present theory of colour
has in its favour the failure of Newton's corpuscular hypothesis and of
Goethe's anti-mathematical hypothesis; but the field of conjecture
remains open. On the other hand, Newton's proof that the solar system is
controlled by a central force, was supported by the demonstration that a
force having any other direction could not have results agreeing with
Kepler's second law of the planetary motions, namely, that, as a planet
moves in its orbit, the areas described by a line drawn from the sun to
the planet are proportional to the times occupied in the planet's
motion. When a planet is nearest to the sun, the area described by such
a line is least for any given distance traversed by the planet; and then
the planet moves fastest: when the planet is furthest from the sun, the
area described by such a line is greatest for an equal distance
traversed; and then the planet moves slowest. This law may be deduced
from the hypothesis of a central force, but not from any other; the
proof, therefore, as Mill says, satisfies the method of Difference.

Apparently, to such completeness of demonstration certain conditions are
necessary: the possibilities must lie between alternatives, such as A or
not-A, or amongst some definite list of cases that may be exhausted,
such as equal, greater or less. He whose hypothesis cannot be brought to
such a definite issue, must try to refute whatever other hypotheses are
offered, and naturally he will attack first the strongest rivals. With
this object in view he looks about for a "crucial instance," that is, an
observation or experiment that stands like a cross (sign-post) at the
parting of the ways to guide us into the right way, or, in plain words,
an instance that can be explained by one hypothesis but not by another.
Thus the phases of Venus, similar to those of the Moon, but concurring
with great changes of apparent size, presented, when discovered by
Galileo, a crucial instance in favour of the Copernican hypothesis, as
against the Ptolemaic, so far at least as to prove that Venus revolved
around the Sun inside the orbit of the Earth. Foucault's experiment
determining the velocity of Light (cited in the last chapter) was at
first intended as an _experimentum crucis_ to decide between the
corpuscular and undulatory theories; and answered this purpose, by
showing that the velocity of a beam passed through water was less than
it should be by the former, but in agreement wi