The process of grinding and polishing plate-glass consists of three principal stages. In the first stage the surfaces of the glass are ground so as to be as perfectly flat and parallel as possible; in order to effect this object as rapidly as possible, a coarse abrasive is used which leaves the glass with a rough grey surface. In the second stage, that of smoothing, these rough grey surfaces are ground down with several grades of successively finer abrasive until finally an exceedingly smooth grey surface is left. In the third and final stage, the smooth grey surface is converted into the brilliant polished surface with which we are familiar by the action of a polishing medium. Originally the various stages of the grinding and polishing processes were carried out by hand, but a whole series of ingenious machines has been produced for effecting the same purpose more rapidly and more perfectly than hand-labour could ever do. We cannot hope to give any detailed account of the various systems of grinding and polishing machines which are even now in use, but must content ourselves with a survey of some of the more important considerations governing the design and construction of such machinery. In the first place, before vigorous mechanical work can be applied to the surface of a plate of glass, that plate must be firmly fixed in a definite position relatively to the rest of the machinery, and such firm fixing of a plate of glass is by no means readily attained, since the plate must be supported over its whole area if local fracture is to be avoided. While the surface of the plate is in the uneven condition in which it leaves the rolling table, such a firm setting of the glass can only be attained by bedding it in plaster, and this must be done in such a manner as to avoid the formation of air-bubbles between plaster and glass; if bubbles are allowed to form, they constitute places where the glass is unsupported. During the grinding and polishing processes these unsupported places yield to the heavy pressure that comes upon them, and irregularities in the finished polished surfaces result. The most perfect adhesion between glass and plaster is attained by spreading the paste of plaster on the up-turned surface of the slab of glass and lowering the iron bed-plate of the grinding table down upon it, the bed-plate with the adhering slab of glass being afterwards turned over and brought into position in the grinding machine. When one side of the glass has been polished, it is generally found sufficient to lay the slab down on a bed of damp cloth, to which it adheres very firmly, although sliding is entirely prevented by a few blocks fixed to the table in such a way as to abut against the edges of the sheet. In many works, however, the glass is set in plaster for the grinding and polishing of the second side as well as of the first.