not been confined to any special epoch or country, but the obvious
result in Kepler's case was to compel him to apply himself to less
expensive matters than the Planetary Tables, and among these must be
included not only the horoscopes or nativities, which owing to his
reputation were always in demand, but also other writings which probably
did not pay so well. In 1604 he published "A Supplement to Vitellion,"
containing the earliest known reasonable theory of optics, and
especially of dioptrics or vision through lenses. He compared the
mechanism of the eye with that of Porta's "Camera Obscura," but made no
attempt to explain how the image formed on the retina is understood by
the brain. He went carefully into the question of refraction, the
importance of which Tycho had been the first astronomer to recognise,
though he only applied it at low altitudes, and had not arrived at a
true theory or accurate values. Kepler wasted a good deal of time and
ingenuity on trial theories. He would invariably start with some
hypothesis, and work out the effect. He would then test it by
experiment, and when it failed would at once recognise that his
hypothesis was _a priori_ bound to fail. He rarely seems to have noticed
the fatal objections in time to save himself trouble. He would then at
once start again on a new hypothesis, equally gratuitous and equally
unfounded. It never seems to have occurred to him that there might be a
better way of approaching a problem. Among the lines he followed in this
particular investigation were, first, that refraction depends only on
the angle of incidence, which, he says, cannot be correct as it would
thus be the same for all refracting substances; next, that it depended
also on the density of the medium. This was a good shot, but he
unfortunately assumed that all rays passing into a denser medium would
apparently penetrate it to a depth depending only on the medium, which
means that there is a constant ratio between the tangents, instead of
the sines, of the inclination of the incident and refracted rays to the