XXI
CHAPTER III.
Falling, Pendulum, and Curvilinear Motion.
130–144
§ 46. 1) Falling. —The cause of falling is the attraction
of the earth. The chief laws are the following:
1) The velocity of a falling body increases in proportion to
the duration of its fall.
2) The space, which a body traverses in subsequent seconds,
increases in proportion to the progression of the odd numbers.
3) The space traversed by a falling body in any given time
is proportional to the square of that time.
4) In a vacuum all bodies fall with equal velocity. 130.
133. 134
§ 47. The laws of falling bodies may also be proved in the
following manner: As a falling body is continually influenced
by gravity its motion is a continually accelerated motion and its
velocity must increase in proportion to the duration of its fall; if
its velocity would be 10′ per second after the first second, it will
be 2 x 10 at the end of the second, 3 x 10 at the end of the
third second i. e. if at the end of the third second gravity
would cease to act upon it, the body would thereafter fall at 30′
per second.
As to the space we must consider, that the velocity of 10′ per
second reached at the end of the first second is composed of
innumerable velocities from 0′ up 10′ per second, which means
the same as if another body would have fallen by an uniform
motion with an average velocity of 0 X 10/2 = 5′, hence the body
has traversed a space of 5′— After two seconds it has acquired a
