he meridian at the opposite point of its apparent circle about
the polestar. Half the sum of these angles gives the latitude of the
place of observation.

As illustrating the accuracy of Tycho's observations, it may be noted
that he rediscovered a third inequality of the moon's motion at its
variation, he, in common with other European astronomers, being then
quite unaware that this inequality had been observed by an Arabian
astronomer. Tycho proved also that the angle of inclination of the
moon's orbit to the ecliptic is subject to slight variation.

The very brilliant new star which shone forth suddenly in the
constellation of Cassiopeia in the year 1572, was made the object of
special studies by Tycho, who proved that the star had no sensible
parallax and consequently was far beyond the planetary regions. The
appearance of a new star was a phenomenon not unknown to the ancients,
since Pliny records that Hipparchus was led by such an appearance
to make his catalogue of the fixed stars. But the phenomenon is
sufficiently uncommon to attract unusual attention. A similar phenomenon
occurred in the year 1604, when the new star--in this case appearing in
the constellation of Serpentarius--was explained by Kepler as probably
proceeding from a vast combustion. This explanation--in which Kepler is
said to have followed. Tycho--is fully in accord with the most recent
theories on the subject, as we shall see in due course. It is surprising
to hear Tycho credited with so startling a theory, but, on the other
hand, such an explanation is precisely what should be expected from
the other astronomer named. For Johann Kepler, or, as he was originally
named, Johann von Kappel, was one of the most speculative astronomers of
any age. He was forever theorizing, but such was the peculiar quality of
his mind that his theories never satisfied him for long unless he could
put them to the test of observation. Thanks to this happy combination
of qualities, Kepler became the discoverer of three famous laws of
planetary motion which lie at the very foundation of modern astronomy,
and which were to be largely instrumental in guiding Newton to his
still greater generalization. These laws of planetary motion were vastly
important as corroborating the Copernican theory of the universe,
though their position in this regard was not immediately recognized
by contemporary thinkers. Let us examine with some detail into their
discovery, meantime catching