MICROSCOPE 267 one at R R . As the focus of the eye-glass is shorter for blue rays than for red rays by just the ditrerenee in the place of these images, their rays, after refraction by it, enter the eye in a parallel direction, and produce a picture free from false colour. If the object-glass had been rendered perfectly achromatic, the blue rays, after passing through the iield-glass, would have been brought to a focus at b, and the red at r ; so that an error would be produced, which would have been increased in stead of being corrected by the eye-glass. Another advantage of a well-constructed Huy- genian eye-piece is that the image produced by the meet ing of the rays after passing through the field-glass is by it rendered concave towards the eye-glass instead of convex, so that every part of it may be in focus at the same time, and the field of view thereby rendered flat. 1 Two or more Huygenian eye- 14 ._ gection of Huygenian Eye pieces, of different magnify- p . ad ted to Over-Corrected ing powers, known as A, B, G, Microscopic Objectives. &c., are usually supplied with a compound microscope. The utility of the higher powers will mainly depend upon the excellence of the objectives ; for, when an achromatic combination of small aperture which is sufficiently well corrected to perform very tolerably with a "low" or "shallow" eye-piece is used with an eye-piece of higher magnifying power (com monly spoken of as a " deeper " one), the image may lose more in brightness and in definition than is gained by its amplification, while the image given by an objective of large angular aperture and very perfect correction shall sustain so little loss of light or of definition by "deep eye-piecing " that the increase of magnifying power shall be almost clear gain. Hence the modes in which different objectives of the same power, whose performance with shallow eye-pieces is nearly the same, are respectively affected by deep eye-pieces afford a good test of their respective merits, since any defect in the correc tions is sure to be brought out by the higher amplification of the image, while a deficiency of aperture is manifested by the want of light. The working microscopist will generally find the A eye piece most suitable, B being occasionally employed when a greater power is required to separate details, whilst C and others still deeper are useful for the purpose of testing the goodness of objectives, or tor special investigations requiring the highest amplification with objectives of the finest quality. But he can commit no greater error than habitually to use deep eye-pieces for the purposes of scientific research, especially when (as in the study of living objects) long-continued and unintermitted observation is necessary For the visual strain thus occasioned is exactly like that resulting from the habitual use of magnifying spectacles in reading, requir ing the book to be held within 2 or 3 inches of the eye. And all experience shows that this feeling of strain cannot be dis regarded, without the most injurious consequences to vision. For viewing large flat objects, such as transverse sections of wood or of Echinus spines, under low magnifying powers, the eye-piece known as Kellner s may be employed with advantage. In this construction the field-glass, which is a double-convex lens, is placed in the focus of the eye-glass, without the interposition of a diaphragm ; and the eye-glass is an achromatic combination of a ] ilano-concave of flint with a double-convex of crown, which is slightly under-corrected, so as to neutralize the over-correction given to the objectives for use with Huygenian eye-pieces. A flat well-illuminated field of as nmch as 14 inches in diameter may thus be obtained with very little loss of light ; but, on the other hand, there is a certain impairment of defining power, which renders the Kellner eye-piece unsuitable for objects presenting minute structural details ; and it is an additional objection thai the smallest speck or smear upon the surface of the field-glass is made so unpleasantly obvious that the most careful cleansing o p that surface is required every time that this eye-piece is used Hence it is better fitted for the occasional display of objects of th( character already specified than for the ordinary wants of the working microscopist. Solid eye-pieces, consisting of cylinders of glass with convex ends are sometimes used in place of the Huygenian, when high magni fying power is required for testing the performance of objectives The loAver surface, which has the lesser convexity, serves as 1 The reader may be referred to Mr Varley s investigation of the properties o the Huygenian eye-piece in the fifty-first volume of the Transactions of th Society of Arts; and to the article "Microscope," by Mr Hoss, in the Perm Cyc opxdia, reprinted, with additions, in the English Cyclopaedia. eld-glass, while the image formed by this is magnified by the ighiy convex upper surface to which the eye is applied, the dvantage derivable from this construction lying in the abolition of he plane surfaces of the two lenses of the ordinary eye-piece. 2 A "positive" or Ramsden s eye-piece in which the field-glass, vhose convex side is turned upwards, is placed so much nearer the ye-glass that the image formed by the objective lies below instead if above it was formerly used for the purpose of micrometry, a livided glass being fitted in the exact plane occupied by the image, o that its scale and that image are both magnified together by the enses interposed between them and the eye. The same end, how ever, may be so readily attained with the Huygenian eye-piece
- hat no essential advantage is gained by the use of that of Ramsden,
the field of which is distinct only in its centre. OBJECTIVES. It has been seen that one of the principal points in the con- otruction of microscopic objectives to which the attention of their makers has been constantly directed has been the enlargement of their " aperture," this term being understood to mean, not
- heir absolute opening as expressed by linear measure, but their
capacity for receiving and bringing to a remote conjugate focus the rays diverging from the several points of a near object. The aper ture of an objective has been usually estimated by its "angle of aperture," that is, by the degree of divergence of the most extreme rays proceeding from the axial point of the object to the margin of the objective (fig. 15) which take part in the formation of the image. It is pointed out, however, by Professor Abbe that, in the case of single lenses used as objectives, their apertures are really propor tional, not to their respective angles of aperture, but to the ratio between the actual diameter or clear opening of each to its focal distance, a ratio which is simply expressed by the sine of its semiangle. And in the case of combinations of lenses it can be demonstrated mathematically that their respective apertures are de- terminable other conditions being the same by the ratio of the dia meters of their back lenses, so far as FIG. 15. Section of Achromatic these are really utilized, to their Object-Glass, composed of respective focal lengths, this ratio three pairs of (flint and being expressed, as before, by the sine crown) lenses, abc is its angle of the semiangle of aperture (sin u). The difference between these two modes of comparison can be readily made obvious by reference to the theoretical maximum of 180, which is attained by opening out the boundaries of the angle abc (fig. 15) until they come into the same straight line, the sine of the semiangle (90) then becoming unity. For, while an objective having an angle of 60 would count by comparison of angles as having only one-third of the theoretical maximum, its real aperture would be half that maximum since the sine of its semiangle (30) =. And, as the sines of angles beyond 60 increase very slowly, an objective of 120 angle will have as much as 87 per cent, of the theoretical maximum of aperture, although its angle is only two-thirds, or 66 6 per cent., of 180. It hence becomes obvious that little is really gained in real aperture by the opening-out of the angle of microscopic objectives to its greatest practicable limit (which may be taken as 170), while such extension even if unattended with any loss either of definition or of colour-correction necessarily involves a great reduction alike in the working dis tance and in the focal depth or penetration of the combination, as will be presently explained. Numerical Aperture. It has now been demonstrated by Professor Abbe that, independently of the advantages already specified as derivable from the application of the immersion system to objectives of short focus and wide aperture, the real aperture of an immer sion objective is considerably greater than that of a dry or air objective of the same angle, the comparative apertures of objec tives working through different media being in the compound ratio of two factors, viz., the sines of their respective semiangles of aperture and the refractive indices of the "immersion fluids. It is the product of these (nsinu) that gives what is termed by Professor Abbe the "numerical aperture, which serves, therefore, as the only true standard of comparison, not only between dry or air and water or oil immersion lenses, but also between immersion lenses adapted to work respectively with water, oil, or any other interposed fluid. That the angle of aperture expressed by the same number of degrees must correspond with very different work- in" apertures in dry, water immersion, and oil or homogeneous infmersion objectives becomes evident when we consider what 2 These eye-pieces are much in vogue in the United States, where they are made
of extremely short foci, even to ^ inch.