When the polishing is done by machinery, which is the custom in Europe, with large lenses, the polisher is slid back and forth over the lens by means of a crank attached to a revolving wheel. The polisher is at the same time slowly revolving around a pivot at its centre, which pivot the crank works into, and the glass below it is slowly turned in an opposite direction. Thus the same effect is produced as in the other system. Those who practice this method claim that by thus using machinery the conditions of a uniform polish for every part of the surface can be more perfectly fulfilled than by a hand motion. The results, however, do not support this view. No European optician will claim to do better than the American firm of Alvan Clark & Sons in producing uniformly good object-glasses, and this firm always does the work by hand, moving the glass over the polisher, and not the polisher over the glass. Having brought both flint and crown glasses into proper figure by this process, they are joined together, and tested by observations either upon a star in the heavens, or some illuminated point at a little distance on the ground. The reflection of the sun from a drop of quicksilver, a thermometer bulb, or even a piece of broken bottle, makes an excellent artificial star. The very best optician will always find that on a first trial his glass is not perfect. He will find that he has not given exactly the proper curves to secure achromatism. He must then change the figure of one or both the glasses by polishing it upon a tool of slightly different curvature. He may also find that there is some spherical aberration outstanding. He must then alter his curve so as to correct this. The correction of these little imperfections in the figures of the lenses so as to secure perfect vision through them is the most difficult branch of the art of the optician, and upon his skill in practising it will depend more than upon anything else his ultimate success and reputation. The shaping of a pair of lenses in the way we have described is not beyond the power of any person of ordinary mechanical ingenuity, possessing the necessary delicacy of touch and appreciation of the problem he is attacking. But to make a perfect objective of considerable size, which shall satisfy all the wants of the astronomer, is an undertaking requiring such accuracy of eyesight, and judgment in determining where the error lies, and such skill in manipulating so as to remove the defects, that the successful men in any one generation can be counted on one's fingers. In order that the telescope may finally perform satisfactorily it is not sufficient that the lenses should both be of proper figure; they must also both be properly centred in their cells. If either lens is tipped aside, or slid out from its proper central line, the definition will be injured. As this is liable to happen with almost any telescope, we shall explain how the proper adjustment is to be made.