ine of fire, _O D_, in successive seconds, the same
distances _AP_, _BQ_, _CR_, &c., as are stated above for a dropped
body.]

All this was experimentally established by Galileo.

A body takes half a second to drop 4 feet; and a quarter of a second to
drop 1 foot. The easiest way of estimating a quarter of a second with
some accuracy is to drop a bullet one foot.

A bullet thrown or shot in any direction falls just as much as if merely
dropped; but instead of falling from the starting-point it drops
vertically from the line of fire. (See fig. 35).

The rate of fall depends on the intensity of gravity; if it could be
doubled, a body would fall twice as far in the same time; but to make it
fall a given distance in half the time the intensity of gravity would
have to be quadrupled. At a place where the intensity of gravity is
1/3600 of what it is here, a body would fall as far in a minute as it
now falls in a second. Such a place occurs at about the distance of the
moon (_cf._ page 177).

The fact that the height fallen through is proportional to the square
of the time proves that the attraction of the earth or the intensity of
gravity is sensibly constant throughout ordinary small ranges. Over
great distances of fall, gravity cannot be considered constant; so for
things falling through great spaces the Galilean law of the square of
the time does not hold.

The fact that things near the earth fall 16 feet in the first second
proves that the intensity of ordinary terrestrial gravity is 32 British
units of force per pound of matter.

The fact that all bodies fall at the same rate (when the resistance of
the air is eliminated), proves that weight is proportional to mass; or
more explicitly, that the gravitative attraction of the earth on matter
near its surface depends on the amount of that matter, as estimated by
its inertia, and on nothing else.

LECTURE IV

GALILEO AND THE INVENTION OF THE TELESCOPE

Contemporary with the life of Kepler, but overlapping it at both ends,
comes the great and eventful life of Galileo Galilei,[5] a man whose
influence on the development of human thought has been greater than that
of any man whom we have yet considered, and upon whom, therefore, it is
necessary for us, in order to carry out the plan of these lectures, to
bestow much time. A man of great and wide culture, a so-called universal
genius, it is as an experimental philosopher that he takes the first
rank. In this