Numerical Aperture.

180° Oil Angle. (Numerical Aperture 1·52.)180° Water Angle. (Numerical Aperture 1·33.)180° Air Angle. 96° Water Angle. 82° Oil Angle. (Numerical Aperture 1·00.)97° Air Angle. (Numerical Aperture ·75.)60° Air Angle. (Numerical Aperture ·50.)Fig. 35.—Relative diameters of the (utilized) back lenses of various dry and immersion objectives of the same power (¼-in.) from an air angle of 60° to an oil angle of 180°.

180° Oil Angle. (Numerical Aperture 1·52.)

180° Water Angle. (Numerical Aperture 1·33.)

180° Air Angle. 96° Water Angle. 82° Oil Angle. (Numerical Aperture 1·00.)

97° Air Angle. (Numerical Aperture ·75.)

60° Air Angle. (Numerical Aperture ·50.)

Fig. 35.—Relative diameters of the (utilized) back lenses of various dry and immersion objectives of the same power (¼-in.) from an air angle of 60° to an oil angle of 180°.

Thus we arrive at a general proposition for all kinds of objectives: 1st, when the power is the same, the admission of rays (or aperture) varies with the diameter of the pencil at its emergence; 2nd, when the powers are different, the same aperture requires different openings in the ratio of the focal lengths, or conversely with the same opening the aperture is in inverse ratio to the focal lengths. We see, therefore, that just as in the telescope the absolute diameter of the object-glass defines itsaperture, so in the microscopethe ratio between the utilised diameter of the back lens and the focal lengthof the objective defines its aperture also, and this is clearly a definition of aperture in its primary and only legitimate meaning as “opening;” that is, the capacity of the objective for admitting rays from the object and transmitting them to the image.

If, by way of illustration, we compare a series of dry and oil-immersion objectives, and commencing with small air angles, progress up to 180° air angle, and then take an oil-immersion of 82° and progress again to 180° oil angle, the ratio of opening to powerprogresses also, and attains its maximum, not in the case of the air angle of 180° (when it is exactly equivalent to the oil angle of only 82°), but is greatest at the oil angle of 180°. If we assume the objectives to have the same power throughout we get rid of one of the factors of the ratio, and we have only to compare the diameters of the emergent beams, and can represent their relations by diagrams.

Fig. 35illustrates five cases of different apertures of ¼-in. objectives, viz.: those of dry objectives of 60°, 97°, and 180° air angle, a water-immersion of 180° water angle, and an oil-immersion of 180° oil angle. The inner dotted circles in the two latter cases are of the same size as that corresponding to the 180° air angle.

A dry objective of the maximum air angle of 180° is only able to utilise a diameter of back lens equal to twice the focal length, while an immersion lens of even only 100° utilises alargerdiameter,i.e., it is able to transmit more rays from the object to the image than any dry objective is capable of transmitting. Whenever the angle of an immersion lens exceeds twice the critical angle for the immersion fluid,i.e., 96° for water or 82° for oil, its aperture is in excess of that of a dry objective of 180°.

Fig. 36.

This excess will beseenif we take an oil-immersion objective of, say 122° balsam angle, illuminating it so that the whole field is filled with the incident rays, and use it first on an object not mounted in balsam, but dry. We then have adry objectiveof nearly 180° angular aperture, for, as will be seen by reference toFig. 36, the cover-glass is virtually the first surface of the objective, as the front lens, the immersion fluid, and the cover-glass are all approximately of the same index, and form, therefore, a front lens of extra thickness. When the object is close to the cover-glass the pencil radiating from it will be very nearly 180°, and the emergent pencil (observed byremoving the eye-piece) will be seen to utilise as much of the back lens of the objective as is equal to twice the focal length, that is, theinnerof the two circles at the head ofFig. 35.

If now balsam be run in beneath the cover-glass so that the angle of the pencil taken up by the objective is no longer 180°, but 122° only (that is,smaller), the diameter of the emergent pencil islargerthan it was before, when the angle of the pencil was 180° in air, and will be approximately represented by theoutercircle ofFig. 35. As the power remains the same in both cases, the larger diameter denotes the greater aperture of the immersion objective over a dry objective of even 180° angle, and the excess of aperture is made plainly visible.

Having settled the principle, it is still necessary, however, to find a propernotationfor comparing apertures. The astronomer can compare the apertures of his various objectives by simply expressing them in inches, but this is obviously not available to the microscopist, who has to deal with the ratio of two varying quantities.

In consequence of a discovery made by Professor Abbe in 1873, that a general relation existed between the pencil admitted into the front of the objective and that emerging from the back of the objective, he was able to show that the ratio of the semi-diameter of the emergent pencil to the focal length of the objective could be expressed by the formulanSinu,i.e., by the sine of half the angle of aperture (u) multiplied by the refractive index of the medium (n) in front of the objective (nbeing 1·0 for air, 1·33 for water, and 1·52 for oil or balsam).

When, then, the values in any given cases of the expressionnSinu(which is known as the “numerical aperture”) has been ascertained, the objectives are instantly compared as regards their aperture, and, moreover, as 180° in air is equal to 1·0 (sincen= 1·0 and the sine of half 180° = 1·0) we see, with equal readiness, whether the aperture is smaller or larger than that corresponding to 180° in air. Thus, suppose we desire to compare the apertures of three objectives, one a dry objective, the second a water immersion, and the third an oil immersion; these would be compared on the angular aperture view as, say 74° air angle, 85° water angle, and 118° oil angle, so that a calculation must be worked out to arrive at the actual relationbetween them. Applying, however, thenumerical15notation, which gives ·60 for the dry objective, ·90 for the water immersion, and 1·30 for the oil immersion, their relative apertures are immediately recognised, and it is seen, for instance, that the aperture of the water immersion is somewhat less than that of a dry objective of 180°, and that the aperture of the oil immersion exceeds that of the latter by 30%.

The advantage of immersion, in comparison with dry objectives, becomes at once apparent. Instead of consisting merely in a diminution of the loss of light by reflection or increased working distance, it is seen that a wide-angled immersion objective has a larger aperture than a dry objective of maximum angle, so that for any of the purposes for which aperture is essential an immersion must necessarily be preferred to a dry objective.

That pencils of identical angular extension but in different media are different physically, will cease to appear in any way paradoxical if we recall the simple optical fact that rays, which in air are spread out over the whole hemisphere, are in a medium of higher refractive index such as oilcompressedinto a cone of 82° round the perpendicular,i.e., twice the critical angle. A cone exceeding twice the critical angle of the medium will therefore embrace asurplusof rays which do not exist even in the hemisphere when the object is in air.

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.

Fig. 37.

Fig. 37a.

If a dry objective is used upon an object in air, as inFig. 37, the angle may approach 180°, but when the object is mounted in balsam, as inFig. 37a, 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 inFig. 37awith 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 balsamFig. 37a) are not rays which are found when the object is in air (Fig. 37), but areadditional and differentrays which do not exist in air, as they cannot be emitted in a substance of so low a refractive index.

Lastly, it should also be noted that it is numerical and not angular aperture which measures the quantity of light admitted to the objective by different pencils.

Fig. 38.Fig. 38a.

Fig. 38.

Fig. 38a.

First take the case of the medium being the same. The popular notion of a pencil of light may be illustrated byFig. 38, which assumes that there is equal intensity of emission in all directions, so that the quantity of light contained in any given pencils may be compared by simply comparing the contents of the solid cones. The Bouguer-Lambert law, however, shows that the quantity of light emitted by any bright point varies with the obliquity of the direction of emission, beinggreaterin a perpendicular than in an oblique direction. The rays are less intense in proportion as they are more inclined to the surface which emits them, so that a pencil is not correctly represented byFig. 38, but byFig. 38a, the density of the rays decreasing continuously from the vertical to the horizontal, and the squares of the sines of the semi-angles (i.e., of the numerical aperture) constituting the true measure of the quantity of light contained in any solid pencil.

If, again, the media are of different refractive indices, as air (1·0), water (1·33), and oil (1·52), the total amount of light emitted over the whole 180° from radiant points in these media under a givenillumination is not the same, but isgreaterin the case of the media of greater refractive indices in the ratio of the squares of those indices (i.e., as 1·0, 1·77 and 2·25). The quantity of light in pencils of different angle and in different media must therefore be compared by squaring the product of the sines and the refractive indices,i.e.(nSinu2), for the square of the numerical aperture.

The fact is therefore made clear that the aperture of a dry objective of 180° does not represent, as was supposed, a maximum, but that aperture increases with the increase in the refractive index of the immersion fluid; and it should be borne in mind that this result has been arrived at in strict accordance with the ordinary propositions of geometrical optics, and without any reference to or deductions from the diffraction theory of Professor Abbe.

There still remains one other point for determination, namely, the proper function of aperture in respect to immersion objectives of large aperture. The explanation of the increased power of vision obtained by increase of aperture was, that by the greater obliquity of the rays to the object “shadow effects” were produced, a view which overlooked the fact, first, that the utilisation of increased aperture depends not only on the obliquity of the rays sent to theobject, but also to theaxis of the microscope; and exactly as there is no acoustic shadow produced by an obstacle, which is only a few multiples of the length of the sound waves, so there can be no shadow produced by minute objects, only a few multiples from the light waves, the latter then passing completelyroundthe object. The Abbe diffraction theory, however, supplies the true explanation of this, and shows that the increased performance of immersion objectives of large aperture is directly connected (as might have been anticipated) with the larger “openings” in the proper sense of the term, which, as we have already explained, such objectives really possess. Furthermore, in order that the image exactly corresponds with the object, all diffracted rays must be gathered up by the objective. Should any be lost we shall have not an actual image of the object, but a spurious one. Now, if we have a coarse object, the diffracted rays are all comprised within a narrow cone round the direct beam, and an objective of small aperture will transmit them all. With a minute object, however, the diffracted rays are widely spread out, so that a small aperture can admit only a fractional part—to admit the whole or a very largepart, and consequently to see the minute structure of the object, or to see it truly, a large aperture is necessary, and in this lies the value ofapertureand of awide-angled immersion objectivefor the observation of minute structures.

Measure of Apertures of Objectives. N.A.—Numerical aperture, as it is termed, is measured by the scale of measurement calculated by the late Professor Abbe, and which has since been generally recognised and adopted. He showed that even in lenses made for the same medium (as air) their comparative aperture as compared with their focus was not correctly measured by the angle of the rays grasped, but by the actual diameters of the pencil of rays transmitted, which depend, as already seen, more upon the back of the lens than the front. To get a geometric measure for comparison, he took the radii, or half diameters (whose relative proportions would be the same), and which geometrically are the sines of the semi-angle of the outermost rays grasped. Abbe further showed that if this sine of half the outside angle were multiplied by the refractive index of the medium used we should have a number which would give the comparativeapertureof any lens, whatever the medium. This number, then, determines both the numerical aperture and the resolving power of the objective.

The following table of numerical apertures shows the respective angular pencils which they express in air, water and cedar oil, or glass.16The first column gives the numerical apertures from 0·20 to 1·33; the second, third, and fourth, the air, water and oil (or balsam) angles of aperture from 23° 4′ air angle to 180° balsam angle. The theoretical resolving power in lines to the inch is shown in the sixth column; the line E of the spectrum being taken from about the middle of the green, the column giving “illuminating power” being of less importance; while in using that of penetrating power, it must be remembered that several data beside that of1/ago to make up the total depth of vision with the microscope.

INDEX:(1) Numerical Aperture. (nsinu=a.)(2)Air(n= 1·00).(3)Water(n= 1·33).(4)Homogeneous Immersion(n= 1·52).(5) White Light. (λ = 0·5269 μ, Line E.)(6) Monochromatic (Blue) Light.(λ = 0·4861 μ, Line F.)(7) Photography. (λ = 0·4000 μ, Near Linehk.)(8) Illuminating Power (a2.)(9) Penetrating Power (1/a.)

Fig. 39.—Abbe’s Apertometer.

The apertometer is an auxiliary piece of apparatus invented by Abbe, for testing the fundamental properties of objectives and determining their numerical and angular apertures. This accessory of the microscope involves the same principles as that of Tolles, which the late Mr. J. Mayall and myself brought to the notice of the Royal Microscopical Society of London in 1876. Abbe’s apertometer (Fig. 39) consists of a flat cylinder of glass, about three inches in diameter, and half an inch thick, with a large chord cut off, so that the portion left is somewhat more than a semicircle; the part where the segment is cut is bevelled from above downwards, to an angle of 45°, and it will be seen that there is a small disc with an aperture in it denoting the centre of the semicircle. To use this instrument the microscope is placed in a vertical position, and the apertometer is placed upon the stage with its circular part to the front and the chord to the back. Diffused light, either from the sun or lamp, is assumed to be in front and on both sides. Suppose the lens to be measured is a dry one-quarter inch; then with a one-inch eye-piece having a large field, the centre disc, with its aperture on the apertometer, is brought into focus. The eye-piece and the draw-tube are now removed, leaving the focal arrangement undisturbed, and a lens supplied with the apertometer is screwed into the end of the draw-tube. This lens, with the eye-piece in the draw-tube, forms a low-power compound microscope. This is now inserted into the body-tube, and the back lens of the objective whose aperture wedesire to measure is brought into focus. In the image of the back lens will be seen stretched across, as it were, the image of the circular part of the apertometer. It will appear as a bright band, because the light which enters normally at the surface is reflected by the bevelled part of the chord in a vertical direction, so that in reality a fan of 180° in air is formed. There are two sliding screens seen on either side of the figure of the apertometer; they slide on the vertical circular portion of the instrument. The images of these screens can be seen in the image of the bright bands.These screens should now be moved so that their edges just touch the periphery of the back lens.They act, as it were, as a diaphragm to cut the fan and reduce it, so that its angle just equals the aperture of the objective and no more.

This angle is now determined by the arc of glass between the screens; thus we get an angle inglassthe exact equivalent of the aperture of the objective. As the numerical apertures of these arcs are engraved on the apertometer, they can be read off by inspection. A difficulty is not infrequently experienced from the fact that it is not easy to determine the exact point at which the edge of the screen touches the periphery of the back lens, or rather the limit of the aperture. Zeiss, to meet this difficulty, made a change in the form of the apparatus—furnished a glass disc mounted on a metal plate, with a slot for the purpose of its more accurate adjustment.17

Professor Wheatstone’s remarkable discovery of stereoscopic vision led, at no distant period, to the application of the principle to the microscope. It may therefore prove of interest to inquire how stereoscopic binocular vision is brought about. Indeed, the curious results obtained in the stereoscope cannot be well understood without a previous knowledge of the fundamental optical principles involved in this contrivance, whereby two slightly dissimilar pictures of any object become fused into one image, having the actual appearance of relief. The invention of the stereoscope by Sir Charles Wheatstone, F.R.S., 1838, and improved by Brewster, was characterised by Sir John Herschel as “one of the most curious discoveries, andbeautiful for its simplicity, in the entire range of experimental optics,” led to a more general appreciation of the value of the conjoint use of both eyes in conveying to the mind impressions of the relative form and position of an object, such as the use of either eye singly does not convey with anything like the same precision. When a near object having three dimensions is looked at, a different perspective representation is seen with each eye. Certain parts are seen by the right eye, the left being closed, that are invisible to the left eye, the right being closed, and the relative positions of the portions visible to each eye in succession differ. These two visual impressions are simultaneously perceived by both eyes, and combined in the brain into one image, producing the effect of perspective and relief. If truthful right-and-left monocular pictures of an object be so presented to the two eyes that the optic axes when directed to them shall converge at the same angle as when directed to the object itself, a solid image will be at once perceived. The perception of relief referred to is closely connected with the doubleness of vision which takes place when the images on corresponding portions of the two retina are not similar. But, if in place of looking at the solid object itself we look with the right and left eyes respectively at pictures of the object corresponding to those which would be formed by it on the retina of the two eyes if it were placed at a moderate distance in front of them, and these visual pictures brought into coincidence, the same conception of a solid form is generated in the mind just as if the object itself were there.

Professor Abbe, however, contended that the method by which dissimilar images are formed in the binocular microscope differs materially from that of ordinary stereoscopic vision, and that the pictures are united solely by the activity of the brain, not by the prisms which ordinarily give rise to sensations ofsolidity. This can be only partially true, as binocularity in the microscope is due to difference of projection exhibited by the different parallax displacement of the images, and also to the perception of depth imparted by the instrument.

Wheatstone was firmly convinced that his stereoscopic principle could be applied to the microscope, and he therefore applied first to Ross and then to Powell to assist him in its adaptation. But whether either of these opticians made any attempt to give effect tohis wishes and suggestions is not known. In the year 1851 Professor Riddell, of America, succeeded in constructing a binocular microscope by employing two rectangular prisms behind the objective. M. Nachet also constructed a binocular with two body-tubes and a series of prisms. But neither Riddell’s nor Nachet’s instrument was ever brought into use; they were either too complicated or too costly.

It will be understood, however, that the binocular stereoscope combines two dissimilar pictures, while the binocular microscope simply enables the observer to look with both eyes at images which are essentially identical. Stereoscopic vision, to be effective, requires that the delineating pencil shall be equally separated, so that one portion of the admitted cone of light is conducted to one eye, and the other portion to the other eye.

Select any object lying in an inclined position, and place it in the centre of the field of view of the microscope; then, with a card held close to the object-glass, stop off alternately the right or left hand portion of the front lens: it will then appear that during each alternate change certain parts of the object will change their relative positions.

Fig. 40.—Portions of Eggs of Cimex.

To illustrate this,Fig. 40a,bare enlarged drawings of a portion of the egg of the common bed-bug (Cimex lecticularis), the operculum which should cover the opening having been forced off at the time the young was hatched. The figures exactly represent the two positions that the inclined orifice will occupy when the right- and left-hand portions of the object-glass are stopped off. This object is viewed as an opaque object, and drawn under a two-thirds object-glass of about 28° aperture. If this experiment is repeated, by holding the card over the eye-piece, and stopping off alternately the right and left half of the ultimate emergent pencil, exactly the same changes and appearances will be observed in the object under view. The two different images just produced are such as are required for obtaining stereoscopic vision. It is therefore evident that if instead of bringing them confusedly together into one eye we can separate them so as to bring togethera,binto the left and right eye, in thecombined effect of the two projections we obtain at once all that is necessary to enable us to form a correct judgment of the solidity and distance of the several parts of the object.

Nearly all objectives from the one inch upwards of any considerable aperture give images of the object seen from a different point of view with the two opposite extremes of the margin of the cone of rays; the resulting effect is that there are a number of dissimilar perspectives of the object blended together at one and the same time on the retina. For this reason, if the object under view possesses bulk, a more accurate image will be obtained by reducing the aperture of the objective.

Fig. 41.

Diagram 3,Fig. 41, represents the method employed by Mr. Wenham for bringing the two eyes sufficiently close to each other to enable them both to see through the double eye-piece at the same moment.a a aare rays converging from the field lens of the eye-piece; after passing the eye-lensb, if not intercepted, they would come to a focus atc; but they are arrested by the inclined surfaces,d d, of two solid glass prisms. From the refraction of the under incident surface of the prisms, the focus of the eye-piece becomes elongated, and falls within the substance of the glass ate. The rays then diverge, and after being reflected by the second inclined surfacef, emerge from the upper side of the prism, when their course is rendered still more divergent, as shown by the figure. The reflecting angle given to the prisms is 47½°, to accommodate which it is necessary to grind away the contact edges of the prisms,as represented, otherwise they prevent the extreme margins of the reflecting surfaces from coming into operation, which are seldom made quite perfect.

Fig. 42.—Professor Abbe’s Stereoscopic Eye-pieces.

Fig. 42represents a sectional view of Abbe’s stereoscopic eye-pieces, which consist of three prisms of crown glass,a,bandb′, placed below the field-glass of the two eye-pieces; the tubecis slipped into the tube or body like an ordinary eye-piece. The two prismsaandbare united so as to form a thick plate with parallel sides, inclined to the axis at an angle of 38·5°. The cone of rays from the objective is thus divided into two parts, one being transmitted and the other reflected; that transmitted passing througha band forming an image of the object in the axial eye-pieceB. Adjustment for different distances between the eyes is effected by the screw placed to the right-hand side of the figure, which moves the eye-pieceB′, together with the prismb′, in a parallel direction. The tubes can also be drawn out, if greater separation is required. The special feature of this instrument is that on halving the cone of rays by turning the caps, an orthoscopic or pseudoscopic effect is produced.This double-eyed piece arrangement of Abbe’s has not been at all brought into use in this country; this is partly owing to its original adaptation for use with the shorter Continental body-tube of 160 mm., and not for our 10-inch body.

The most perfect method of securing pleasing satisfactory stereoscopic vision of objects is that devised by Mr. Wenham. In his binocular microscope an equal division of the cone of rays, after passing through the objective is secured and again united in the eye-pieces, which act as one, so that each eye is furnished with an appropriate and simultaneous view of the object. The methods contrived by the earlier experimenters not only materially interfered with the definition of the objective and object, but also required expensive alterations and adaptations of the microscope, and sometimes separate stands for their employment. Mr. Wenham’s invention, on the contrary, offers no such obstacle to its use, and the utility of the microscope as amonocularis in no way impaired either when using the higher powers.

Fig. 43.

The most important improvement, then, effected by Wenham consists in the splitting up or dividing the pencil of rays proceeding from the objective by the interposition of a prism of the form shown inFig. 43. This is placed in the body or tube of the microscope so as to interrupt only one-half (a c) of the pencil, the other half (a b) proceeding continuously to the field-glass, eye-piece, of the principal body. The interrupted half of the pencil on its entrance into the prism is subjected to very slight refraction, since its axial ray is perpendicular to the surface it meets. Within, the prism is subjected to two reflections atbandc, which send it forth again obliquely on the linebtowards the eye-piece of the secondary body, to the left-hand side of the figure; and since at its emergence its axial ray is again perpendicular to the surface of the glass, it suffers no further refraction on passing out of the prism than on entering. By this arrangement, the image sent to the right eye is formed by rays which have passed through the left half of the objective; whilst the image sent to the left eye is formed by rays which have passedthrough the right half, and which have been subjective to two reflections within the prism, and passing through two surfaces ofglass. The prism is held by the ends only on the sides of a small brass drawer, so that all the four polished surfaces are accessible, and should slide in so far that its edge may just reach the central line of the objective, and be drawn back against a stop, so as to clear the aperture of the same.

Fig. 44.—Sectional view of the Wenham Binocular.

The binocular, then (Fig. 44), consists of a small prism mounted in a brass boxA, which slides into an opening immediately above the object-glass, and reflects one-half of the rays which form an image of the object, into an additional tubeB, attached at an inclination to the ordinary bodyC. One half of the rays take the usual course with their performance unaltered; and the remainder, though reflected twice, show no loss of light or definition worthy of notice, if the prism be well made.

As the eyes of different persons are not the same distance apart, the first and most important point to observe in using the binocular is that each eye has a full and clear view of the object. This is easily tried by closing each eye alternately without moving the head, when it may be found that some adjustment is necessary by racking out the draw-tubesD,E, of the bodies by means of the small milled head near the eye-pieces; this will increase the distance of the centres; and, on the contrary, the tubes, when racked down, will suit those eyes that are nearer together.

If the prism be drawn back till stopped by the small milled head, the field of view in the inclined body is darkened, and the rays from the whole aperture of the object-glass pass into the main body as usual, neither the prism nor the additional body interfering in any way with the use of the instrument as a monocular microscope.

The prism can be withdrawn altogether for the purpose of being wiped: this should be done frequently, and very carefully, on all four surfaces, with a perfectly clean cambric or silk handkerchief or a piece of wash-leather; but no hard substance must be used. During this process the small piece of blackened cork fitted between the prism and the thick end of the brass box may be removed; but it must be carefully replaced in the same position, as it serves an important purpose in stopping out extraneous light.

As the binocular microscope gives a real and natural appearance to objects, this effect is considerably increased by employing thosekinds of illumination to which the naked eye is accustomed. The most suitable are all the opaque methods where the light is thrown down upon the surface; but for those objects that are semi-transparent, as sections of bone or teeth, diatomaceæ, living aquatic animalcules, &c., the dark-field illumination by means of the parabolic reflector will give an equally good result.

For perfectly transparent illumination, it is much better to diffuse the light by placing under the object various substances, such as tissue-paper, ground glass, very thin porcelain, or a film of yellow bees’ wax, run between two pieces of thin glass.

To ensure the full advantage and relief to both eyes in prolonged observations with high as well as low powers, and with objectives of large aperture, Mr. Wenham devised a compound prism for use with his binocular microscope, the body tubes of which are also made expressly to suit the prism, as extreme accuracy is necessary to bring them into proper position. The main prism somewhat resembles in form the ordinary Wenham prism. Over the first reflecting surface is placed a second smaller prism, the top plane of which is parallel with the base of the first, so that direct rays pass through without deviation, but at the two inclined surfaces of the prisms (nearly in contact) there is a partial reflection from each, which, combined, give as much light as in the direct tube. The reflected image from these two surfaces is directed up into the inclined tube as usual. A somewhat later improvement is that of Dr. Schroeder, the high power prism, by means of which the whole of the rays emanating from the objective pass through it, and the full aperture of any power is thereby effectively utilised. Furthermore, Messrs. Ross have also constructed a right- and left-hand pair of eye-pieces, which ensure greater perfection of the image. It was, in fact, noticed that the size of the image in the left-hand field glass slightly differed from that of the right when examined by the ordinary Huyghenian eye-pieces. To compensate for this difference, the left-hand eye-piece has been carefully calculated, and its focus is now so accurately adjusted that the position of each eye in observing is brought into one plane of the binocular. The pairs of the several series of eye-piecesA,BandChave also been altered, and the effect is to greatly improve the image and give increased comfort to the observer.

Dr. Carpenter, who warmly espoused the binocular, and constantly employed it in his work, very truly said of it: “The important advantages I find it to possess are in penetrating power, or focal depth, which is in every way superior to that of the monocular microscope, so that an object whose surface presents considerable inequalities is very much more distinctly seen with the former than with the latter.”

This difference may in part be attributed to the practical modification in the angle of aperture of the objective, produced by the division of the cone of rays transmitted through the two halves, so that the picture or image received through each half of the objective of 60° is formed by rays diverging at an angle of only about 30°. He confesses, however, that this does not satisfactorily explain the fact that the binocular brings to themind’seye thesolidimage of the object, and thus gives to the observer a good idea of its form and which could hardly be obtained by the monocular microscope. Carpenter cites in support of his views the wing of a little-known moth,Zenzera Œsculi, which has an undulating surface, whereon the scales are set at various angles instead of having the usual imbricated arrangement, a good object for demonstrating; the general inequality of surface and the obliquity of its scales, which are at once seen by the binocular with a completeness not obtained by the monocular instrument.

To one unaccustomed to work with the binocular the views expressed by Dr. Carpenter as to the extreme value of the instrument for ordinary work may appear somewhat exaggerated, but from my own experience, having long had in constant use a Ross-Zentmayer binocular, furnished with a special prism, constructed for working with a1⁄8dry objective or a1⁄10immersion, the perfection of picture obtained was in every case quite equal to that of the monocular microscope. The relief to the eyes can hardly be over-estimated; the slight inequality of the pencil rays may be regarded rather as a part of the welcome rest afforded when a prolonged examination is made; it certainly appears to me to equalise the slight physiological difference known to exist between the eyes of most people. If one image is seen a little clearer by the stronger eye, the weaker eye assists rather more the stereoscopic effect of the object under observation. The advantage gained by the binocular is perhapsmore appreciated when opaque objects are under examination, as the eggs of insects, and the tongue of the blow-fly, specimens of mosses, lichens, parasites (vegetable and animal), whose planes and inequalities of surface require penetration, and which usually demand more time for their observation.

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