forded him an opportunity of obtaining access to the numerous
astronomical observations made by Tycho, which were of great assistance
to him in the investigation of the subject which he had chosen--viz. the
laws which govern the motions of the planets, and the form and size of
the planetary orbits.

As an acknowledgment of the Emperor's great kindness, the two
astronomers resolved to compute a new set of astronomical tables, and in
honour of his Majesty they were to be called the 'Rudolphine Tables.'
This project pleased the Emperor, who promised to defray the expense of
their publication. Logomontanus, Tycho's chief assistant, had entrusted
to him that portion of the work relating to observations on the stars,
and Kepler had charge of the part which embraced the calculations
belonging to the planets and their orbits. This important work had
scarcely been begun when the departure of Logomontanus, who obtained an
appointment in Denmark, and the death of Tycho Brahe in October 1601,
necessitated its suspension for a time. Kepler was appointed Chief
Mathematician to the Emperor in succession to Tycho--a position of
honour and distinction, and to which was attached a handsome salary,
that was paid out of the Imperial treasury. But owing to the continuance
of expensive wars, which entailed a severe drain upon the resources of
the country, the public funds became very low, and Kepler's salary was
always in arrear. This condition of things involved him in serious
pecuniary difficulties, and the responsibility of having to maintain an
increasing family added to his anxieties. It was with the greatest
difficulty that he succeeded in obtaining payment of even a portion of
his salary, and he was reduced to such straits as to be under the
necessity of casting nativities in order to obtain money to meet his
most pressing requirements.

In 1609 Kepler published his great work, entitled 'The New Astronomy;
or, Commentaries on the Motions of Mars.' It was by his observation of
Mars, which has an orbit of greater eccentricity than that of any of the
other planets, with the exception of Mercury, that he was enabled, after
years of patient study, to announce in this volume the discovery of two
of the three famous theorems known as Kepler's Laws. The first is, that
all the planets move round the Sun in elliptic orbits, and that the orb
occupies one of the foci. The second is, that the radius-vector, or
imaginary line joining the centre of