It will be at once seen that the axes of the pencils of rays from all parts of the object, as shown by the heavy lines, act as if they diverged from the optical center of the objective, but diverging still more by refraction through the concave eye lens _e_, fall mostly outside the pupil of the observer’s eye. In fact the field is approximately measured by the angle subtended by the pupil from the center of _o_. To the credit of the Galilean form may be set down the convenient erect image, a sharp, if small, field somewhat bettered by a partial compensation of the aberrations of the objective by the concave eye lens, and good illumination. For a distant object the lenses were spaced at the difference of their focal lengths, and the magnifying power was the ratio of these, _f_{o}/f_{e}_. [Illustration: FIG. 4.—Diagram of Galileo’s Telescope.] But the difficulty of obtaining high power with a fairly sizeable field was ultimately fatal and the type now survives only in the form of opera and field glasses, usually of 2 to 5 power, and in an occasional negative eye lens for erecting the image in observatory work. Practically all the modern instruments have achromatic objectives and commonly achromatic oculars. [Illustration: FIG. 5.—Diagram of Kepler’s Telescope.] The necessary step forward was made by Johann Kepler (1571-1630), the immortal discoverer of the laws of planetary motion. In his _Dioptrice_ (1611) he set forth the astronomical telescope, substantially, save for the changes brought by achromatism, as it has been used ever since. His arrangement was that of Fig. 5 in which the letters have the same significance as in Fig. 4. There are here three striking differences from the Galilean form. There is a real image in the front focus of the eye lens _e_, the rays passing it are refracted inwards instead of outwards, to the great advantage of the field, and any object placed in the image plane will be magnified together with the image. The first two points Kepler fully realized, the third he probably did not, though it is the basis of the micrometer. The lenses _o_ and _e_ are obviously spaced at the sum of their focal lengths, and as before the magnifying power is the ratio of these lengths, the visible image being inverted. Kepler, so far as known, did not actually use the new telescope, that honor falling about half a dozen years later, to Christopher Scheiner, a Jesuit professor of mathematics at Ingolstadt, best known as a very early and most persistent, not to say verbose, observer of sun spots. His _Rosa Ursina_ (1630) indicates free use of Kepler’s telescope for some years previously, in just what size and power is uncertain.[3] Fontana of Naples also appears to have been early in the field.