We suppose the microscope to be inclined at an angle of about 70° to the horizontal, with a low-power objective attached to it, a one-inch by preference. Opposite to the microscope, and about a foot away from it, is a lamp with the edge of the flame presented to the microscope, the concave mirror of which is so arranged as to receive the rays from the flame and direct them up the tube of the microscope. Upon the stage is placed a piece of ground-glass, and the mirror-arm is now to be moved up or down upon its support until the ground-glass receives the maximum of illumination, which it will do when the lamp-flame is at one conjugate focus of the mirror and the ground-glass at the other. The focus will not be an image of the flame, but a bar of light. If an object be now placed upon the stage, instead of the ground-glass, and the objective focused upon it, it will, if the mirror be properly adjusted, be brilliantly illuminated. It will be understood that every concave mirror has a focus, and converges the rays which fall upon it to this focus, behaving exactly like a convex lens. The principal focus of a concave mirror is its radius of curvature, and this is not difficult to determine. Place side by side a deep cardboard box and the lamp, so that the concave mirror may send the rays back, along a path only slightly inclined to that by which they reached it, to the bottom of the box. The lamp and box being equidistant from the mirror, it is evident that when the mirror forms an image of the former upon the latter equal to the flame in size, we have the equivalent of the equal conjugate foci shown in Fig. 2. Now move the box to the distance from the mirror which corresponds to the distance of the stage of the microscope from the mirror when the latter is in position upon the microscope, and then move the lamp to or fro until the mirror casts a sharp image of the flame upon the bottom of the box, which is not to be moved. The lamp distance so found will be the correct one for working with the concave mirror. The writer is led to lay special stress upon this matter, from the fact that he almost invariably finds that the mirror is arranged to be used for parallel rays, _i.e._ for daylight, and is therefore fixed far too close to the stage to be available for correct or advantageous working with the lamp, unless, indeed, the bull’s-eye condenser be used, as hereinafter described, to parallelise the rays from the lamp. Work done with the concave mirror can, however, under the most favourable conditions, only be looked upon as a _pis aller_. The advantages gained by the use of some substage condenser, even the most simple, in conjunction with the plane mirror, or even without any mirror at all, are so manifold that the beginner is strongly urged to provide himself with some form or other of it, and we now proceed to describe the way in which this should be used to produce the best effect.