every body, if let alone, will continue to move in a straight line with uniform velocity; any change,
either in the rapidity or the direction of motion, requires to be explained as due to the action of
some "force." This principle was enunciated by Newton as the "first law of motion." It is also
called the law of inertia. I shall return to its purport later, but first something must be said as to the
detail of Galileo's discoveries.
Galileo was the first to establish the law of falling bodies. This law, given the concept of
"acceleration," is of the utmost simplicity. It says that, when a body is falling freely, its
acceleration is constant, except in so far as the resistance of the air may interfere; further, the
acceleration is the same for all bodies, heavy or light, great or small. The complete proof of this
law was not possible until the air pump had been invented, which was about 1654. After this, it
was possible to observe bodies falling in what was practically a vacuum, and it was found that
feathers fell as fast as lead. What Galileo proved was that there is no measurable difference
between large and small lumps of the same substance. Until his time it had been supposed that a
large lump of lead would fall much quicker than a small one, but Galileo proved by experiment
that this is not the case. Measurement, in his day, was not such an accurate business as it has since
become; nevertheless he arrived at the true law of falling bodies. If a body is falling freely in a
vacuum, its velocity increases at a constant rate. At the end of the first second, its velocity will be
32 feet per second; at the end of another second, 64 feet per second; at the end of the third, 96 feet
per second; and so on. The acceleration, i.e., the rate at which the velocity increases, is always the
same; in each second, the increase of velocity is (approximately) 32 feet per second.
Galileo also studied projectiles, a subject of importance to his employer, the duke of Tuscany. It
had been thought that a projectile fired horizontally will move horizontally for a while, and then
suddenly begin to fall vertically. Galileo showed that, apart from the resistance of the air, the
horizontal velocity would remain constant, in accordance with the law of inertia, but a vertical
velocity would be added, which would grow according to the law of falling bodies. To find out
how the projectile will move during some short time, say a second, after it has been in flight for
some time, we proceed as follows: First, if it were not falling, it would cover a certain horizontal
distance,