[3] Scheiner also devised a crude parallactic mount which he used in his solar observations, probably the first European to grasp the principle of the equatorial. It was only near the end of the century that Roemer followed his example, and both had been anticipated by Chinese instruments with sights. But the new instrument despite its much larger field and far greater possibilities of power, brought with it some very serious problems. With increased power came greatly aggravated trouble from spherical aberration and chromatic aberration as well, and the additive aberrations of the eye lens made matters still worse. The earlier Keplerian instruments were probably rather bad if the drawings of Fontana from 1629 to 1636 fairly represent them. If one may judge from the course of developments, the first great impulse to improvement came with the publication of Descartes’ (1596-1650) study of dioptrics in 1637. Therein was set forth much of the theory of spherical aberration and astronomers promptly followed the clues, practical and impractical, thus disclosed. Without going into the theory of aberrations the fact of importance to the improvement of the early telescope is that the longitudinal spherical aberration of any simple lens is directly proportional to its thickness due to curvature. Hence, other things being equal, the longer the focus for the same aperture the less the spherical aberration both absolutely and relatively to the image. Further, although Descartes knew nothing of chromatic aberration, and the colored fringe about objects seen through the telescope must then have seemed altogether mysterious, it, also, was greatly relieved by lengthening the focus. For the chromatic circle produced by a simple lens of given diameter has a radial width substantially irrespective of the focal length. But increasing the focal length increases in exact proportion the size of the image, correspondingly decreasing the relative effect of the chromatic error. Descartes also suggested several designs of lenses which would be altogether free of spherical aberration, formed with elliptical or hyperbolic curvature, and for some time fruitless efforts were made to realize this in practice. It was in fact to be near a century before anyone successfully figured non-spherical surfaces. It was spherical quite as much as chromatic aberration that drove astronomers to long telescopes. Meanwhile the astronomical telescope fell into better hands than those of Scheiner. The first fully to grasp its possibilities was William Gascoigne, a gallant young gentleman of Middleton, Yorkshire, born about 1620 (some say as early as 1612) and who died fighting on the King’s side at Marston Moor, July 2, 1644. To him came as early as 1638 the inspiration of utilizing the real focus of the objective for establishing a telescopic sight. [Illustration: FIG. 6.—Diagram of Terrestrial Ocular.]