The foregoing rule has been also applied to estimate the magnifying power of the compound microscope. To this application, Mr. Magny, in the “Journal d’Economie pour le mois d’Aout 1753,” has made several objections: one or two of these I shall just mention; the first is the difficulty of ascertaining with accuracy the precise focus of a small lens; the second is the want of a fixed or known measure, with which to compare the focus when ascertained. These considerations, though apparently trifling, will be found of importance in the calculations which are relative to deep magnifiers. To this it may be further added, that the same standard or fixed measure cannot be assumed for a short-sighted, that is used for a well-constituted eye. To obviate these difficulties, and some errors in the methods which were recommended by Mess. Baker and Needham, Mr. Magny offers the following PROPOSITION. All convex lenses of whatsoever foci, double the apparent diameter of an object, provided that the object be at the focus of the glass on one side, and the eye be at the same distance, or on the focus of the glass, at the opposite side. EXPERIMENT. Take a double convex lens, of six or eight inches focus, and fix it as at A, Fig. 1, Plate II. A, into the piece A, which is fixed perpendicular to the rule F G, and may be slid along it by means of its socket: the rule is divided into inches and parts. Paste a piece of white paper, two or three tenths of an inch broad, and three inches long, on the board D; draw three lines with ink on this piece of paper, so as to divide it into four equal parts, taking care that the middle of the paper corresponds with the center of the lens. There is also a sliding eye-piece, which is represented at e. Take this apparatus into the darkest part of the room, but opposite to the window; direct the glass towards any remarkable and distant object which is out of doors, and move the sliding piece B, until the image of the object on the paper be sharp and clear. The distance between the face of the paper and the lens (which is shewn on the side of the rule by the divisions thereon) is the focus of the glass; now set the eye-piece e E to the same distance on the other side of the glass, then with one eye close to the sight at e, look at the magnified image of the lines, and with the other eye at the lines themselves: the image, seen by means of the glass, and expressed in the figure by the dotted lines, will be double the breadth of the same object seen by the natural eye. This will be found to be true, whatsoever is the focus of the lens with which the experiment is made. This experiment is rendered more simple to those who are not accustomed to observe with both eyes at the same time, by making use of half a lens, and placing the diameter perpendicular to the rule, as they may then readily view the magnified image and real object with the same glance of the eye, and thus compare them together with ease and accuracy.