The lenses in the eye-pieces formerly described, though stated to be plano-convexes, are for the most part _crossed glasses_, that is ground on tools of a long focus on the one side, and to a short focus on the other. The construction of the eye-piece of the Dutch telescope above described, is one which might be adopted with a good effect in most of our achromatic telescopes; and I am persuaded, from the application I have made of it to various telescopes, that it is even superior, in distinctness and accuracy, and in the _flatness of field_ which it produces to the eye-piece in common use. The two astronomical eye-pieces of which it consists, when applied to large achromatic telescopes, perform with great accuracy, and are excellently adapted for celestial observations. SECT. 3.--DESCRIPTION OF THE PANCRATIC EYE-TUBE. From what we have stated, when describing the common terrestrial eye-piece now applied to achromatic instruments, (p. 349, fig. 79.), it appears obvious, that any variety of magnifying powers, within certain limits, may be obtained by removing the set of lenses CD, fig. 79, nearer to or farther from the tube which contains the lenses A and B, on the same principle as the magnifying power of a compound microscope is increased by removing the eye-glasses to a greater distance from the object-lens. If then, the pair of eye-lenses CD be attached to an inner tube that will draw out and increase their distance from the inner pair of lenses, as the tube _a b c d_, the magnifying power may be indefinitely increased or diminished, by pushing in or drawing out the sliding tube, and a scale might be placed on this tube, which, if divided into equal intervals, will be a scale of magnifying powers, by which the power of the telescope will be seen at every division, when the lowest power is once determined.