In this figure ABCD represent the tube of the 6 inch telescope, CD, the plate object-glass, F the first focus of rays, _de_ the fluid concave lens, distant from the former 24 inches. The focal length MF being 48, and consequently, as 48 : 6 :: 24 : 3 inches, the diameter of the fluid lens. The resulting compound focus is 62.5 inches. It is obvious, therefore, that the rays _df_, _ef_, arrive at the focus under the same convergency, and with the same light as if they proceeded from a lens of 6 inches diameter, placed at a distance beyond the object-glass CD (as GH,) determined by producing those rays till they meet the sides of the tube in GH, namely at 62.5 inches beyond the fluid lens. Hence, it is obvious, the rays will converge as they would do from an object-glass GH of the usual kind with a focus of 10 feet 5 inches. We have thus, therefore, shortened the tube 38.5 inches, or have at least the advantage of a focus 38.5 inches longer than our tube; and the same principle may be carried much farther, so as to reduce the usual length of refracting telescopes nearly one half without increasing the aberration in the first glass beyond the least that can possibly belong to a telescope of the usual kind of the whole length. It should likewise be observed that the adjustment for focus may be made either in the usual way, or by a slight movement of the fluid lens, as in the Gregorian Reflectors, by means of the small speculum. Mr. Barlow afterwards constructed another and a larger telescope on the same principle, the clear aperture of which is 7.8 inches. Its tube is 11 feet, which, together with the eye-piece, makes the whole length 12 feet, but its effective focus is on the principle stated above, 18 feet. It carries a power of 700 on the closest double stars in South’s and Herschel’s catalogue, and the stars are, with that power, round and defined, although the field is not then so bright as could be desired. The telescope is mounted on a revolving stand, which works with considerable accuracy as an azimuth and altitude instrument. To give steadiness to the stand it has been made substantial and heavy; its weight by estimation being 400 pounds, and that of the telescope 130 pounds, yet its motions are so smooth, and the power so arranged, that it may be managed by one person with the greatest ease, the star being followed by a slight touch, scarcely exceeding that of the keys of a piano-forte. The focal length of the plate lens is 78 inches, and of the fluid lens 59.8 inches--which at the distance of 40 inches produce a focal length of 104 inches, a total length of 12 feet, and an equivalent focus of 18 feet. The curves of the parallel meniscus checks for containing the fluid are--30 inches, and 144 inches, the latter towards the eye. The curves for the plate lens are 56.4 and 144. There is an interior tube 5 inches diameter, and 3 feet 6 inches long, which carries the cell in which the fluid is enclosed, and an