This apparatus may appear unnecessarily complex, but it is worth while to set it up, for it makes the operation of casting a speculum fairly certain. If the metal is at the right temperature it will form a uniformly liquid disc inside the ring. The mass sets almost directly, and as soon as this occurs it is pushed to the edge of the plate and the metal in the lip broken off by a smart upward tap with a hammer. The dovetailed bit of iron is knocked downwards and falls off, and the ring may then be lifted clear of the casting. The object of the dovetail will now be understood, for without it there is great risk of breaking into the speculum in knocking the "tail" off. A box of quite dry sawdust is prepared in readiness for the process of annealing before the speculum is cast. The box must be a sound wooden or metal box, and must be approximately air-tight. For a speculum a foot in diameter the box must measure at least 3 feet both ways in plan, and be 2 feet 6 inches deep. Half the sawdust is in the box and is well pressed down so as to half fill it. The other half must be conveniently ready to hand. As soon as possible after casting, the speculum is thrown into the box, covered over with the sawdust, and the lid is put on. The object in having the box nearly air-tight is to avoid air-currents, which would increase the rate of cooling. A speculum a foot in diameter may conveniently take about three days to anneal, and should be sensibly warm when the box is opened on the fourth day. For larger sizes longer times will be required. We will say that the sawdust thickness on each side must be proportional to the dimensions of the speculum, or may even increase faster with advantage if time is of no moment. The process of annealing may be considered successful if the disc does not fly to pieces in working; it is to be worked on the chilled side. The object of giving the chill the approximate counterpart form will now appear; it saves some rough grinding, and causes the finished surface to be more homogeneous than it would be if the centre were sunk by grinding through the chilled surface. In 1889 I learned from Mr. Schneider, Professor Row-land's assistant at Baltimore, that in casting specula for concave gratings a good deal of trouble had been saved by carrying out the operation in an atmosphere consisting mostly of coal gas. It was claimed that in this way the presence of specks of oxide was avoided. I did not see the process in operation, but the results attained are known and admired by all experimenters. Sec. 71. Grinding and polishing Specula.