The concave-mirror system now gained a decided ascendant, and was brought to unexampled perfection by James Short of Edinburgh during the years 1732-68. Its resources were, however, first fully developed by William Herschel. The energy and inventiveness of this extraordinary man marked an epoch wherever they were applied. His ardent desire to measure and gauge the stupendous array of worlds which his specula revealed to him, made him continually intent upon adding to their "space-penetrating power" by increasing their light-gathering surface. These, as he was the first to explain,[308] are in a constant proportion one to the other. For a telescope with twice the linear aperture of another will collect four times as much light, and will consequently disclose an object four times as faint as could be seen with the first, or, what comes to the same, an object equally bright at twice the distance. In other words, it will possess double the space-penetrating power of the smaller instrument. Herschel's great mirrors--the first examples of the giant telescopes of modern times--were then primarily engines for extending the bounds of the visible universe; and from the sublimity of this "final cause" was derived the vivid enthusiasm which animated his efforts to success. It seems probable that the seven-foot telescope constructed by him in 1775--that is within little more than a year after his experiments in shaping and polishing metal had begun--already exceeded in effective power any work by an earlier optician; and both his skill and his ambition rapidly developed. His efforts culminated, after mirrors of ten, twenty, and thirty feet focal length had successively left his hands, in the gigantic forty-foot, completed August 28, 1789. It was the first reflector in which only a single mirror was employed. In the "Gregorian" form, the focussed rays are, by a second reflection from a small concave[309] mirror, thrown _straight back_ through a central aperture in the larger one, behind which the eye-piece is fixed. The object under examination is thus seen in the natural direction. The "Newtonian," on the other hand, shows the object in a line of sight at right angles to the true one, the light collected by the speculum being diverted to one side of the tube by the interposition of a small plane mirror, situated at an angle of 45° to the axis of the instrument. Upon these two systems Herschel worked until 1787, when, becoming convinced of the supreme importance of economising light (necessarily wasted by the second reflection), he laid aside the small mirror of his forty-foot then in course of construction, and turned it into a "front-view" reflector. This was done--according to the plan proposed by Lemaire in 1732--by slightly inclining the speculum so as to enable the image formed by it to be viewed with an eye-glass fixed at the upper margin of the tube. The observer thus stood with his back turned to the object he was engaged in scrutinising.