_Effects of Heat._--The preceding changes in glass when isolated appear very simple, and their remedy, to keep the proper diameter perpendicular, is so obvious that it may seem surprising that they should have given origin to any embarrassment. In fact it is now desirable to have a disk in which they are well marked. But in practice they are complicated in the most trying manner with variations produced by heat pervading the various parts of the glass unequally. The following case illustrates the effects of heat:-- [Illustration: Fig. 4. Effects of Heat on a Reflecting Surface.] A 15-1/2 inch mirror, which was giving at its centre of curvature a very fine image (_a_, Fig. 4) of an illuminated pin-hole, was heated at the edge by placing the right hand on the back of the mirror, at one end of the horizontal diameter. In a few seconds an arc of light came out from the image as at _b′_, and on putting the left hand on the other extremity of the same diameter the appearance _c′_ was that of two arcs of light crossing each other, and having an image at each intersection. The mirror did not recover its original condition in ten minutes. Another person on a subsequent occasion touching the ends of the perpendicular diameter at the same time that the horizontal were warmed, caused the image _d′_ to become somewhat like two of _c′_, put at right angles to each other. A little distance outside the focus the complementary appearances, _b_, _c_, _d_, were found. By unsymmetrical warming still more remarkable forms emerged in succession, some of which were more like certain nebulæ with their milky light, than any regular geometrical figure. If the glass had, after one of these experiments, been immediately put on the polishing machine and re-polished, the changes in surface would to a certain extent have become permanent, as in Chinese specula, and the mirror would have required either re-grinding or prolonged polishing to get rid of them. This occurred unfortunately very frequently in the earlier stages of this series of experiments, and gave origin on one occasion to a surface which could only show the image of a pin-hole as a lozenge (_b_, Fig. 5), with an image at each angle inside the focus, and as an image a with four wings outside. [Illustration: Fig. 5. Effects of Heat rendered permanent.] But it must not be supposed that such apparent causes as these are required to disturb a surface injuriously. Frequently mirrors in the process for correction of spherical aberration will change the quality of their images without any perceptible reason for the alteration. A current of cold or warm air, a gleam of sunlight, the close approach of some person, an unguarded touch, the application of cold water injudiciously will ruin the labor of days. The avoidance of these and similar causes requires personal experience, and the amateur can only be advised to use too much caution rather than too little.