his pupils, Toricelli or
Viviani, who were allowed to visit him in his last two or three years;
it was kept by them for some time, and then published surreptitiously in
Holland. Not that there is anything in it bearing in any visible way on
any theological controversy; but it is unlikely that the Inquisition
would have suffered it to pass notwithstanding.

I have appended to the summary preceding this lecture (p. 160) the three
axioms or laws of motion discovered by Galileo. They are stated by
Newton with unexampled clearness and accuracy, and are hence known as
Newton's laws, but they are based on Galileo's work. The first is the
simplest; though ignorance of it gave the ancients a deal of trouble. It
is simply a statement that force is needed to change the motion of a
body; _i.e._ that if no force act on a body it will continue to move
uniformly both in speed and direction--in other words, steadily, in a
straight line. The old idea had been that some force was needed to
maintain motion. On the contrary, the first law asserts, some force is
needed to destroy it. Leave a body alone, free from all friction or
other retarding forces, and it will go on for ever. The planetary motion
through empty space therefore wants no keeping up; it is not the motion
that demands a force to maintain it, it is the curvature of the path
that needs a force to produce it continually. The motion of a planet is
approximately uniform so far as speed is concerned, but it is not
constant in direction; it is nearly a circle. The real force needed is
not a propelling but a deflecting force.

The second law asserts that when a force acts, the motion changes,
either in speed or in direction, or both, at a pace proportional to the
magnitude of the force, and in the same direction as that in which the
force acts. Now since it is almost solely in direction that planetary
motion alters, a deflecting force only is needed; a force at right
angles to the direction of motion, a force normal to the path.
Considering the motion as circular, a force along the radius, a radial
or centripetal force, must be acting continually. Whirl a weight round
and round by a bit of elastic, the elastic is stretched; whirl it
faster, it is stretched more. The moving mass pulls at the elastic--that
is its centrifugal force; the hand at the centre pulls also--that is
centripetal force.

The third law asserts that these two forces are equal, and together
constitute the tensio