To determine the radius or focus of a concave lens, apply to its surface a convex lens of the same focus, and holding the two together as one glass, between the thumb and finger, at some distance before the eye, give the hand a gentle motion to and fro, and if the objects looked at through the lenses now in contact appear fixed, equal, and of their natural size, then is the focus of the one correspondent to that of the other; but if the convex lens is not of the same focal length as the concave to which it is thus applied, then all objects looked upon will appear to shake and have a tremulous motion. Another method of ascertaining whether one concave lens is of the same number, and worked in tools of the same radius as another, is to hold one in each hand, placing their edges against each other, with their centres in a parallel line; now withdraw ten or twelve feet from the window, and observe the top and bottom bars of a square of glass: if they appear equal and uniform in all their parts, parallel to each other, and agreeing with the other squares in the window, then are they of the same radius; but if they do not match, the bars will appear disjointed, and higher or lower in one square than in the other. The trial box of sights will be found very useful in making these experiments. Brazil pebbles, or crystallized quartz, are imported to this country in rough blocks; these are cut or slit, by the aid of pulverized diamond, into slabs or pieces, of the diameter required. Those pieces in which bubbles, waves, or blemishes appear, are thrown aside by the optician who is tenacious of his fair fame, as their imperfections become more apparent in every after-stage of their progress; and when polished, centred, and shaped for the spectacle-frame, they are really improper to be used at all; nevertheless, the needy, or dishonest, rather than lose a fraction of their gains, often persist in working up such imperfect material, and harping upon their being pebble—real pebble—palm them off upon the uninitiated as genuine articles. Pebbles have the following important advantages: they are of equal density, and exceedingly hard, firm, and clear; their surfaces are not liable to become misty or scratched (which circumstance alone often compels a change of glasses): they are of a pure, cool nature, and shew this contrast to glass (which is, on the contrary, produced by the action of artificial heat) in the touch of the finger or tongue to their surfaces.[3] They are, in consequence of these properties, calculated to suit the sight for a longer period than glass; but they need not be thrown aside, when, from the indications already referred to, we find an increase of magnifying power is required, as they can be re-worked readily enough to meet the requirement of the eyes, and at an expense scarcely more than a new pair of glasses, or about one-third of their original cost. The directions for ascertaining the focus of concave or