The whole aperture question, notwithstanding the innumerable perplexities which heretofore surrounded it, is in reality completely solved by these two simple considerations: First, that “aperture” is to be applied in its ordinary meaning as representing the greater or less capacity of the objective for receiving and transmitting rays; and second, that when so applied the aperture of an objective is determined by the ratio between its opening and its focal length; the objective that utilises the larger back lens (or opening) relatively to its focal length having necessarily the larger aperture. It would hardly, therefore, serve any useful purpose if we were here to discuss the various erroneous ideas that gave rise to the contention that 180° in air must be the maximum aperture. Amongst these was the suggestion that the larger emergent beams of immersion objectives were due to the fact that the immersion fluid abolished the refractive action of the first plane surface which, in the case of air, prevented there being any pencil exceeding 82° within the glass. Also the very curious mistake which arose from the assumption that a hemisphere did not magnify an object at its centre because the rays passed through without refraction. A further erroneous view has, however, been so widespread that it seems to be desirable to devote a few lines to it, especially as it always appears at first sight to be both simple and conclusive. [Illustration: Fig. 37.] [Illustration: Fig. 37_a_.] If a dry objective is used upon an object in air, as in Fig. 37, the angle may approach 180°, but when the object is mounted in balsam, as in Fig. 37_a_, the angle at the object cannot exceed 82°, all rays outside that limit (shown by dotted lines) being reflected back at the cover-glass and not emerging into air. On using an immersion objective, however, the immersion fluid which replaces the air above the cover-glass allows the rays formerly reflected back to pass through to the objective, so that the angle at the object may again be nearly 180° as with the dry lens. The action of the immersion objective was, therefore, supposed to be simply that it repaired the loss in angle which was occasioned when the object was transferred from air to balsam, and merely restored the conditions existing in Fig. 37_a_ with the dry objective on a dry object. As the result of this erroneous supposition, it followed that an immersion objective could have no advantage over a dry objective, except in the case of the latter being used upon a balsam-mounted object, its aperture then being (as was supposed) “cut down.” The error lies simply in overlooking the fact that the rays which are reflected back when the object is mounted in balsam (Fig. 37_a_) are not rays which are found when the object is in air (Fig. 37), but are _additional and different_ rays which do not exist in air, as they cannot be emitted in a substance of so low a refractive index.