The polishing machine, of which a type used by Dr. Draper is shown in Fig. 44, produces a similar motion, the disc slowly revolving and the rather small tool moving over it in oval strokes kept off the center. More often the tool is of approximately the same diameter as the disc under it. The general character of the motion is evident from the construction. The disc _a_ is chucked by _c c′_ on the bed, turned by the post _d_ and worm wheel _e_. This is operated from the pulleys, _i_, _g_, which drive through _k_, the crank _m_, adjustable in throw by the nuts _n_, _n′_, and in position of tool by the clamps _r_, _r_. The motion may be considerably varied by adjustment of the machine, always keeping the stroke from repeating on the same part of the disc, by making the period of the revolution and of the stroke incommensurable so far as may be. Even in spectacle grinding machines the stroke may repeat only once in hundreds of times, and even this frequency in a big objective would, if followed in the polishing, leave tool marks which could be detected in the final testing. In the fine grinding, especially near the end of the process, the templets do not give sufficient precision in testing the curves, and recourse is had to the spherometer, by which measurements down to about 1/100000 inch can be consistently made. The next stage of operations is polishing, which transforms the grey translucency of the fine ground lens into the clear and brilliant surface which at last permits rigorous optical tests to be used for the final finish of the lens. This polishing is done generally on the fine grinding machine but with a very different tool and with rouge of the utmost fineness. The polishing tool is in any case ground true and is then faced with a somewhat yielding material to carry the charge of rouge. Cheap lenses are commonly worked on a cloth polisher, a texture similar to billiard cloth being suitable, or sometimes on paper worked dry. With care either may produce a fairly good surface, with, however, a tendency to polish out the minute hollows left by grinding rather than to cut a true surface clear down to their bottoms. Hence cloth or paper is likely to leave microscopic inequalities apparently polished, and this may be sufficient to scatter over the field a very perceptible amount of light which should go to forming the image. All first class objectives and mirrors are in fact polished on optician’s pitch. This is not the ordinary pitch of commerce but a substance of various composition, sometimes an asphaltic compound, again on a base of tar, or of resin brought to the right consistency by turpentine. Whatever the exact composition, the fundamental property is that the material, apparently fairly hard and even brittle when cold, is actually somewhat plastic to continued pressure. Sealing wax has something of this quality, for a stick which may readily be broken will yet bend under its own weight if supported at the ends.