138. Soon after Tycho’s death Kepler was appointed his successor as mathematician to the Emperor Rudolph (1602), but at only half his predecessor’s salary, and even this was paid with great irregularity, so that complaints as to arrears and constant pecuniary difficulties played an important part in his future life, as they had done during the later years at Gratz. Tycho’s instruments never passed into his possession, but as he had little taste or skill for observing, the loss was probably not great; fortunately, after some difficulties with the heirs, he secured control of the greater part of Tycho’s incomparable series of observations, the working up of which into an improved theory of the solar system was the main occupation of the next 25 years of his life. Before, however, he had achieved any substantial result in this direction, he published several minor works—for example, two pamphlets on a new star which appeared in 1604, and a treatise on the applications of optics to astronomy (published in 1604 with a title beginning _Ad Vitellionem Paralipomena quibus Astronomiae Pars Optica Traditur_ ...), the most interesting and important part of which was a considerable improvement in the theory of astronomical refraction (chapter II., § 46, and chapter V., § 110). A later optical treatise (the _Dioptrice_ of 1611) contained a suggestion for the construction of a telescope by the use of two convex lenses, which is the form now most commonly adopted, and is a notable improvement on Galilei’s instrument (chapter VI., § 118), one of the lenses of which is concave; but Kepler does not seem himself to have had enough mechanical skill to actually construct a telescope on this plan, or to have had access to workmen capable of doing so for him; and it is probable that Galilei’s enemy Scheiner (chapter VI., §§ 124, 125) was the first person to use (about 1613) an instrument of this kind. [Illustration: KEPLER.]