with those near the horizon, so Kepler “went
off at a tangent” and tried a totally new set
of ideas, which all reduced to the absurdity of a
refraction which vanished at the horizon. These
were followed by another set, involving either a constant
amount of refraction or one becoming infinite.
He then came to the conclusion that these geometrical
methods must fail because the refracted image is not
real, and determined to try by analogy only, comparing
the equally unreal image formed by a mirror with that
formed by refraction in water. He noticed how
the bottom of a vessel containing water appears to
rise more and more away from the vertical, and at
once jumped to the analogy of a concave mirror, which
magnifies the image, while a convex mirror was likened
to a rarer medium. This line of attack also failed
him, as did various attempts to find relations between
his measurements of refraction and conic sections,
and he broke off suddenly with a diatribe against
Tycho’s critics, whom he likened to blind men
disputing about colours. Not many years later
Snell discovered the true law of refraction, but Kepler’s
contribution to the subject, though he failed to discover
the actual law, includes several of the adopted “by-laws”.
He noted that atmospheric refraction would alter with
the height of the atmosphere and with temperature,
and also recognised the fact that rainbow colours
depend on the angle of refraction, whether seen in
the rainbow itself, or in dew, glass, water, or any
similar medium. He thus came near to anticipating
Newton. Before leaving the subject of Kepler’s
optics it will be well to recall that a few years later
after hearing of Galileo’s telescope, Kepler
suggested that for astronomical purposes two convex
lenses should be used, so that there should be a real
image where measuring wires could be placed for reference.
He did not carry out the idea himself, and it was
left to the Englishman Gascoigne to produce the first
instrument on this “Keplerian” principle,
universally known as the Astronomical Telescope.
In 1606 came a second treatise on the new star, discussing
various theories to account for its appearance, and
refusing to accept the notion that it was a “fortuitous
concourse of atoms”. This was followed
in 1607 by a treatise on comets, suggested by the comet
appearing that year, known as Halley’s comet
after its next return. He regarded comets as
“planets” moving in straight lines, never
having examined sufficient observations of any comet
to convince himself that their paths are curved.
If he had not assumed that they were external to the
system and so could not be expected to return, he
might have anticipated Halley’s discovery.
Another suggestive remark of his was to the effect
that the planets must be self-luminous, as otherwise
Mercury and Venus, at any rate, ought to show phases.
This was put to the test not long afterwards by means
of Galileo’s telescope.