Here, in the one case, the increase of half an inch in the diameter of the object-glass, adds about £16. to the expense; and in the other case no less than £26. 5s. The proportion of light in those two telescopes, compared with that of 2-3/4 inches aperture, is as follows:--The square of the 2-3/4 object-glass is 7.56; that of 3-1/4, 10.56, and that of the 3-3/4, 14.06; so that the light admitted by the 3-1/4 compared with the 2-3/4 aperture, is nearly as 10 to 7; and the light admitted by the 3-3/4 object-glass is nearly double that of the 2-3/4 aperture, and will bear nearly a proportional increase of magnifying power. 3. _The 5 feet Achromatic telescope._ The focal length of the object-glass of this telescope is 5 feet 3 inches, and the diameter of its aperture 3-8/10 inches. The usual magnifying powers applied to it are, for land objects 65 times; and for celestial objects, 110, 190, 250, and sometimes one or two higher powers. The quantity of light it possesses is not much larger than that of the 3-1/2 feet telescope, with 3-3/4 inches aperture; but the larger focal length of this telescope is considered to be an advantage; since the longer the focus of the object-glass, the less will be its chromatic and spherical aberrations, and the larger may be the eye-glasses, and the flatter the field of view. The following are the prices of these telescopes as marked in Mr. Tulley’s catalogue. £ s. d. 5 feet telescopes 3-3/4 inches aperture, on an universal equatorial stand, with achromatic finder, 4 eye pieces for astronomical purposes, and 1 for day objects to vary the power, packed in a mahogany box 100 guineas to 157 10 0 7 feet ditto, 5 inches aperture, on a newly improved universal equatorial stand, 6 eye pieces for astronomical purposes, and 1 for day objects to vary the magnifying power, with achromatic finder, and Troughton’s Micrometer 207 5 0 The above are all the kinds of achromatic telescopes _generally_ made by the London opticians. Those of the larger kind, as 5 and 7 feet telescopes, and the 3-1/2 feet with 3-3/4 inches aperture, are generally made to order, and are not always to be procured. But the 2-1/2 and 3-1/2 feet achromatics of 2-3/4 inches aperture, are generally to be found ready-made at most of the optician’s shops in the metropolis. The prices of these instruments are nearly the same in most of the optician’s shops in London. Some of them demand a higher price, but few of them are ever sold lower than what has been stated above, unless in certain cases, where a discount is allowed. [Illustration: _figure 57._]