This done, having applied the eye to the eye-piece and directed all his attention to the telescopic image of the advertisement, Herschel did not perceive that the taking away and then replacing the screen made the least change in the brightness or definition of the letters. It was therefore of no consequence, in the one instance as well as in the other, whether the immense quantity of solar rays crossed each other at the very place where, _in another direction_, the rays united that formed the image of the letters. I have marked in Italics the words that especially show in what this curious experiment differs from the previous experiments, and yet does not entirely contradict them. In this instance the rays of various origin, those coming from the advertisement and from the sun, crossed each other respectively in almost rectangular directions; during the comparative examination of the stars with convex and with concave eye-pieces, the rays that seemed to have a mutual influence, had a common origin and crossed each other at very acute angles. There seems to be nothing, then, in the difference of the results at which we need to be much surprised. Herschel increased the catalogue, already so extensive, of the mysteries of vision, when he explained in what manner we must endeavour to distinguish separately the two members of certain double stars very close to each other. He said if you wish to assure yourself that _e_ Coronae is a double star, first direct your telescope to _a_ Geminorum, to _z_ Aquarii, to _m_ Draconis, to _r_ Herculis, to _a_ Piscium, to _e_ Lyrae. Look at those stars for a long time, so as to acquire the habit of observing such objects. Then pass on to _x_ Ursae majoris, where the closeness of the two members is still greater. In a third essay select _i_ Bootis (marked 44 by Flamsteed and _i_ in Harris's maps)[21], the star that precedes _a_ Orionis, _n_ of the same constellation, and you will then be prepared for the more difficult observation of _e_ Coronae. Indeed _e_ Coronae is a sort of miniature of _i_ Bootis, which may itself be considered as a miniature of _a_ Gem. (_Philosophical Transactions_, 1782, p. 100.) As soon as Piazzi, Olbers, and Harding had discovered three of the numerous telescopic planets now known, Herschel proposed to himself to determine their real magnitudes; but telescopes not having then been applied to the measurement of excessively small angles, it became requisite, in order to avoid any illusion, to try some experiments adapted to giving a scale of the powers of those instruments. Such was the labour of that indefatigable astronomer, of which I am going to give a compressed abridgment.