MICROSCOPE 269 (p. 273) could not possibly be formed if our vision were strictly limited to the exact plane 1 or which our eyes are focussed. Hence it is obvious that, in the case of objectives of low and moderate amplification, focal depth or penetration is a quality for the want of which no other excellence can compensate, the opening-out of their apertures being only advantageous in so far as it does not seriously interfere with their penetrating power. It is, no doubt, quite possible to construct a 1 inch objective with an aperture so large that, when the requisite ampli fication has been gained by deep eye-piecing, it shall resolve the lined "tests" ordinarily used for a J, or to construct an objective of ^ inch focus which shall in like manner do the ordinary work of a ^. But, as such objectives are thereby spoiled for their own proper work, the loss to the microscopist is but poorly compensated by his ability to resolve with them, under such deep eye-pieces as cannot be habitually used without serious risk to the eye-sight, the lined and dotted tests which can be much better shown under objectives of shorter focus and wider aperture, with eye pieces of low amplification. For, whilst deep eye-pieces cannot be habitually employed for continuous observation, without putting a strain upon the eyes resembling that which results from the constant use of a magnifying glass, even the very highest objectives may be used continuously for long periods in combination with shallow eye-pieces, with scarcely any fatigue, and therefore (it is probable) without sensible injury. 1 In estimating the goodness of a microscopic objective, five distinct qualities have to be separately considered: (1) its work ing distance, or the actual interval between its front lens and the object on which it is focussed; (2) its penetrating power, or focal depth; (3) the flatness of its field; (4) its definition, or power of giving a distinct image of all well-marked features of an object, and especially of their boundary lines ; and (5) its resolving power, by which it separates closely approximated lines, dots, or strise. 1. The " working distance " of an objective has no fixed relation to its focal length, the latter being estimated by its equality in power with a single lens of given radius of curvature (such as 1 inch, inch, ^ inch, &c. ), while the former varies with the mode in which the combination is constructed and with the aperture given to it. For low and moderate powers, ranging up to T V inch focus, good working distance is especially important, alike because it is closely related to penetrating power, and also because it facilitates the use of side-illumination for opaque objects. And in such objectives of high power as are to be used, not for the resolution of lined or dotted tests, but for the observation of living and moving objects of extreme minuteness, good working distance is no less important, on account of its relation to focal depth. In the case of those objectives, on the other hand, in which resolving power is made the first consideration, it is only needful that the working distance shall be such as to permit the interposition of a thin glass cover ; and this, although necessarily diminished with the widening of the aperture, can be always obtained by the adoption of the immersion system. 2. The " penetrating power" or "focal depth "of an objective may be defined as consisting in the vertical range through which the parts of an object not precisely in the focal plane may be seen with sufficient distinctness to enable their relations with what lies exactly in that plane to be clearly traced out, just as would be done by ordinary vision if the object were itself enlarged to the dimen sions of its microscopic image. The close relation between this quality and the preceding becomes obvious when it is considered that the longer the working distance of an objective the less will the distinctness of the image it forms be affected by any given alteration (say the TTTTTTT of an inch) in its focal adjustment. Con sequently, of two objectives having the same magnifying power but different working distances, that one will have the most focal depth whose working distance is the greater. On the other hand, as the penetrating power of an objective is reduced in direct accordance with the increase of its numerical aperture, it must be sacrificed wherever the highest resolving power is to be attained. Hence, as already remarked, this attribute will be very differently valued by different observers, according to the work on which they are respectively engaged. For the general purposes of biological research, not only with low or moderate (for the reasons already stated), but also with high powers, a considerable amount of focal depth is essential. It is impossible, for example, to follow satisfactorily the movements of an Amoeba, or to study the "cyclosis" in the cell of a Vallisncria, or to trace the distribution of a nerve-thread, with an objective in which focal depth is so completely sacrificed to aperture that nothing can be discerned save what is precisely in the focal plane, since, instead of passing gradationally from one focal plane to another, as the observer can do with an objective of good penetration, he can only get a succes sion of " dissolving views, " with an interval of "chaos" between 1 Hence, for work of this kind, the shallower eye-pieces and lonpcr tubes of English microscopes are to be preferred to the deeper eye-pieces and shorter tubes of the ordinary Continental model, the shallowest eye-pieces of the latter being usually equal iu power to the ordinary B eye-pieces of the former. each pair. When, on the other hand, it is desired to scrutinize with the greatest precision such minute details as are presented in one and the same focal plane (as, for example, those of the thinnest possible film of tissue spread out between a glass slide ami its cover ing glass), the microscopist will prefer an objective in which focal depth is subordinated to aperture, for the sake of the resolving power which he can thus command. And it will often happen in biological research that it is advantageous thus to bring objectives of the latter class to bear xipon objects which could not have been detected in the first instance save by objectives of much inferior resolving power but greater focal depth. 3. The "flatness of the field" afforded by the objective is a condition of great importance to the advantageous use of the micro scope, since the extent of the area clearly seen at one time practi cally depends upon it. Many objectives are so constructed that, even when the object is perfectly flat, the foci of the central and peripheral parts of the field are so different that, when the adjust ment is made for one, the other is more or less indistinct. Hence, when the central part of the area is in focus, no more information is gained respecting the peripheral than if the latter had been alto gether stopped out. With a really good objective, not only should the image be distinct over the whole field at once, but the marginal portion should be as free from colour as the central. As imperfec tion in this respect is often masked by the contraction of the aperture of the diaphragm in the eye-piece, the relative merits of two objectives, as regards flatness of field, should always be tested under an eye-piece giving a large aperture. 4. The "defining power " of an objective, which depends upon the completeness of its corrections for spherical and for chromatic aberration, and upon the accurate centring of its component lenses, is an attribute essential to its satisfactory performance, whatever may be its other qualities, its importance in scientific research being such that no superiority in resolving power can compensate for the want of it; and, though it is possible to obtain perfect correction for spherical aberration up to the highest practicable limit of angle, yet the difficulty of securing it increases rapidly with the augmentation of aperture, the want of it being made perceptible, especially when deep eye-pieces are put on, by the blurring of clearly -marked lines or edges, and by general "fog." Perfect colour-correction, on the other hand, is not possible for dry lenses of the widest angle, on account of the irrationality of the secondary spectrum ; but this may be neutralized by the use of the immersion system. As already stated, what has to be aimed at in the construction of microscopic objectives is not absolute colour-correction, but a slight degree of over-correction, which, by compensating the chromatic dispersion of the Huygenian eye-piece, shall produce an image free from false colour. As this can be secured far more easily in the construction of objectives of moderate than in those of very wide aperture, the cost of the former is proportionally small, an additional reason for the preference to be given to them on other grounds, in regard to all save very special kinds of microscopic work. 5. "Resolving power," being that by which very minute and closely approximated markings whether lines, striae, dots, or apertures can be separately discerned, is a function which is only of primary importance in objectives whose amplifying power specially fits them for the study of objects of this class. It appears from the mathematical researches of Professor Abbe that the maximum resolving power (with a theoretical angle of 180) would be capable of separating 146,528 lines to the inch ; but he considers the limit of visual resolution depending on the power of the eye to be about mVrnj of an inch ; and this limit seems to have been nearly reached. To make such a separation distinctly perceptible, an amplification of at least 3000 linear would be requisite ; and this can only be obtained either by the use of an objective of very high power (such as 7 V inch focus) in combination with a low or medium eye-piece or by putting a very deep eye-piece upon an objective of lower power (such as a ^ inch), the former method, for the reasons already given, being decidedly preferable. For the resolution of less closely approximated markings objectives of $, T V, -rV> an( l k inch answer very well ; and the resolving power which they require may be obtained without any excessive widening of the aperture. For the loss of resolving power consequent upon the contraction of the angle of a water-immersion objective to 128J is only one-tenth of the theoretical maximum 128,212 ; while a reduc tion to 105f only lowers the number of separable lines to 102,184 to the inch, thus diminishing the resolving power by little more than one-fifth, while the working distance and focal depth of the combination are greatly increased, and perfect definition is more certainly attainable. The | inch is (according to the writer s experience, which is confirmed by the theoretical deductions of Professor Abbe) the lowest objective in which resolving power should be made the primary qualification, the J, , J, and T inch being specially suited to kinds of biological work in which this is far less important than focal depth and dioptric precision. This view is strengthened by the very important consideration that the resolving power given by wide aperture cannot be utilized,
except by a method of illumination that causes light to pass through