he cask. From this accident, Kepler was led to study the subject of
gauging, and to write the book which we have mentioned, and which
contains the earliest specimens of the modern analysis.

About this period, Kepler was summoned to the Diet at Ratisbon, to give
his opinion on the reformation of the kalendar, and he published a short
essay on the subject; but though the Government did not scruple to avail
themselves of his services, yet his pension was allowed to fall in
arrear, and, in order to support his family, he was obliged to publish
an Almanac, suited to the taste of the age. "In order," says he, "to
defray the expense of the Ephemeris for two years,[49] I have been
obliged to compose _a vile prophesying Almanac, which is scarcely more
respectable than begging_, unless from its saving the Emperor's credit,
who abandons me entirely, and would suffer me to perish with hunger."

[49] These Ephemerides, from 1617 to 1620, were published at Linz
in 1616. The one for 1620 was dedicated to Baron Napier of
Merchiston.

Although Kepler's residence at Linz was rendered uncomfortable by the
Roman Catholics, who had excommunicated him on account of his refusing
to subscribe to some opinions respecting the ubiquity of our Saviour,
or, as others maintain, on account of some opinions which he had
expressed respecting transubstantiation, yet he refused, in 1617, to
accept of an invitation to fill the mathematical chair at Bologna. The
prospect of his fortune being bettered by such a change could not
reconcile him to live in a country where his freedom of speech and
manners might expose him to suspicion; and he accordingly declined, in
the most respectful manner, the offer which was made him.

CHAPTER III.

_Kepler's continued Embarrassments--Death of Mathias--Liberality of
Ferdinand--Kepler's "Harmonies of the World"--The Epitome of the
Copernican Astronomy--It is prohibited by the Inquisition--Sir
Henry Wotton, the British Ambassador, invites Kepler to England--He
declines the Invitation--Neglect of Genius by the English
Government--Trial of Kepler's Mother--Her final Acquittal--And
Death at the age of Seventy-five--The States of Styria burn
publicly Kepler's Calendar--He receives his Arrears of Salary from
Ferdinand--The Rudolphine Tables published in 1628--He receives a
Gold Chain from the Grand Dulce of Tuscany--He is Patronised by the
Duke of