor consideration. The great importance of his idea
consists in the recognition that such a force as that of
gravitation acts in precisely the same way upon all unsupported
bodies, whether or not such bodies be at the same time acted upon
by a force of translation.

Out of these studies of moving bodies was gradually developed a
correct notion of several important general laws of