Page:Popular Science Monthly Volume 66.djvu/266

This page has been validated.

262

POPULAR SCIENCE MONTHLY.

ling the paper into a solid ball, it could be made to fall as rapidly as a ball of wood or iron. Experiments of this nature led Galileo to the discovery of the first law of motion, to wit: The velocity of falling bodies varies directly as the time.

At the beginning of the fall the velocity is zero; at the end of the first second, it is a certain quantity which experiment shows to be the same for all bodies. Let us call this velocity $g$ . Galileo's experiments showed that at the end of the second second the terminal velocity was $2g$ , at the end of the third, $3g$ and so on. The algebraic expression of the first law is, then,

(I.)

v=g.t

(experiment shows that

g=9.81

meters approximately).

The second law of motion refers to the relation of the spaces through which the body falls in different intervals of time; it is: The spaces through which a body falls vary as the squares of the times. All bodies obey this law, also, no matter of what materials they are made up.

(II.)

s={\tfrac {1}{2}}g.t^{2}

(

s={\text{space}},t={\text{time}}

).

At the beginning of the fall the time ( $t$ ) is zero, and the velocity ( $v$ ) is also zero. At the end of the first second, $t=I$ and $v=g$ (by I.). The velocity has increased from 0 to $g$ and its average value is therefore $0+g/2={\tfrac {1}{2}}g$ . The space traversed at the end of the first second is (by II.) ${\tfrac {1}{2}}g$ ; at the end of the second second, $2g$ ; at the end of the third second, ${\tfrac {9}{2}}g$ , and so on. The two laws are not independent but are separated for convenience. They are sometimes united into one, and the law of inertia (also known to Galileo) added in this form: Every body preserves its state of rest or of uniform motion in a right line unless it is compelled to change that state by forces impressed thereon.^[1]

It is this latter law that changed the whole face of science. It was supposed by the ancients and by Copernicus that the normal condition of all bodies was rest; that if they were moving it was because some force was perpetually impelling them. On the earth a pendulum stops because of the resistance of the air and the friction at its supports. Remove the air and annul the friction and it will swing forever until some impressed force stops it, so Galileo announced. Kepler was incessantly trying to conceive how a planet could continue to move in its

↑ The statement of the law is Newton's. It is implicit in Galileo's laws of falling bodies and must have been understood by Leonardo da Vinci. Kepler, perhaps, anticipated Galileo in its discovery. It is a necessary part of Huyghens's theory of central forces, but it was not clearly enunciated until the day of Newton.

[1] The statement of the law is Newton's. It is implicit in Galileo's laws of falling bodies and must have been understood by Leonardo da Vinci. Kepler, perhaps, anticipated Galileo in its discovery. It is a necessary part of Huyghens's theory of central forces, but it was not clearly enunciated until the day of Newton.

[1]