normal. Experiment proved that this gave too high values for refraction
near the vertical compared 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