It will be seen that the variations between the two screen patterns on _C_ and _D_, together with the difference between them, give accurately the performance of each point of the objective represented by an aperture in the screen. And similar investigations by substantially the same method may be extended to the astigmatic variations, to the general color correction, and to the difference in the aberrations for the several colors. The original papers cited should be consulted for the details of applying this very precise and interesting test. It gives an invaluable record of the detailed corrections of an objective, and while it is one with which the ordinary observer has little concern there are times when nothing else can give with equal precision the necessary record of performance. There are divers other tests used for one purpose or another in examining objectives and mirrors, but those here described are ample for nearly all practical purposes, and indeed the first two commonly disclose all that it is necessary to know. Now and then one has to deal with an objective which is unmitigatedly dirty. It can be given a casual preliminary cleaning in the way already mentioned, but sometimes even this will not leave it in condition for testing. Then one must get down to the bottom of things and make a thorough job of it. The chief point to remember in undertaking this is that the thing which one is cleaning is glass, and very easy to scratch if one rubs dust into it, but quite easy to clean if one is careful. The second thing to be remembered is that once cleaned it must be replaced as it was before and not in some other manner. The possessor of a dirty objective is generally advised to take it to the maker or some reliable optician. If the maker is handy, or an optician of large experience in dealing with telescope objectives is available, the advice is good, but there is no difficulty whatever in cleaning an objective with the exercise of that ordinary care which the user of a telescope may be reasonably expected to possess. It is a fussy job, but not difficult, and the best advice as to how to clean a telescope objective is to “tub” it, literally, if beyond the stage where the superficial wiping described is sufficient. To go about the task one first sets down the objective in its cell on a horizontal surface and removes the screws that hold in the retaining ring, or unscrews the ring itself as the case may be. This leaves the cell and objective with the latter uppermost and free to be taken out. Prepare on a table a pad of anything soft, a little smaller than the objective, topping the pad with soft and clean old cloth; then, raising up the cell at an edge, slip the two thumbs under it and lay the fingers lightly on the outer lens of the objective, then invert the whole affair upon the pad and lift off the cell, leaving the objective on its soft bed.