XXVII
2) The radius-vector (or line connecting the planet's centre
with that of the sun) describes equal areas in equal times.
3) The squares of the periodic times of any two planets
have the same ratio as the cubes of their mean distances.
Remark. Here we have one of the great many instances of proportion
ality (cf. § 46. 53. 100, 181. 236. etc.) in nature. Where there is propor
tionality it must be concluded, that it is the result of though and points
back to an intellect, to a legislation in nature.
Applications of the Centrifugal force are: a ball attached to
a thread, 138; mud thrown off by the wheels of a carriage, 139;
a tumbler full of water put inside a hoop, 14o; a hoop trindled
along the ground— Slings, sugar refineries and washing esta
blishments afford other applications of the Centrifugal force.
§ 64. The Centrifugal force increases with the velocity of
the moving body; this must be taken into consideration, when
a train or a horseman moves along a curve. 141.
§ 65. When a ball is in curvilinear motion all parts of its
surface have not the same velocity; in case the parts of such a
ball are liable to be disintegrated by this force, then an accumu
lation of matter must take place about the middle of the ball
whilst at the poles, where there is hardly any motion at all, the
ball will be flattened. This accounts for the operation of the
potter's wheel and for the flattening of the earth, (originally in
a state of fusion) at the poles. 142.
The mechanism of mills and clocks (or watches) is based
upon the laws of the lever, the pendulum, curvilinear motion
and Centrifugal force. 143. 144.
