The particular defect due to want of centering in a lens may be observed by using it as the objective of a telescope, and observing a star slightly out of focus. The interference fringes will not be concentric circles unless the lens is properly centred. I ought to say that I have not looked into the theory of this, but have merely taken it as a generally admitted fact. The diseases of lenses and the modes of treating them are dealt with in a book by Messrs. Cook of York, entitled On the Adjustment and Testing of Telescopic Objectives. The final process of figuring will be dealt with later on (Sec. Sec. 66 and 67), as it applies not only to lenses but to mirrors, prisms, etc. If the instructions given have been carefully carried out on a 2-inch lens, it should perform fairly well, and possibly perfectly, without any further adjustment of the glass. Sec. 64. Preparation of Small Lenses, where great Accuracy is not of the first Importance. Such lenses may generally be made out of bits of good plate or sheet glass, and are of constant use in the physical laboratory. They may be purchased so cheaply, however, that only those who have the misfortune to work in out-of-the-way places need be driven to make them. Suitable glass having been obtained and the curves calculated from the index of refraction, as obtained by any of the ordinary methods applicable to plates (the microscope method, in general, is quite good enough), squares circumscribing the desired circles are cut out by the help of a diamond. [Footnote: Glazebrook and Shaw's Practical Physics, p. 383 (4th ed.).] The squares are roughly snipped by means of a pair of pliers or spectacle-maker's shanks. The rough circles are then mounted on the end of a brass or iron rod of rather greater diameter than the finished lenses are to possess. This mounting is best done by centering cement. The discs are then dressed circular on a grindstone, the rod serving both as a gauge and handle. A sufficient number of these discs having been prepared, a pair of brass tools of the form shown in the sketch (Fig. 55), and of about the proper radius of curvature, are made. One of these tools is used as a support for the glass discs. Fig. 55. A compass being set to scribe circles of the same diameter as the glass discs, centre marks are made on the surface of the appropriate tool, circles are drawn on this, and facets are filed or milled (for which the spiral head of the milling machine is excellent). In the case of concave supporting surfaces, i.e. in making concave lenses, I apprehend filing would be difficult, and the facets would have to be made by a rose cutter or mill; but if the discs are fairly round, then, in fact, no facets are required.