icular height of the triangle from the base AC. (Fig. 70.)
Now the blow at A, being along the base, has no effect upon _h_; and
consequently the area remains just what it would have been without the
blow. A blow directed to any point other than C would at once alter the
area of the triangle.

One interesting deduction may at once be drawn. If gravity were a
radiant force emitted from the sun with a velocity like that of light,
the moving planet would encounter it at a certain apparent angle
(aberration), and the force experienced would come from a point a little
in advance of the sun. The rate of description of areas would thus tend
to increase; whereas in reality it is constant. Hence the force of
gravity, if it travel at all, does so with a speed far greater than that
of light. It appears to be practically instantaneous. (Cf. "Modern Views
of Electricity," Sec. 126, end of chap. xii.) Again, anything like a
retarding effect of the medium through which the planets move would
constitute a tangential force, entirely un-directed towards the sun.
Hence no such frictional or retarding force can appreciably exist. It
is, however, conceivable that both these effects might occur and just
neutralize each other. The neutralization is unlikely to be exact for
all the planets; and the fact is, that no trace of either effect has as
yet been discovered. (See also p. 176.)

The planets are, however, subject to forces not directed towards the
sun, viz. their attractions for each other; and these perturbing forces
do produce a slight discrepancy from Kepler's second law, but a
discrepancy which is completely subject to calculation.

No. 2. Kepler's first law proves that this central force diminishes in
the same proportion as the square of the distance increases.

To prove the connection between the inverse-square law of distance, and
the travelling in a conic section with the centre of force in one focus
(the other focus being empty), is not so simple. It obviously involves
some geometry, and must therefore be left to properly armed students.
But it may be useful to state that the inverse-square law of distance,
although the simplest possible law for force emanating from a point or
sphere, is not to be regarded as self-evident or as needing no
demonstration. The force of a magnetic pole on a magnetized steel scrap,
for instance, varies as the inverse cube of the distance; and the curve
described by such a particle would be quite dif