s
of revolution, and their distances from the sun. Ultimately hit upon his
fanciful regular-solid hypothesis, and published his first book in 1597.
In 1599 was invited by Tycho to Prague, and there appointed Imperial
mathematician, at a handsome but seldom paid salary. Observed the new
star of 1604. Endeavoured to find the law of refraction of light from
Vitellio's measurements, but failed. Analyzed Tycho's observations to
find the true law of motion of Mars. After incredible labour, through
innumerable wrong guesses, and six years of almost incessant
calculation, he at length emerged in his two "laws"--discoveries which
swept away all epicycles, deferents, equants, and other remnants of the
Greek system, and ushered in the dawn of modern astronomy.

LAW I. _Planets move in ellipses, with the Sun in one focus._

LAW II. _The radius vector (or line joining sun and planet) sweeps out
equal areas in equal times._

Published his second book containing these laws in 1609. Death of
Rudolph in 1612, and subsequent increased misery and misfortune of
Kepler. Ultimately discovered the connection between the times and
distances of the planets for which he had been groping all his mature
life, and announced it in 1618:--

LAW III. _The square of the time of revolution (or year) of each planet
is proportional to the cube of its mean distance from the sun._

The book in which this law was published ("On Celestial Harmonies") was
dedicated to James of England. In 1620 had to intervene to protect his
mother from being tortured for witchcraft. Accepted a professorship at
Linz. Published the Rudolphine tables in 1627, embodying Tycho's
observations and his own theory. Made a last effort to overcome his
poverty by getting the arrears of his salary paid at Prague, but was
unsuccessful, and, contracting brain fever on the journey, died in
November, 1630, aged 59.

A man of keen imagination, indomitable perseverance, and uncompromising
love of truth, Kepler overcame ill-health, poverty, and misfortune, and
placed himself in the very highest rank of scientific men. His laws, so
extraordinarily discovered, introduced order and simplicity into what
else would have been a chaos of detailed observations; and they served
as a secure basis for the splendid erection made on them by Newton.

_Seven planets of the Ptolemaic system--_
Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn.

_Six planets of the Copernican system--_
M