un and Moon." Astronomers had long been
perplexed with the refraction of the atmosphere, and so little was known
of the general subject, as well as of this branch of it, that Tycho
believed the refraction of the atmosphere to cease at 45 deg. of altitude.
Even at the beginning of the second century, Claudius Ptolemy of
Alexandria had unravelled its principal mysteries, and had given in his
Optics a theory of astronomical refraction more complete than that of
any astronomer before the time of Cassini;[46] but the MSS. had
unfortunately been mislaid, and Alhazen and Vitellio and Kepler were
obliged to take up the subject from its commencement. Ptolemy had not
only determined that the refraction of the atmosphere had gradually
increased from the zenith to the horizon, but he had measured with
singular accuracy the angles of refraction for water and glass, from a
perpendicular incidence to a horizontal one.

[46] Cassini was born in 1625, and died in 1712.

Kepler treated this branch of science in his own peculiar way,
"hunting down," as he expressed it, every hypothesis which his fertile
imagination had successively presented to him. In his various attempts
to discover the law of refraction, or a measure of it, as varying with
the density of the body and the angle of incidence of the light, he was
nearer the goal, in his first speculation, than in any of the rest; and
he seems to have failed in consequence of his not separating the
question as it related to density from the question as it related to
incidence. "I did not leave untried," says he, "whether, by assuming a
horizontal refraction according to the density of the medium, the rest
would correspond to the sines of the distances from a vertical
direction, but calculation proved that it was not so: and, indeed, there
was no occasion to have tried it, for thus the _refraction would
increase according to the same law in all mediums, which is contradicted
by experiment_."

Although completely foiled in his search after the law of refraction,
which was subsequently discovered by Willebrord Snell, and sometime
afterwards by James Gregory, he was, singularly successful in his
inquiries respecting vision. Regarding the eye as analogous in its
structure with the camera obscura of Baptista Porta, he discovered that
the images of external objects were painted in an inverted position on
the retina, by the union of the pencils of rays which issued from every
point of the