Being thus left a widower with a ten-year-old daughter Susanna, and a boy Louis of half her age, he looked for a second wife to take charge of them.  He has given an account of eleven ladies whose suitability he considered.  The first, an intimate friend of his first wife, ultimately declined; one was too old, another an invalid, another too proud of her birth and quarterings, another could do nothing useful, and so on.  Number eight kept him guessing for three months, until he tired of her constant indecision, and confided his disappointment to number nine, who was not impressed.  Number ten, introduced by a friend, Kepler found exceedingly ugly and enormously fat, and number eleven apparently too young.  Kepler then reconsidered one of the earlier ones, disregarding the advice of his friends who objected to her lowly station.  She was the orphan daughter of a cabinetmaker, educated for twelve years by favour of the Lady of Stahrenburg, and Kepler writes of her:  “Her person and manners are suitable to mine; no pride, no extravagance; she can bear to work; she has a tolerable knowledge of how to manage a family; middle-aged and of a disposition and capability to acquire what she still wants”.

Wine from the Austrian vineyards was plentiful and cheap at the time of the marriage, and Kepler bought a few casks for his household.  When the seller came to ascertain the quantity, Kepler noticed that no proper allowance was made for the bulging parts, and the upshot of his objections was that he wrote a book on a new method of gauging—­one of the earliest specimens of modern analysis, extending the properties of plane figures to segments of cones and cylinders as being “incorporated circles”.  He was summoned before the Diet at Ratisbon to give his opinion on the Gregorian Reform of the Calendar, and soon afterwards was excommunicated, having fallen foul of the Roman Catholic party at Linz just as he had previously at Gratz, the reason apparently being that he desired to think for himself.  Meanwhile his salary was not paid any more regularly than before, and he was forced to supplement it by publishing what he called a “vile prophesying almanac which is scarcely more respectable than begging unless it be because it saves the Emperor’s credit, who abandons me entirely, and with all his frequent and recent orders in council, would suffer me to perish with hunger”.

In 1617 he was invited to Italy to succeed Magini as Professor of Mathematics at Bologna.  Galileo urged him to accept the post, but he excused himself on the ground that he was a German and brought up among Germans with such liberty of speech as he thought might get him into trouble in Italy.  In 1619 Matthias died and was succeeded by Ferdinand III, who again retained Kepler in his post.  In the same year Kepler reprinted his “Mysterium Cosmographicum,” and also published his “Harmonics” in five books dedicated to James I of England.  “The first geometrical, on the origin and demonstration