MICROSCOPE is an optical instrument for the examination of minute objects or parts of objects, which enlarges the visual pictures formed upon the retina of the observer by the rays proceeding from them.

Microscopes are distinguished as simple or compound. In the former, the rays which enter the eye of the observer come from an object brought near to it after refraction through either a single lens or a combination of lenses acting as a single lens, - its action as a "magnifier " depending on its enabling the eye to form a distinct image of the object at a much shorter distance than would otherwise be possible. The latter consists of at least two lenses, so placed relatively to the object, to the eye, and to one another that an enlarged image of the object, formed by the lens placed nearest to it (the " object-glass"), is looked at through the lens nearest the eye (the " eye-glass "), which acts as a simple microscope in "magnifying" it; so that the compound microscope may be described as a simple microscope used to look at an enlarged image of the object, instead of at the object itself.

History of the Simple Microscope. - Any solid or liquid transparent medium of lenticular form, having either one convex and one flat surface or two convex surfaces whose axes are coincident, may serve as a "magnifier," - what is essential being that it shall have the power of so refracting the rays which pass through it as to cause widely diverging rays to become either parallel or but slightly divergent. Thus if a minute object be placed on a slip of glass, and a single drop of water be carefully placed upon it, the drop will act as a magnifier in virtue of the convexity of its upper surface; so that when the eye is brought sufficiently near it (the glass being of course held horizontally, so as not to distort the spherical curvature of the drop) the object will be seen much enlarged. And if a small hole be made in a thin plate of metal, and a minute drop of water be inserted in it, this drop, having two convex surfaces, will serve as a still more powerful magnifier. There is reason to believe that the magnifying power of transparent media with convex surfaces was very early known. A convex lens of rock-crystal was found by Layard among the ruins of the palace of Nimrud. And it is pretty certain that, after the invention of glass, hollow spheres blown of that material and filled with water were commonly used as magnifiers (comp. vol. xiv. p. 577). The perfection of gem-cutting shown in ancient gems, especially in those of very minute size, could not have been attained without the use of such aids to the visual power ; and there can be little doubt that the artificers who could execute these wonderful works could also shape and polish the magnifiers best suited for their own or others' use. Though it is impossible to say when convex lenses of glass were first made by grinding, it is quite certain that they were first generally used to assist ordinary vision as *" spectacles," the use of which can be traced back nearly six centuries ; and not only were spectacle-makers the first to produce glass magnifiers (or simple microscopes), but by them also the telescope and the compound microscope were first invented. There seems no reason to believe, however, that lenses of very high magnifying power (or short focus) were produced until a demand for them had been created by the introduction of the compound microscope, in which such lenses are required as " object-glasses "; and the difficulty of working lenses of high curvature with the requisite accuracy led in the first instance to the employment of globules made by fusing the ends of threads of spun glass. It was in tit's way that Robert Hooke shaped the minutest of the lenses with which he made many of the numerous discoveries recorded in his Micrographia; and the same method was employed by the Italian microscopist Father Di Torre. It seems to have been Leeuwenhoek that first succeeded in grinding and polishing lenses of such short focus and perfect figure as to render the simple microscope a better instrument for most purposes than any compound microscope then constructed, - its inferiority in magnifying power being more than counterbalanced by the superior clearness of the retinal picture. And, in despair of any such modification in the compound form as should remove the optical defects which seemed inherent in its plan of construction, scientific opticians and microscopic observers alike gave their chief attention for a considerable period to the improvement of the simple microscope. In order that the nature of these improvements may be understood, the principle of its action must be first explained.

The normal human eye has a considerable power of self-adjustment, by which its focal length is so varied that it forms equally distinct pictures of objects brought within ordinary reading distance (say 10 inches) and of objects whose distance is many times that length, - the size of the visual picture of any object diminishing, however, with the increase in the distance to which it is removed, and the amount of detail distinguishable in it following the same proportion. Thus a man who looks across the street at a placard posted on the opposite wall may very distinctly see its general form and the arrangement of its beading, and may be able to read what is set forth in its largest type, whilst unable to separate the lines, still more to read the words, of what is set forth below. But by crossing the street so as to bring his eye nearer the picture he finds himself able, to read the smaller type as easily as he before read the larger, - the visual picture on his retina having been magnified, say 10 times in linear dimension, by the reduction of the distance of his eye from 40 feet to 4. Similarly, if he holds a page of excessively minute type at arm's length (say 40 inches) from his eye, he may be unable to read it, not because his eye does not form a distinct retinal picture of the page at that distance, but because the details of that picture are too minute for him to distinguish them. But if he brings the page from 40 inches to 10 inches distance, he may be able to read it without difficulty, - the retinal picture being enlarged four times linear (or sixteen times superficial) by this approximation. Now the rays that enter the eye from each point of a remote object diverge so little as to be virtually parallel ; but the divergence increases with the approximation of the object to the eye, and at 10 inches the angle of their divergence is as wide as permits the ordinary eye to bring them to a focus on the retina. When the object is approximated more closely, an automatic contraction of the pupil takes place, so that the most diverging rays of each pencil are cut off, and a distinct picture may be formed (though not without a feeling of strain) when the object is (say) from 5 to 8 inches distant, - giving still greater minuteness of visual detail in conformity with the increase of size. A further magnifying power may be obtained without the interposition of any lens, by looking at an object, at 2 or 3 inches distance, through a pin-bole in a card ; for by thus cutting off the more divergent rays of each pencil, so as to admit only those which can be made to converge to a focus on the retina at that distance, a distinct and detailed picture may be obtained, though at the expense of a great loss of light. Moreover, although an ordinary eye does not form a distinct picture of an object at less than from 10 to 6 inches distance, a " myopic " or " short-sighted " eye (whose greater refractive power enables it to bring rays of wider divergence to a focus on the retina) may form an equally distinct picture of an object at from 5 to 3 inches distance ; and, as the linear dimensions of that picture will be double that of the preceding, the object will be " magnified " in that proportion, and its details more clearly seen.

The effect of the interposition of a convex lens between the eye and an object nearly approximated to it primarily consists in its reduction in the divergence of the rays of the pencils which issue from its several points, so that they enter the eye at the moderate divergence which they would have if the object were at the ordinary nearest limit of distinct vision. And, since the shorter the focus of the lens the more closely may the object be approximated to the eye, the retinal picture is enlarged, causing the object to appear magnified in the same proportion. Not only, however, are the component rays bf each pencil brought from divergence into convergence, but the course of the pencils themselves is changed, so that they enter the eye under an angle corresponding to that under which they would have arrived from a larger object situated at a greater distance ; and thus, as the picture formed upon the retina by the small object ab, fig. 1, corresponds in all

It is obvious that the "magnifying power" of any convex lens so used is measured by the ratio between the dimensions of the retinal picture formed with its assistance and those of the picture formed by the unaided eye. Thus, if by the use of a convex lens having 1 inch focal length we can form a distinct retinal image of an object at only an inch distance, this image will have ten times the linear dimensions of that formed by the same object at a distance of 10 inches, but will be only eight times as large as the picture formed when the object can be seen by ordinary vision at 8 inches distance, and only four times as large as the picture of the same object formed by a myopic eye at a distance of 4 inches. It is usual to estimate the magnifying power of single lenses (or of combinations that are used as such) by the number of times that their focal length is contained in 10 inches, - that of 1 inch focus being thus taken as ten times, that of A inch as one hundred times, and so on. But the rule is obviously arbitrary, as the actual magnifying power varies in each individual with the nearest limit of distinct vision. Thus for the myopic who can see an object clearly at 4 inches distance, the magnifying powers of a 1 inch and inch lens will be only 4 and 40 respectively. The amplifying power of every single convex lens, however, is impaired (1) by that inability to bring to the same focus the rays which fall upon the central and the marginal parts of its surface which is called "spherical aberration," and (2) by that dispersion of the rays of different wave-lengths, in virtue of their different refrangibilities, which produces coloured fringes around the points and lines of the visual picture, and is therefore called " chromatic aberration" (see Liairr). These aberrations increase with the "angle of aperture" given to the lens, that is, with the proportion between the diameter of its actual "opening" and the focal distance of the object ; and thus, when a single lens of very short focus is used in order to gain a high magnifying power, such a reduction of its aperture by a perforated diaphragm or " stop " becomes necessary (in order, by excluding the peripheral rays, to obtain tolerable " definition " with freedom from false colour) that the amount of light admitted to the eye is so small as only to allow the most transparent objects to be thus viewed, and these only very imperfectly. In order to remedy this drawback, it was proposed by Sir D. Brewster to use instead of glass, in the construction of simple microscopes, such transparent minerals as have high refractive with low dispersive power ; in which case the same optical effect could be obtained with lenses of much lower curvature, and the aperture might be proportionately enlarged. This combination of qualities is found in the diamond, whose index of refraction bears such a proportion to that of glass that a diamond lens having a radius of curvature of 8 would give the same magnifying power as a glass lens whose radius of curvature is 3, while the " longitudinal aberration " (or distance between the foci of central and of marginal rays) would be in a diamond lens only one-ninth of that of a glass lens having the same power and aperture. Putting aside, however, the costliness of the material and the difficulty of working it, a source of imperfection arises from a frequent want of homogeneousness in the diamond crystal, which has proved sufficient to make a lens worked from it give a double or even a triple image. Similar attempts made by Mr Pritchard with sapphire proved more successful; and, as a sapphire lens having a radius of curvature of 5 has the same focus and gives the same magnifying power as a crown-glass lens having a radius of 3, it was found to bear a much larger aperture without serious impairment by either spherical or chromatic aberration. As the sapphire, however, possesses the property of double refraction, the duplication of the markings of the object in their retinal image constitutes a very serious drawback to the utility of lenses constructed of this mineral; for, though the double refraction may be reduced almost to nothing by turning the convex side of the lens towards the object, yet, as this is the worst position in regard to spherical aberration, more is lost than is gained. Fortunately, however, for biological investigators working with simple microscopes, the introduction of the Wollaston doublet superseded the necessity of any further attempts at turning costly jewels to account as high-power magnifiers.

Wollaston Doublet. - This consists of a combination of two plano-convex lenses, whose focal lengths (as directed by Dr Wollaston) should be as 3 to 1, with their plane sides turned towards the object, - the smaller lens being placed lowest, and the upper lens at a distance of one and a half times its focal length above it. This construction, however, has been subsequently improved - (1) by the introduction of a perforated diaphragm between the lenses ; (2) by a more effective adjustment of the distance between the two lenses, which seems to be most satisfactory when it equals the difference of their respective focal lengths, allowance being made for their thickness ; and (3) by the division of the power of the lower lens (when a shorter focus than Tb inch is required) into two, so as to form a " triplet." When combinations of this kind are well constructed, spherical aberration is almost wholly got rid of, and chromatic dispersion is so slight that the angle of aperture may be considerably enlarged without much sacrifice of distinctness. Such "doublets" and "triplets," having been brought into use in England while the compound microscope still retained its original imperfections, proved very serviceable to such as were at that time prosecuting minute biological investigations : for example, the admirable researches of Dr Sharpey on ciliary action in animals (1830-35) and Mr Henry Slack's beautiful dissections of the elementary tissues of plants, as well as his excellent observations on vegetable cyclosis (1831), were made by their means. No one, however, would now use Wollaston "doublets " or " triplets " of high power in place of a compound achromatic microscope ; and for the simple microscopes of low power that are useful either for dissecting or for picking out minute specimens (such as diatoms) other constructions are preferable, as giving a larger field and more light. As a hand-magnifier the " Coddington " lens - which is a sphere of glass with a deep groove ground out of its equatorial portion - has many advantages.' By making this groove sufficiently deep, both spherical and chromatic aberrations can be rendered almost insensible ; and, as the rays falling on any part of the spherical surface can only pass to the eye either through or near the centre, the action of every part of that surface is the same, so that the image of the object will be equally distinct (when properly focussed) whether its parts lie nearer to the axis of the sphere or more remote from it, or the axis be itself turned to one side or the other. Again, it was mathematically shown by Sir John Herschel in 1821 that by the combination of a meniscus with a double convex lens - the four surfaces of these lenses having certain proportionate curvatures - spherical aberration could be entirely extinguished for rays parallel to the axis, the combination being thus an "aplanatic " doublet, while another combination, which he termed a "periscopic" doublet, gives a remarkable range of oblique vision with low powers, and almost entirely extinguishes chromatic aberration, although at the expense of residual spherical aberration. These combinations have been mounted both as hand-magnifiers and as single microscopes, for both which purposes they are much superior to single lenses of the same magnifying power. But such combinations have been greatly improved by the introduction of concaves of flint glass, so as to render them achromatic as well as aplanatic ; and nothing, according to the writer's experience, can now be used with greater advantage for all the purposes answered either by the simple microscope or the hand-magnifier than Browning's " platyscopic " lenses or the "achromatic doublets" of Steinheil of Munich. Each of these combinations gives a large flat field, with plenty of light, admirable definition, and freedom from false colour.

At the period when " doublets" of very short focus were used in order to obtain high magnifying power, it was requisite to mount these on such a stand as would enable the focal adjustment to be made, and would admit the use of a special illuminating apparatus with great exactness. But now that comparatively low powers only are employed the ordinary rack-and-pinion movement is quite sufficient for their focal adjustment, and nothing more is required I It is difficult to understand how the name of Coddington came to be attached to the grooved sphere, seeing that he neither was nor claimed to be the inventor of it. Dr Wollaston's first "doublet" consisted of a pair of plano-convex lenses with their plane surfaces opposed to each other, and a diaphragm with central aperture placed between them. Sir D. Brewster showed that this construction is most advantageous when the two lenses are hemispheres, and the central aperture 'between their two plane surfaces is filled up by a transparent cement having the same refractive index as glass. And from this the transition is obvious to the grooved sphere, which had been made for Sir D. Brewster long before the high commendation it received from Mr Coddington brought it into general repute.

for the illumination of the object than a concave mirror beneath the stage when it is transparent, and a condensing lens above when it is opaque. The various patterns of simple microscope now made by ditierent makers vary in their construction, chiefly in regard to portability, the size of their stages, and the mode in which "rests" or supports to the hands are provided. These, in Continental instruments, are very commonly attached to the stage ; but, unless the stage itself and the pillar to which it is fixed are extremely massive, the resting of the hands on the supports is apt to depress the stage in a degree that affects the focal adjustment ; and where portability is not an object it seems better that the hand-supports should be independent of the stage. For a laboratory microscope, the pattern represented in fig. 2 has been found very convenient, - the framework being of mahogany or other hard wood, the stage

Compound Microscope.--The placing of two convex lenses in such relative positions that one should magnify an enlarged image of a small near object formed by the other naturally soon followed the invention of the telescope, and seems to have first occurred to Hans Zansz or his son Zacharias Zansz, spectacle-makers at Middelburg in Holland, about 1590. One of their compound microscopes, which they presented to Prince Maurice, was in the year 1617 in the possession of Cornelius Drebell of Alkmaar, who then resided in London as mathematician to king James I. In order to make clear the successive stages by which the rude and imperfect microscope of that period has, after remaining for two centuries unimproved in any essential particular, been developed within the last half-century into one of the most important instruments of scientific research that the combination of theoretical acumen and manipulative skill has ever produced, it is necessary to explain the principle of its construction, and to show wherein lay the imperfection of its earlier form.

In its simplest construction, as already stated, the compound microscope consists of only two lenses, - the "object-glass" CD, fig. 3, which receives the light-rays direct from the object AB placed near it, and forms an enlarged but reversed image A'B' at a greater distance on the other side, and the "eye-glass" LM, which receives the rays that diverge from the several points of this image as if they proceeded from the points of an actual object occupying the position and enlarged to the dimensions A'B', and brings these to the eye at E, so altering their course as to act as a simple microscope in magnifying that image to the observer. It was early found useful, however, to interpose another lens FF, fig. 4 (the " field-glass "), between the object-glass and the image formed by it, for the purpose of giving such a slight convergence to the pencil of rays as shall reduce the dimensions of the image, and thus allow a larger part of it to come within the range of the eye

It is obvious that the magnifying power of such an instrument would depend (1) on the proportion between the size of the image formed at BB and that of the actual object, and (2) upon the magnifying power of the eye-glass. And further the proportion which the size of the image bears to that of the object depends upon two factors, - (1) the focal length of the object-glass, and (2) the distance between the object-glass and the plane BB occupied by the image it forms. If we diminish the focal length of the object-glass, the object must be brought nearer to it, so that, while the distance of the image on the other side remains unchanged, that distance comes to bear a larger proportion to the distance of the object, and the size of the image is augmented in a corresponding ratio. On the other hand, the object-glass remaining unchanged, the distance at which it forms the image of the object can be increased by a lengthening of the tube of the microscope ; and, as this involves a shortening of the distance between the object-glass and the object, the proportion which the former bears to the latter is augmented, and the image is correspondingly enlarged. Thus an increase in the magnifying power of the compound microscope may be gained in three modes, which may be used either separately or in double or triple combination, - viz., (1) shortening the focus of the object-glass, (2) lengthening the tube of the microscope, and (3) increasing the magnifying power of the eye-glass by shortening its focus. This, it may be remarked, also lengthens the distance of the image from the object-glass, by bringing the focal plane BB nearer the eye-glass. The second of these methods was not unfrequently used in the older microscopes, which were sometimes made to draw out like telescopes, so as to increase the amplifying power of their object-glasses. But, whilst very inconvenient to the observer, such a lengthening of the one distance involved such a 1 hortening of the other as greatly impaired the distinctness of the image by increasing the aberrations of the object-glass, so that this method came to be generally abandoned for one of the other two.

When lenses of from 1 to 4 inches focus were used as object-glasses, and their apertures were restricted by a stop to the central part of each, tolerably distinct images were given of the larger structural arrangements of such objects as sections of wood or the more transparent wings of insects, - which images would bear a further moderate enlargement by the eye-glass without any serious deterioration either by want of definition or the introduction of colour-fringes. But when lenses of loss than 1 inch focus were employed in order to obtain a higher magnifying power, the greater obliquity of the rays so greatly increased their aberrations that defective definition and the introduction of false colours went far to nullify any advantage obtainable from the higher amplification ; while the limitation of the aperture required to keep these aberrations within even moderate limits occasioned such a loss of light as most seriously to detract from the value of the picture. On the other hand, the use of deeper eye-pieces to enlarge the images formed by the object-glasses not only brought out more strongly all the defects of those images, but introduced a new set of errors of their own, so that very little was gained by that mode of amplification. Hence many of the best of the older microscopists (notably LEEIINVENHOEK, q.v.) made some of their most valuable discoveries by the use of the simple microscope ; and the amount of excellent work thus done surprises every one who studies the history of microscopic inquiry. This was still more the case, as already stated, when the use of single lenses of very short focus was superseded by the introduction of the Wollaston doublet. And the substitution of these doublets for the single lenses of object-glasses, while the single lens of the eye-glass was replaced by a Herschel's aplanatic doublet, and the field-glass was a convex lens whose two curves had the proportion of 1:6 (the form of least spherical aberration), constituted the greatest improvement of which the instrument seemed capable in pre-achromatic times.' It has been only within the last sixty years (1820-30) that the microscope has undergone the important improvement which had been worked out by Dollond in the refracting telescope more than sixty years previously, - namely, the correction of the chromatic aberration of its objectives by the combination of concave lenses of flintglass with convex lenses of crown, while their spherical aberration is corrected by the combination (as in Herschel's aplanatic doublet) of convex and concave surfaces of different curvatures. The minute size and high curvature of the lenses required as microscopic objectives were long considered as altogether precluding the possibility of success in the production of such combinations, more especially as the conditions they would have to meet differ altogether from those under which telescopic object-glasses are employed. For the rays from distant objects fall upon the latter with virtual parallelism ; and the higher the power required the longer is the focus given to them, and the smaller is the deflexion of the rays. In the microscope, on the other hand, the object is so closely approximated to the objective that the rays which proceed to it from the latter have always a very considerable divergence ; and the deflexion to which they are subjected increases with that reduction of the focal length of the objective which is the necessary condition of the increase of its magnifying power. And thus, although the telescopic " triplet " worked out by Dollond (consisting of a double-concave of flint glass, interposed between two double-convex lenses of crown) can be so constructed as to be not only completely aplanatic (or free from spherical aberration) but almost completely achromatic (or free from chromatic aberration), this construction is only suitable for microscopic objectives of long focus and small angular aperture, the rays falling on which have but a very moderate divergence. And though, as will presently appear, some of the early attempts at the achromatization of the microscope were made in this direction, it was soon abandoned for other plans of construction, which were found to be alike theoretically and practically superior.

It seems to have been by Professor Amici, then of Modena, about 1812, that the first attempts were made at the achromatization of microscopic objectives ; but, these attempts not proving successful, he turned his attention to the production of a reflecting microscope, which was a decided improvement upon the non-achromatized compound microscopes then in use. In the year 1820, however, the subject was taken up by Selligues and Chevalier of Paris, who adopted the plan of superposing three or four combinations, each consisting of a double-convex of crown cemented to a plano-concave of flint. The back combination (that nearest to the eye) was of somewhat lower power than those placed in front of it, but these last were all of the same focus, and no attempt was made by these opticians to vary the construction of the several pairs thus united, so as to make them correct each others' aberrations. Hence, although a considerable magnifying power could be thus obtained, with an almost complete extinction of chromatic aberration, the aperture of these objectives could not be greatly widened without the impairment of the distinctness of the image by a " coma " proceeding from uncorrected spherical aberration.

In ignorance, it would appear, of what was being done by the Paris opticians, and at the instigation of Dr Goring (a scientific amateur), Mr Tulley - well known in London as an able constructor of telescopic objectives - began, about the year 1824, to work object-glasses for the microscope on the telescopic plan. After many trials 1 he succeeded, in 1825, in producing a triplet of inch focus, admitting a pencil of 18°, which was so well corrected as to perform very satisfactorily with an eye-piece giving a magnifying power of 120 diameters. He afterwards made a similar triplet of shorter focus, which, when placed in front of the previous one, increased the angle of the transmitted pencil to 38°, and bore an eye-piece giving a magnifying power of 300 diameters. These triplets are said by Mr Ross to have never been exceeded by any similar combinations for accurate correction throughout the field.

Having come into possession, at the end of 1826, of an objective of Chevalier's construction, Mr J. J. Lister carefully examined its properties, and compared them with those of Tulley's triplets ; and this comparison having led him to institute further experiments he obtained results which were at first so conflicting that they must have proved utterly bewildering to a less acute mind,2 but which finally led him to the enunciation of the principle on which all the best microscopic objectives are now constructed. For he discovered that the performance of such composite objectives greatly depends upon the relative position of their component combinations, - the effect of the flint plano-concave upon the spherical aberration produced by the double-convex of crown varying remarkably according to the distance of the luminous point from the front of the objective. If the radiant is at a considerable distance, the rays proceeding from it have their spherical error under-corrected ; but, as the source of light is brought nearer to the glass, the flint lens produces greater proportionate effect, and the under-correction diminishes, until at length a point is reached where it disappears entirely, the rays being all brought to one point at the conjugate focus of the lens. This, then, is one aplanatic focus. If, however, the luminous point is brought still nearer to the glass, the influence of the flint continues for a time to increase, and the opposite condition of over-correction shows itself. But, on still further approximation of the radiant, the flint comes to •operate with less effect, the excess of correction diminishes and at a point still nearer to the glass vanishes, and a second aplanatic focus appears. From this point onwards under-correction takes the place of over-correction, and increases till the object touches the surface of the glass. As every such doublet, therefore, has two aplanatic foci for all points between which it is over-corrected, while for all points beyond it is under-corrected, the optician is enabled to combine two or more doublets with perfect security against spherical error. This will be entirely avoided if the rays be received by the front glass from its shorter aplanatic focus, and transmitted through the back glass in the direction of its longer aplanatic pencil. By the approximation of the two doublets over-correction will be reduced, while their separation will produce under-correction ; and thus, by merely varying the distance between two such combinations, the correction of the spherical error may be either increased or diminished according to a definite rule. Slight defects in one glass may thus be remedied by simply altering its position in relation to the other, - an alteration which may be made with very little disturbance of the colour-correction. This important principle was developed and illustrated by Mr Lister in a memoir read to the Royal Society on January 21, 1830, On some Properties in Achromatic Object-glasses, applicable to the Improvement of the Microscope ; and it was by working on the lines there laid down that the three London opticians Ross,3 Powell, and James Smith soon produced microscopic objectives that surpassed any then constructed on the Continent, while the subsequent adoption of the same principles by French and German opticians, as also by Professor Amici of Florence, soon raised their objectives to a corresponding level.

It has proved more advantageous in practice to make the several components of an achromatic objective correct each others' aberrations than to attempt to render each perfect in itself ; and the mode in which this is accomplished will vary with the focus and angular aperture given to each combination. Thus, while a single " telescopic triplet " answers very well for the lowest power usually made (4 inches focus), and the same plan may be used - though at the sacrifice of angular aperture - for objectives of 3 inches, 2 inches, and even 1 inch focus, the best performance of these powers requires the combination of two doublets. And, while this last system also serves for objectives of inch and / inch of low angle, a third component is required for giving to these objectives the aperture that renders them most serviceable, as well as for all higher powers. Instead of combining three achromatic doublets, however, many makers prefer placing in front a plano-convex of crown, and adding a third lens of crown to the doublet at the back, still using a doublet in the middle, - the whole combination thus consisting of six lenses, four of crown and two of flint. Further, Mr Wenham has shown that the whole colour-correction may be effected in the middle by interposing a double concave of dense flint between two double-convex lenses of crown, - the back lens, as well as the front, being then a plano-convex of crown, making five lenses in all. This plan of construction, though suitable to objectives of moderate angular aperture, and advantageous in regard to comparative simplicity and economy of construction, does not seem so well adapted for objectives to which the largest attainable aperture is to be given, - these being usually constructed with a triplet in front, a doublet in the middle, and a triplet at the back, so as to consist of eight separate lenses. And the first-class constructors of achromatic objectives in the United States usually place in front of these, in their highest powers, a single plano-convex of crown, by the addition of which a greater working distance can be obtained. But, as every such addition increases the liability to error from imperfections in the centring and grinding of the lenses (as well as loss of light by the partial reflexion of oblique rays from their surfaces), it is obvious that the most exact workmanship, involving a proportionate costliness, is required to bring out the full effect of such complex construction. And where angular aperture is regarded as the quality of primary importance it will be usually found preferable to have recourse to objectives constructed on either the " water " or the " oil " immersion system, to be presently described.

The great increase thus attained in the perfection of the corrections of microscopic objectives for both spherical and chromatic aberration of course rendered it possible to make a corresponding increase in their angular aperture. The minute scales of the wings of butterflies and other insects were naturally among the objects much examined ; and it was soon perceived that certain lines and other markings became clearly discernible on these scales with objectives of what was then considered large angle which were utterly undistinguishable with non-achromatized microscopes (however high their magnifying power), and very imperfectly shown under achromatic objectives of small angle. Hence these scales came to be used as " test-objects," for judging of the " definition " and " resolving power" of microscopic objectives, - the former property consisting in the clearness, sharpness, and freedom from false colour of the microscopic images of boundary lines, and depending on the accuracy with which the abet-. rations are corrected, while the latter term designates that power of separating very closely approximated markings which is now known to be a " function " of aperture. The insect-scales formerly most valued for these purposes were those of the .2Worpho menelaus (fig. 5) and the similarly lined scales of the Polyommatus argus (azure-blue), the " battledoor " scales of the same butterfly (fig. 6), the ribbed scales of the Lepisma saccharin (sugar-louse), and the minute and peculiarly marked scales of the Lepidocyrtus curuicollis (fig. 7), commonly known as the Podura. The writer recollects the time when the satisfactory " resolution " of the first three of these tests was considered a sufficient proof of the goodness of even high-power objectives, and when the Podura-markings, if visible at all, could only be distinguished as striae. The further opening-out of the aperture, however, enabled these striae to be resolved into rows of " exclamation marks " ; and, while there is still some uncertainty as to the precise structure of which these markings are the optical expression, practical opticians are generally agreed that the Podura-scale is very useful as a test for definition, with even the highest objectives, though it only serves as a test for a very moderate degree of resolving power. For the latter purpose it has been completely superseded by the closely approximated markings of the silicified envelopes of certain diatoms (which, however, show themselves in very different aspects accord ing to the conditions under which they are viewed, figs. 8-11), and also by lines artificially ruled on glass, as in Nobert's "test-plate," the number of lines in the nineteen bands of which is stated by M. Nobert to range from 1000 to 10,000 to a Paris line, while Dr Royston Pigott gives the numbers in an English inch as 11,529 to the inch in the first band, and 112,595 in the nineteenth. This last dimension (as will afterwards appear) approaches the minimum distance at which such markings are theoretically separable by any magnifying power of the microscope.

The enlargement of the angle of aperture of microscopic objectives and the greater completeness of their corrections, which were obtained in the first instance by the adoption of Mr Lister's principles, and were demonstrated by the resolution of the test-objects then in use, soon rendered sensible an imperfection in their performance under certain circumstances, which had previously passed unnoticed; and the important discovery was made by Mr Andrew Ross that a very decided difference exists in the precision of the image according as the object is viewed with or without a covering of thin glass, as also according as this cover is thin or thick.1 As this difference increases in proportion to the widening of the aperture, it would obviously be a

Immersion System. - It was long since pointed out by Professor Amici that the introduction of a drop of water between the front surface of the objective and either the object itself or its covering-glass would diminish the loss of light resulting from the passage of the rays from the object or its covering-glass into air, and from air into the front glass of the objective. It was obvious to him, moreover, that when the rays enter the object-glass from water, instead of from air, both its refractive and its dispersive action will be so greatly changed as to need an important constructive modification to meet the new condition. This modification seems never to have been successfully effected by Amici himself ; but his idea was taken up by the two eminent Paris opticians, MM. Hartnack and Nachet, who showed that the application of what is now known as the "immersion system " to objectives of short focus and large angular aperture is attended, not merely with the advantages expected by Professor Amici, but with others on which he did not reckon. As the loss of light by the refiexion of a portion of the incident rays increases with the obliquity of their incidence, and as the proportional loss is far smaller when the oblique rays pass into glass from water than when they enter it from air, the advantage of increasing the angular aperture is more fully experienced with " immersion " than with " dry" objectives, - just as Professor Amici anticipated. But, further, the immersion system allows of a greater working distance between the objective and the object than can be attained with a dry or air objective having the same angular aperture ; and this increase affords not only a greater freedom of manipulation, but also a greater range of " penetration " or " focal depth." Further, the observer is rendered so much less dependent upon the exactness of his cover-correction that it is found that water-immersion objectives of high power and considerable angular aperture, extremely well adapted for the ordinary purposes of scientific investigation, can be constructed without it, - a small departure from the standard thickness of covering-glass to which such objectives are adjusted by the maker having scarcely any effect upon the distinctness of the image. It is now the practice of several makers to supply two fronts to objectives of Tiv or T1,,- inch focus, one of them fitting the objective for use " dry " (that is, in air), whilst the substitution of the other converts it into a water-immersion objective. And in the objectives constructed on Mr Wenham's system no change in the front glass is needed, all that is necessary fcr making them work as immersion-lenses being a yet closer approximation of the front lens to the second combination, which can be made by the screw-collar.

Within the last few years, however, the immersion system has undergone a still further and most important development, by the adoption of a method originally suggested by Mr Wenham (though never carried out by him), and independently suggested by Mr Stephenson to Professor Abbe of Jena, under whose direction it was first worked out by Zeiss (the very able optician of Jena), who has been followed by Powell and Lealand of London, as well as by several other constructors of achromatic objec•tivcs both in England and elsewhere, with complete success. This method consists in the replacement of the water previously interposed between the covering-glass and the front glass of the objective by a liquid having the same refractive and dispersive powers as crown-glass, so that the rays issuing at any angle from the upper plane surface of the covering-glass shall enter the plane front of the objective, without any deflexion from their straight course, and without any sensible loss by reflexion - even the most oblique rays that proceed from the object keeping their direction unchanged until they meet the back or convex surface of the front lens of the objective. It is obvious that all the advantages derivable from the system of water-immersion will be still more thoroughly attained by this .system of "homogeneous " immersion, provided that a fluid can be obtained which meets its requirements. After a long course of experiments, Professor Abbe found that oil of cedar wood so nearly corresponds with crown-glass, alike in refractive and in dispersive power, as to serve the purpose extremely well, except when it is desired to take special advantage of the most divergent or marginal rays, oil of fennel being then preferable. There are, however, strong objections to the use of these essential oils in the ordinary work of research ; and it seems not unlikely that a solution of some one or more saline substances will be found more suitable. In addition to the benefit conferred by the water-immersion system, and more completely attained with the homogeneous, it may be specially pointed out that, as no correction for the thickness of the covering-glass is here required, the microscopist can feel assured that he has such a view of his object as only the most perfect correction of an air-objective can afford. This is a matter of no small importance, for while, in looking at a known object, the practised microscopist can so adjust his air-objective to the thickness of its covering-glass as to bring out its best performance, he cannot be sure, in regard to an unknown object, what appearances it ought to present, and may be led by imperfect cover-correction to an erroneous conception of its structure.

It has been recently argued that, as the slightest variation in the refractive index of either the immersion fluid or the covering-glass, a change of eye-pieces, or the least alteration in the length of the body - in a word, any circumstances differing in the slightest degree from those under which the objective was corrected - must affect the performance of homogeneous-immersion objectives of the highest class, they should still be made adjustable. The truth of this contention can, no doubt, be proved, not only theoretically, but practically, - the introduction of the adjustment enabling an experienced manipulator to attain the highest degree of perfection in the exhibition of many mounted objects, which cannot be so well shown with objectives in fixed settings. But it may well be questioned whether it is likely to do the same service in the bands of an ordinary working histologist, and whether the scientific investigator will not find it preferable, when using these objectives, to accept what their maker has fixed as their point of best performance. The principal source of error in his employment of them lies in the thickness of the optical section of the object; for the rays proceeding from its deeper plane, having to pass through a medium intervening between that plane and the cover-glass, whose refractive and dispersive indices differ from those of the glass and immersion-fluid, cannot be brought to so accurate a focus as those proceeding from the plane immediately beneath the cover-glass. The remedy for this, however, seems to lie rather in making the preparation as thin as possible than in the introduction of what is likely, in any but the most skilful and experienced hands, to prove a new source of error. Every one who has examined muscular fibre, for example, under a dry objective of very high power and large aperture, well knows that so greatan alteration is produced in its aspect by the slightest change in either the focal adjustment or the cover-correction that it is impossible to say with certainty what are the appearances which give the most correct optical expression of its structure. This being a matter of judgment on the part of each observer, it seems obvious that the nearest approach to a correct view will be probably given by the focal adjustment of the best homogeneous immersion-objectives, in fixed settings, to the plane of the preparation irnrnedia.tely beneath the cover-glass (see Tour. Roy. Micros. Soc., 1882, pp. 407, 854, 906).

In every particular in which the water-innnersion system is superior to the dry, it is itself surpassed by the oil or other homogeneous system, the anticipations of those by whom it was suggested being thus fully realized. But the advantages already spoken of as derivable from the use of the " immersion system " are altogether surpassed by that which the theoretical studies of Professor Abbe have led him to assign to it, and of which he has practically demonstrated its possession. For he has shown (as will be explained below) that the interposition of either water or oil so greatly increases the real " aperture " of the objective that immersion-objectives may be constructed having a far greater virtual aperture than even the theoretical maximum (180°) of the angular aperture of an air-objective.

The same eminent physicist, working on the basis supplied by the mathematical investigations of Professor Helmholtz and himself on the undulatory theory of light, has further established an entirely new doctrine in regard to the production of highly magnified representations of closely approximated markings. All that has hitherto been said of the formation of images by the compound microscope relates to such as are produced, in accordance with the laws of refraction, by the alteration in direction which the light-rays undergo in their passage through the lenses interposed between the object and the eye. These dioptric images, when formed by lenses free from spherical and chromatic aberration, are geometrically correct pictures, truly representing the appearances which the objects themselves would present were they enlarged to the same scale and viewed under similar illumination. And we seem justified, therefore, in drawing from such microscopic images the same conclusions in regard to the objects they picture as we should draw from the direct vision of actual objects having the same dimensions. The principal source of error in such interpretations arises out of the "interference " to which the rays of light are subjected along the edges of the minute objects through which they pass, or along any such lines or margins in their inner part as are sufficiently opaque to throw a definite shadow. For every such shadow must be bordered, more or less obviously, by interference- or diffraction-spectra ; and thus the images of strongly-lined objects with very transparent intermediate spaces may be so troubled or confused by these " diffraction-spectra " as to render it very doubtful what interpretation is to be put upon their appearances.

A good example of this kind is afforded by the scales of the gnat or mosquito, which are composed of a very delicate double membrane, strengthened by longitudinal ribs on both sides, those of the opposite sides uniting at the broad end of the scale, where they generally terminate as bristle-shaped appendages beyond the intermediate membrane. These are crossed by fine markings, which are probably ridge-like corrugations of the membrane, common to both sides of the scale. Between each pair of longitudinal ridges there may be seen, under certain adjustments of focus and illumination, three uniform parallel rows of beads, which have been supposed to represent a true structure in the membrane. By Dr Woodward (colonel in the United States army), however, it has been shown that this beaded appearance is merely the result of the "interferences" produced by the longitudinal and transverse lines of the scale. For the longitudinal diffraction-lines are clearly seen, alike in the microscopic image and in photographs (fig. 13), to extend into empty space beyond the contour of the scales, almost as far as the ends of the bristles in which the parallel ribs terminate; and they vary in number with the varying obliquity of illumination, so that in the same scale two, three, four, or even five rows of beads can be seen, and photographed at pleasure, in every intercostal space.1 Every microscopist who has worked much with high powers is well aware of the difficulty of distinguishing between real and spectral markings, - a difficulty which can only be overcome by training and experience. It seems, however, to have been now fully ascertained by Professor Abbe that it is only through such diffraction-spectra that the microscope can make us acquainted with the minutest structural features of objects, since, according to the calculations of Professor Helmholtz and himself (based on the constants of the undulatory theory), no amount of magnifying power can separate dioptrically two lines, apertures, or markings of any kind, not more than „\51). of an inch apart. The visual differentiation or " resolution " of lines or other markings whose distance lies

It is obvious, however, that, while the dioptric image represents the actual object, the diffraction-image thus formed by the reunion of a portion of the interference pencils is only an optical expression of the result of their partial recombination, which may represent something entirely different from the real structure. For it has been proved experimentally, by placing finely-ruled gratings in the position of objects, and by limiting the apertures of objectives by diaphragms with variously disposed perforations, that the same arrangement of lines shall be presented to the eye by differently lined surfaces, and different arrangements by similarly lined surfaces, according to the numbers and relative positions of the reunited spectra. Hence it is clear that there must• be an essential difference in character and trustworthiness between the images dioptrically formed of the general outlines and larger details of microscopic objects and those representations of their finer details which are given by the recombination of their diffraction-spectra,' and that the confidence to be placed in the latter class of representations will be greater in proportion to the completeness of the recombination of the separated interference-spectra, which, again, will be proportional (accurate correction of the aberrations being assumed) to the aperture of the objective.2 now enabled the best constructors of achromatic ob jectives to attain.' The progressive improvements thus effected in the construction of microscopic objectives have been accompanied by other improvements, alike in the optical and in the mechanical arrangements by which the best performance of these objectives can be secured; and it will be desirable now to describe in succession the most approved forms of the eye-piece, the objective, and the illuminating apparatus respectively, and then those of the instrument as a whole, pointing out the special adaptiveness of each to the requirements of different classes of scientific investigators.

It very early became obvious to those who were engaged ix the achromatization of microscopic objectives that their best performance was obtained when the image given by them was further enlarged by the eye-piece known as the Huygenian, as having been devised by Huygens for his telescopes. It consists of two plano-eonvex lenses (EE and FF, fig. 4), with their plane sides towards the eye ; these are placed at a distance equal to half the sum of their focal lengths, - or, to speak with more precision, at half the sum of the focal length of the eye-glass, and of the distance from the field-glass at which an image of the object-glass would be formed by it. A " stop " or diaphragm BB must be placed between the two lenses, in the visual focus of the eye-glass, which is, of course, the position wherein the image of the object will be formed by the rays brought into convergence by their passage through the field-glass. Huygens devised this arrangement merely to diminish the spherical aberration ; but it was subsequently shown by Boscovich that the chromatic dispersion was also in great part corrected by it. Since the introduction of achromatic object-glasses for compound microscopes, it has been further shown that nearly all error may be avoided by a slight over-correction of these, so that the blue and red rays may be caused to enter the eye in a parallel direction (though not actually coincident), and thus to produce a colourless image. Thus let N, Dl, N (fig. 14) represent the two extreme rays of three pencils, which without the field-glass would form a blue image convex to the eye-glass at B13, and a red one at RR ; then, by the intervention of the field-glass, a blue image concave to the eye-glass is formed at B'B', and a red This doctrine was first fully developed by Professor Abbe in the Arab., fur Microsk. Anatomic, vol. ix. (1874), and is more fully expounded in his subsequent contributions to Jour. Roy. Micros. Soc. See also the papers of Mr Stephenson and Mr Crisp in that journal, and in the preceding Monthly Microscopical Journal.

one at R'R'. As the focus of the eye-glass is shorter for blue rays than for red rays by just the difference 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 field-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 hiereased in• stead of being corrected by the eye-glass. Another advantage of a well-constructed Huygenian eye-piece is that the image produced by the meeting 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.' Two or more Huygenian eyepieces, of different magnifying powers, known as A, B, C, &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 (commonly 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 corrections 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 for 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, requiring 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 Echinns 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 plano-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 much 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 that the smallest speck or smear upon the surface of the field-glass is made so unpleasantly obvious that the most careful cleansing of that surface is required every time that this eye-piece is used. I fence it is better fitted for the occasional display of objects of the character already specified than for the ordinary wants of the working microscopist.

Solid eye-pieces, consisting of cylinders of lass with convex ends, are sometimes used in place of the Huygenian, when high magnifying power is required for testing the performance of objectives. The lower surface, which has the lesser convexity, serves as a field-glass; while the ima,ge formed by this is magnified by the highly convex upper surface to which the eye is applied, - the advantage derivable from this construction lying in the abolition of the plane surfaces of the two lenses of the ordinary eye-piece.' A " positive " or Ramsden's eye-piece - in which the field-glass, whose convex side is turned upwards, is placed so much nearer the eye-glass that the image formed by the objective lies below instead of above it - was formerly used for the purpose of inicrometry, - a divided glass being fitted in the exact plane occupied by the image, so that its scale and that image are both magnified together by the lenses interposed between them and the eye. The same end, however, may be so readily attained with the Huygenian eye-piece that no essential advantage is gained by the use of that of Ramsden, the field of which is distinct only in its centre.

It has been seen that one of the principal points in the construction 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 their 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 aperture 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 wart 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 proportional, 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 i sine of its semiangle. And in the case of combinations of lenses it can be demonstrated mathematically that their respective apertures are determinable - other conditions being the same - by the ratio of the diameters of their back lenses, so far as these are really utilized, to their respective focal lengths, - this ratio being expressed, as before, by the sine of the semiangle of aperture (sin ti).

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 (arc (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 havine. 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 Ter cent. of the theoretical maximum of aperture, although its angle is only t•o-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 distance 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 immersion objective is considerably greater than that of a dry or air objective of the same angle, - the comparative apertures of objectives working through different media being in the compound ratio of two factors, viz., the sines of their respective serniangles of aperture and the refractive indices of the " immersion " fluids. It is the product of these (nsinu) that Fives 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 working apertures in dry, water immersion, and oil or homogeneous immersion objectives becomes evident when we consider what happens when divergent pencils of rays pass from one medium into another of higher refractive index. For such divergent pencils, proceeding from air into water or oil, will be closed together or compressed ; so that the rays which, when an object is mounted in air, spread out over the whole hemisphere then form comparatively narrow pencils, and can thus be utilized by an immersion objective of smaller aperture than is required in a dry objective to admit the most diverging rays of air-pencils. It follows, therefore, that a given angle in a water or oil immersion objective represents a much larger aperture than does the same angle in an air-objective ; and thus it comes to pass that by opening out the angle of immersion objectives they may be made to receive and utilize rays of much greater divergence than can possibly enter dry objectives of even maximum aperture.

The following table, abridged from that given by Professor Abbe for every 0'02 of numerical aperture from 0.50 up to the maximum of 1.52, brings this contrast into clear view : -

But, as the actual angle of either a water or an oil immersion objective can be opened out to the same extent as that of an air or dry objective, it follows that the aperture of the former can be augmented far beyond even the theoretical maximum of the latter. Thus the numerical aperture of a water-immersion lens of the maximum angle of 180° is 1.33, or one-third greater than that of an air-lens of the same angle ; and this aperture would be given by an oil-immersion objective of only 122°. Again, the numerical aperture of an oil-immersion objective having the theoretical maximum angle of 180° would be 1.52, or more than one-half greater than that of an air-lens of the same angle. And the numerical apertures corresponding to angles of 170°, which have been actually attained in both cases, fall very little short of the proportions just given.

So, again, an oil-immersion objective whose angle of aperture is only 60° has as high a numerical aperture (0.76) as a water-immersion objective of 69i°, or as a dry objective of 99°; and a dry objective of 140° has no greater a numerical aperture (0-94) than a water-immersion of 90° or an oil-immersion of 76e This important doctrine may be best made practically intelligible by a comparison of the relative diameters of the back lenses of dry with those of water and oil immersion objectives of the same power, from an " air-angle " of 60° to an " oil-angle " of 180°, - these diameters expressing, in each case, the opening between the extreme pencil-forming rays at their issue from the posterior surface of the combination, to meet in its conjugate focus for the formation of the image, the relation of which opening in each case to the focal length of the combination is the real measure of its aperture (fig. 16). Thus the dry objective of 60° angle (5 in fig. 16) has its air-angle represented by shill= 0.50 numerical aperture. The dry objective of 97° (4) has its air-angle represented by sinus t-0.75 numerical aperture. And the dry objective having the (theoretical) angle of 180° (3) has its air-angle represented by sinu - 1.00 numerical aperture, - this corresponding to 96° water-angle and 82° oil-angle. But the water-immersion lens having the (theoretical) angle of 180° (2) has its water-angle represented by nsinu =1.33 numerical aperture. And the oil-immersion lens having the (theoretical) angle of 180° (1) has its oil-angle represented by n sin u = 1 -52 numerical aperture."' These theoretical apertures for water and oil immersion lenses having been found as nearly attainable in practice as the theoretical maximum for dry objectives, such lenses can utilize rays from objects mounted in balsam or other dense media, which are entirely lost for the image (since they do not exist physically) when the same object is in air or is observed through a film of air. And this loss cannot be compensated by an increase of illumination ; because the rays which are lost are different rays physically from those obtained by any illumination, however intense, through an aeri form medium.

It is by increasing the number of diffrac tion-speetra that the additional rays thus received by objectives of great numerical aperture impart to them an increased resolving power for lined and dotted objects, - the truth of the image formed by the recombination of these spectra being (as already shown) essentially dependent on the number of them that the objective may be capable of receiving.

But whilst the resolving power of microscopic objectives increases in the ratio of their respective numerical apertures, and whilst their illuminating power (dependent upon the quantity of light that passes through them) increases with the square of the numerical aperture, the case is reversed with another most important quality, - that of penetration or focal depth ; for this diminishes as the numerical aperture increases, until nothing but what is precisely in the focal plane can be even discerned with objectives possessed of the highest resolving power. Thus, the penetrating power of an objective of 60° air-angle being expressed as 2.000, an extension of that angle to 76° reduces it to 1.613, an extension to 89° reduces it to 1.429, and an extension to 99° reduces it to 1-316; further extension to 118r reduces it to 1.163, while an objective whose air-angle is 140° has a penetrating power of only 1.064. So, again, the oil-immersion objective which has tl e numerical aperture of 1.00 corresponding to the theoretical air-angle of 180° has a penetrating power of 1.000; this is brought-down to .752 when its angle is so increased as to make its numerical aperture 1.33, equalling the theoretical maximum of a water-immersion objective, and is .658 at the theoretical maximum (1.52) of an oil-objective.

Hence it is clear that, as some of the qualities to be sought in microscopic objectives are absolutely incompatible, a preference is to be accorded to objectives of greatest resolving power but very little penetration, or to those of moderate resolving power and great penetration, according to the uses to which they are to be applied; and some general principles will now be laid down in regard to this matter, based alike on science and experience.

In the first place, a marked distinction is to be drawn between those objectives of low or moderate power which are to be worked dioptrically and those of high power which are to be worked diffractively. The objects on which the former are to be for the most part used are either minute transparent bodies having solid forms which the observer should be able to take in as wholes (as in the case of Polycystina, the larger diatoms, Infusoria, &c.); or transparent sections, dissections, or injections, whose parts lie in different planes, the general relations of which he desires to study, while reserving their details for more special scrutiny ; or opaque objects, whose structure can only be apprehended from the examination of their surfaces, when the inequalities of those surfaces are seen in their relations to each other. In all these cases it is desirable that microscopic vision should resemble ordinary vision as much as possible. If the eye were so constructed as to enable us to discern only those parts of an object that lie precisely in the plane to which we focus it, our visual conceptions of the forms and relations of these parts, and consequently of the object as a whole, would in general be very inadequate, and often erroneous. It is because, while focussing our eye successively on the several planes of the object, we can see the relation of each to what is nearer and more remote that we can readily acquire a visual conception of its shape as a whole, and that unmistakable perception of solid form which is given by the combination of the two dissimilar perspectives of near objects in binocular vision (p. 273) could not possibly be formed if our vision were strictly limited to the exact plane for 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 amplification has been gained by deep eye-piecing, it shall resolve the lined " tests " ordinarily used for a I, or to construct an objective of inch focus which shall in like manner do the ordinary work of a 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 eyepieces 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 auy fatigue, and therefore (it is probable) without sensible injury.' In estimating the goodness of a microscopic objective, five distinct qualities have to be separately considered: - (1) its working 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 stria.

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 dimensions 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 „100 of an inch) in its focal adjustment. Consequently, of two objectives having the same magnifying power hut 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 Amceba, or to study the " cyclosis " in the cell of a Vallisneria, 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 succession of "dissolving views," with an interval of "chaos" between 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 and its covering 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 upon objects which could not have been detected in the first instance save by objectives of much inferior resolving power but greater focal depth.

The "flatness of the field" afforded by the objective is a condition of great importance to the advantageous use of the microscope, since the extent of the area clearly seen at one time practically 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 adjustment 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 altogether 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 imperfection 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.

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.

the object at an obliquity corresponding to that at which the most divergent rays enter the objective. Now, although in the case of objects whose markings are only superficial such obliquity may not be productive of false appearances (though even this is scarcely conceivable), it must have that effect when the object is thick enough to have an internal structure ; and the experience of all biological observers who have carried out the most delicate and difficult investigations is in accord, not only as to the advantage of direct illumination, but as to the deceptiveness of the appearances given by oblique, and the consequent danger of error in any inferences drawn from the latter. Thus, for example, the admirable researches of Strassburger, Fleming, Klein, and others upon the changes which take place in cell-nuclei during their subdivision can only be followed and verified (as the writer can personally testify) by examination of these objects under axial illumination, with objectives of an angle so moderate as to possess focal depth enough to follow the wonderful differentiation of component parts brought out by staining processes through their whole thickness.

The most perfect objectives for the ordinary purposes of scientific research, therefore, will be obviously those which combine exact definition and flatness of field with the widest aperture that can be given without an inconvenient reduction of working distance and loss of the degree of focal depth suitable to the work on which they are respectively to be employed. These last attributes are especially needed in the study of living and moving objects ; and, in the case of these, dry objectives are decidedly preferable to immersion, since the shifting of the slide which is requisite to enable the movement of the object to be followed is very apt to produce disarrangement of the interposed drop. And, owing to the solvent power which the essential oils employed for homogeneous immersion have for the ordinary cements and varnishes, such care is necessary in the use of objectives constructed to work with them as can only be given when the observer desires to make a very minute and critical examination of a securely-mounted object.

The following table expresses the magnifying powers of objectives constructed on the English scale of inches and parts of an inch, with the 10 inch body and the A and B eye-pieces usually supplied by English makers, and also specifies the angle of aperture which, in the writer's judgment, is most suitable for each. He has tine satisfaction of finding that his opinions on this latter point, which are based on long experience in the microscopic study of a wider range of animal and vegetable objects than has fallen within the purview of most of his contemporaries, are in accordance with the conclusions drawn by Professor Abbe from his profound investigations into the theory of microscopic vision,' which have been carried into practical accomplishment in the excellent productions of Mr Zeiss.

For ordinary biological work, the g, A, and 11,2- objectives, with angles of from 100° to 120°, will be found to answer extremely well if constructed on the water-immersion system.

Each of these powers should be tested upon objects most suited to determine its capacity for the particular kind of work on which it is to be employed ; and, in such testing, the application of deeper eyepieces than can be habitually employed with advantage will often serve to bring out marked differences between two objectives which seem to work almost equally well under those ordinarily used, - defects in definition or colour-correction, and want of light, which might otherwise have escaped notice, being thus made apparent. No single object is of such general utility for these purposes as a large well-marked Podura scale ; for the eye which has been trained to the use of a particular specimen of it will soon learn to recognize by its means the qualities of any objective between 1 inch and k inch focus ; and it may be safely asserted that the objective which most clearly and sharply exhibits its characteristic markings is the best for the ordinary work of the histologist.

For the special attribute of resolving power, on the other hand, tests of an entirely different order are required ; and these are furnished, as already stated, either by the more " difficult " diatoms, or by the highest numbers of Nobert's ruled test-plate. The diatom-valve at present most in use as a test for resolving power is the Amphipleura pellueida, the lines on which were long supposed to be more closely approximated than those of Nobert's nineteenth band, being affirmed by Mr Sollitt to range from 120 to 130 in react of an inch. But the admirable photographs of this valve obtained by Colonel Dr Woodward have confirmed the conclusion long previously expressed by the writer, that this estimate was far too high, being based on the "spurious lineation" produced by diffraction, and show that the striae on the largest valves do not exceed 91, while those on the smallest are never more numerous than 100, in -/-1310-iy of an inch. The same admirable manipulator has also obtained excellent photographs of another very difficult test-diatom, Surirella gemma, from which it appears that its transverse stria count longitudinally at the rate of 72,000 to the inch, whilst the beaded appearances into which these may be resolved count transversely at the rate of 84,000 to the inch. Thus it appears that the complete resolution of these "vexatious" diatoms does not require by any means the maximum of aperture, but is probably dependent at least as much on the perfection of the corrections and the effectiveness of the illumination.

It must be understood that there is no intention in these remarks to undervalue the efforts which have been perseveringly made by the ablest constructors of microscopic objectives in the direction of enlargement of aperture. For these efforts, besides increasing the resolving power of the instrument, have done the great service of producing a vast improvement in the quality of those objectives of moderate aperture which are most valuable to the scientific biologist ; and the microscopist who wishes his armamentum to be complete will provide himself with objectives of those different qualities, as well as different powers, which shall best suit his particular requirements.' Every improvement in the optical performance of the compound achromatic microscope has called forth a corresponding improvement in the illinnination of the objects viewed by it, since it soon came to be apparent that without such improvement the full advantage of the increased defining and resolving powers of the objectives could not be obtained. For the illumination of transparent objects examined by light transmitted through them under low powers of moderate angle a converging pencil of rays reflected upon their under surface by a concave mirror is generally sufficient, - a "condenser " being only needed when the imperfect transparency of the object requires the transmission of more light through it. And the microscopist engaged in ordinary biological studies, who works on very transparent objects with objectives of or inch focus, or A inch immersion, will find that the small concave mirror of short focus with which the Continental models are furnished (see fig. 28) will generally prove sufficient for his needs. This mirror is usually hung at such a distance beneath the stage that parallel rays falling on it are brought to a focus in the object as it lies on a slip of glass resting on the stage ; and thus, when the instrument is used by day, the light of a bright cloud (which is preferable to any other) gives a well-illuminated field, even with the powers last-mentioned. But when lamplight is aced its divergent rays are not brought to a focus in the object by a mirror that is fixed as just stated ; and the distance of the mirror beneath the stage should be made capable of increase (which is easily done by attaching it to a lengthening bar), so as to obtain the requisite focal convergence. Still the best effects of objectives of less than inch focus cannot be secured without the aid of an achromatic condenser, interposed between the mirror and the object, so as to bring a larger body of rays to a snore exact convergence.

When objectives of still higher power are employed, the employment of such a condenser becomes indispensable ; and when the highest powers are being used by lamplight, it is desirable to dispense with the mirror altogether, and to place the flame exactly in the optic axis of the microscope. The condenser should be an achromatic combination, corrected for the ordinary thickness of the glass slip on which the object lies, and capable of being so adjusted as to focus the illuminating pencil in the object.

As it is often found desirable that an object should be illuminated by central rays alone, or that the quantity of light transmitted through it should be reduced (for bringing into view delicate details of structure which are invisible when the object is flooded with light), every microscope should be provided with some means of cutting off the outer rays of the illuminating cone. The " diaphragm-plate " ordinarily used for this purpose is a disk of black metal, pivoted to the under side of the stage, and perforated with a graduated series of apertures of different diameters, any one of which can be brought, by the rotation of the disk, exactly into the optic axis of the microscope. But the required effect can be much more advantageously obtained by the "iris-diaphragm," in which a number of converging plates of metal are made so to slide over each other by the motion of a lever or screw that the aperture is either enlarged or diminished, while always remaining practically circular as well as central ; and in this manner a continuous view of the object is obtained, with a gradational modification of the light. Another method, commonly adopted in German microscopes, is to place a draw-tube in the optic axis between the stage and the mirror, and to drop into the top of this tube one of a set of "stops" perforated with apertures of different sizes ; this allows a gradational effect to be obtained by raising or lowering the tube, so as to place the stop nearer to or more remote from the object ; but it is not nearly so convenient as the iris-diaphragm ; and the effect of the stop is not nearly so good when it is removed to some distance beneath the object as when it is very near to the under surface of the glass object-slide. When an achromatic condenser is used, either a diaphragm-plate or an iris-diaphragm should be placed below its back lens, so as to cut off any required proportion of the outer rays that form its illuminating cone..

Such an arrangement, while suitine. all the ordinary requirements of the microscopist who uses the highest powers of his instrument for the purposes of biological investigation (as, for example, in the study of Bacteria or of the reproduction of the Monadina), does not serve to bring into effective use the special resolving power possessed by objectives of large aperture. It has long been known that for the discernment of very closely approximated markings oblique illumination is advantageous, - an objective which exhibits such a diatom-valve as Pleurosigma angulatusn with a smooth unmarked surface when illuminated by the central rays of the achromatic condenser making its characteristic marking's (figs. 8-11) distinctly visible when the central rays of the condenser are kept back by a stop, and the object is illuminated by its convergent marginal rays only. And it has also been practically known for some time that the resolution of lined or dotted tests can be often effected by mirror illumination alone, if the mirror be so mounted as to be able to reflect rays through the object at such obliquity to the optic axis of the microscope as to reach the margin of a wide-angled objective. But it has only been since Professor Abbe's researches have given the true theory of " resolution " that the special advantage of oblique illumination has been fully comprehended, and that the best means have been devised for using it effectively. Two different systems have now come into use, each of which has its special advantages.

One consists in the attachment of the illuminating apparatus (mirror and achromatic condenser) to a "swinging tail-piece " (see fig. 32), which, moving radially upon a pivot whose axis intersects the optic axis at right angles in the plane of the object, can transmit the illuminating pencil through it at any degree of obliquity that the construction of the stage allows. The direction of this pencil being of course limited to one azimuth, it is requisite, in order to bring out its full resolving effect, that the object should be made to rotate, by making the stage that carries it revolve round the optic axis, so that the oblique pencil may impinge upon the lines or other markings of the object in every direction successively. It will then be found that the appearances presented by the same object often vary considerably, - one set of lines being shown when the object lies in one azimuth, and another when its azimuth has been changed by rotation through 60°, 90°, or some other angle. Various contrivances have also been devised for throwing very oblique illuminating pencils on the object by means of prisms placed beneath the stage.

Illumination of at least equal obliquity to that afforded by the swinging tail-piece may now, however, be obtained by the use of condensers specially constructed to give a divergence of 170° to the rays which they transmit when used immersionally, by bringing their flat tops into approximation to the under side of the glass slide on which the object is mounted, with the interposition of a film of water or (preferably) of glycerin. By using a central stop, marginal rays alone may be allowed to pass ; and these will be transmitted through the object in every azimuth at the same time. But diaphragms with apertures limiting the transmitted rays to one part of the periphery may be so fixed in a tube beneath the condenser as to be easily made to rotate, thus sending its oblique pencils through the object in every azimuth in succession. And where this rotation of the diaphragm brings out two sets of lines at a certain angular interval a diaphragm with two marginal openings at a corresponding angular distance will enable both to be seen at once. Numerous arrangements of this kind have been devised by those who devote their special attention to the resolution of difficult diatom-tests ; but they are of little or no use to those who use the microscope for biological research.

For the illumination of the surfaces of opaque objects which must be seen by reflected light the means employed will vary with the focal length of the objective employed. For large bright objects viewed under a low magnifying power good ordinary daylight is sufficient ; but if the surface of the object is dull, reflecting but little light, the aid of a bull's-eye or large hi-convex lens must be employed in order to give it sufficient brilliance. This aid will always be required by lamplight ; and by a proper adjustment of the relative distances of the lamp and the object the rays from the lamp may be made either to spread themselves over a wide area or to converge upon a small spot. The former is the method suitable to large objects viewed under a low magnifying power ; the latter to the illumination of small objects which are to be examined under objectives of (say) 1 inch or I inch focus. Another method which may be conveniently had recourse to when the microscope is provided with a swinging tail-piece is to turn this on its pivot until the concave mirror is brought above the stage, so that rays which it gathers either from natural or artificial sources may be reflected downwards upon the surface of the object.

The illumination of an opaque object to be seen with a higher power than the I ors inch objectives was formerly provided for by a concave speculum (termed a Lieberkiihn after its inventor), with a perforation in the centre for the passage of the rays to the objective to which it is fitted, - the curvature of the speculum being so adapted to the focus of the objective which carries it that, when the latter is duly adjusted, the rays reflected upwards around the object from the mirror to the speculum shall converge strongly on the object. The various disadvantages of this mode of illumination, however, have caused it to be now generally superseded by other arrangements. For powers between llj inch and 140- inch, and even for a i or inch of small angle and good working distance, nothing is so convenient as the parabolic speculum or side-illuminator (F, fig. 17) invented by the late Richard Beck. This is attached to a spring-clip that slides on the tubes of low-power objectives, so that its distance from the object and the direction of its reflected pencil are readily adjusted ; and for use with higher powers it may be either mounted on a separ ate arm attached to some part of the stand of the microscope, or may be hung in the manner shown in fig. 17 from an " adapter " A interposed between the objective and the body. By rotating the collar B and making use of the joints C, C, the lengthening rod D, and the ball and socket E, any position may be given to the speculum F that may best suit the objective with which it is used.

When, however, it is desired to illuminate objects to be seen under objectives of high power and very short working distance, side illumination of any kind becomes difficult, though not absolutely impossible ;1 and various modes have been devised for the illumination of the object by means of light sent down upon it, through the objective, from above. This is done in the vertical illuminator of Messrs Beck (fig. 18) - the original idea of which was first

Black-Ground Illumination. - There are certain classes of objects which, though sufficiently transparent to be seen with light transmitted through them, are best viewed when illuminated by rays of such obliquity as not to pass directly into the objective, - such a proportion of these rays being retained by the object as to render it self-luminous, when, all direct light being cut offi the general field is perfectly dark. This method is particularly effective in the case of such delicate mineral structures as the siliceous tests of Polycystinet and the " frustules " of Diedomacew. And it is one advantage of this kind of illumination that it brings out with considerable effect the solid forms of objects suited to it, even when they are viewed monocularly. Two modes of providing this illumination are in use, each of which has its special advantages. One consists in placing a central stop either upon or immediately beneath a condenser of wide aperture, which shall cut off all rays save those that, after passing through the object (as in fig. 20), diverge at an angle greater than that of the objective used ; so that, while the ground is darkened, the object is seen brightly standing out upon it. But if the divergence of the rays is but moderate (say 60°), and the angle of the objective is large (say 90°), the most divergent rays of the condenser will enter the marginal portion of the objective, and, the field not being darkened, the black-ground effect will not be produced. This method has the great convenience of allowing black-ground illumination to be substituted for the ordinary illumination under different powers, without any other change in the apparatus than the turning of a diaphragm-plate fitted with stops of different sizes suitable to the several apertures of the objectives ; and the modern achromatic condensers of wide aperture can be thus used with objectives of 120° angle.

An excellent black-ground illumination is also given by the parabolic illuminator (fig. 19), originally worked out as a silvered speculum by Mr Wenham, hut now made as a paraboloid of glass that reflects to its focus the rays which fall upon its internal surface. A diagrammatic section of this instrument, showing the course of the rays through it, is given in fig. 20, the shaded portion representing the paraboloid. The parallel rays r, r, r", entering its lower surface perpendicularly, pass on until they meet its parabolic surface, on which they fall at such an angle as to be totally reflected by it, and are all directed towards its focus F. The top of the paraboloid being ground out into a spherical curve of which F is the centre, the rays in emerging from it undergo no refraction, since each falls perpendicularly upon the part of the surface through which it passes. A stop placed at S prevents any of the rays reflected upwards by the mirror from passing to the object, which, being placed at F, is illuminated by the rays reflected into it from all sides of the paraboloid. Those rays which pass through it diverge again at various angles ; and if the least of these, Gni, be greater than the angle of aperture of the object-glass, none of them can enter it. The stop is attached to a stem of wire, which passes vertically through the paraboloid and terminates in a knob beneath, as shown in fig. 19 ; and by means of this it may be pushed upwards, so as to cut off the less divergent rays in their passage towards the object, thus giving a black-ground illumination with objectives of an angle of aperture much wider than GFII. In using the paraboloid for delicate objects, the rays which are made to enter it should be parallel ; consequently the plane mirror should always be employed ; and when, instead of the parallel rays of daylight, we are obliged to use the diverging rays of a lamp, these should be rendered as parallel as possible, previously to their reflexion from

In order to adapt this paraboloid to objectives of very wide angle of aperture, a special modification of it, originally devised by Mr Wenham, has been latterly reintroduced under the designation of "immersion-paraboloid," with most excellent effect. This consists in making the top of the paraboloid flat instead of concave, and in interposing a film of glycerin between its surface and the under surface of the glass slide carrying the object. Only rays of such extreme obliquity are allowed to pass into the slide as would be totally reflected from its under surface if they fell upon it through air ; and, as these illuminate the object without passing into the objective, it can be thus examined under even the highest powers.

Stereoscopic Binoculars. - The admirable invention of the stereoscope by Professor Wheatstone has led to a general appreciation of the value of the conjoint use of both eyes, in conveying to the mind a conception of the solid forms of objects such as the use of either eye singly does not generate with the like certainty or effectiveness (see STEREOSCOPE). This conception is the product of the mental combination of the dissimilar perspective projections which our right and left retina receive of any object that is sufficiently near the eyes for the formation of two images that are sensibly dissimilar. Nov it is obvious that a similar difference must exist between the two perspective projections of any object in relief that are formed by the right and left halves of a microscopic objective and that this difference must increase with the angular aperture of the objective. And the fact of this difference may be easily made apparent experimentally, by adapting a semicircular "stop" to any objective of from 20° to 30° angle in such a manner that it can be turned so as to cover either its right or its left half ; for not only will the two images of any projecting object formed by the rays transmitted through the two uncovered halves be found sensibly different, but, if they be photographed or accurately drawn the "pairing" of their pictures in the stereoscope will bring out the form of the object in vivid relief. What is needed, therefore, to give the true stereoseopi" 4ect to a binocular microscope is a means of so bisecting the cone of rays transmitted by the objective that its two lateral halves shall be transmitted the one to the right and the other to the left eye, and that the two images shall be crossed (the image formed by the right half of the objective being sent to the left eye, and that formed by the left half of the objective being sent to the right eye) in order to neutralize the reversing effect of the microscope itself. If this crossing does not take place, the effect will be rendered " pseudoscopic," not " ortboseopic," - its projections becoming depressions, and its depressions being brought out as prominences. It was from a want of due appreciation of this fact that the earlier attempts at constructing a stereoscopic binocular gave representations of objects placed under it, not in their true orthoscopie, but in their pseudoseopic aspect. This was the case, for example, whh the binocular microscope first devised by Professor Riddell of New Orleans in 1851, which separated the cone of rays by a pair of rectangular prisms so placed edge to edge above the objective that the rays passing through its right half were reflected horizontally to the right side, to be changed to the vertical direction and sent to the right eye by a lateral rectangular prism, while the rays from the left half of the objective were sent to the left eye in a similar manner. Professor Riddell describes the "conversion of relief" produced by this arrangement with the ordinary eye-piece as making a metal sphernle appear "as a glass ball silvered on the under side, and a crystal of galena like an empty box." And to render the images " normal and natural " he found himself obliged to use erecting eyepieces, which should produce a second reversal of the images that had been reversed in their first formation.' Subsequently, however, Professor Riddell devised and perfected another arrangement giving a true orthoseopic effect, which, after being long disregarded, has been latterly taken up and brought into use by Mr Stephenson. The cone of rays passing upwards from the objective meets a pair of prisms (A, A fig. 21) fixed immediately above its back lens, which divides it into two halves ; each of these is subjected to internal reflexion from the inner side of the prism through which it passes ; and the slight separation of the two prisms at their upper end gives to the two pencils 13,13, on their emergence from the upper surfaces of the prisms, a divergence which directs them through two obliquely-placed bodies to their respective eye-pieces. By this internal reflexion a lateral reversal is produced, which neutralizes that of the ordinary microscopic image, so that, while each eye receives the image formed by its own half of the objective, the pairing of the two pictures produces a true orthoseopic effect.2 About the same date MM. Nachet of Paris succeeded in devising a binocular that should give a true orthoscopic image, by placing above the object-glass an equiangular prism (P. fig. 22) with one of its surfaces parallel to its back lens, which, receiving the pencils ab forming the right half of the cone, internally reflects them obliquely upwards to the left, and in like manner reflects the pencils a'b' from the left half of the cone obliquely upwards to the right. These pencils, passing out of the left and right oblique faces of the prism at right angles (so as not to undergo either refraction or dispersion), enter right and left lateral prisms, also at right angles, and, after being internally reflected by these, pass out vertically, at right angles to their upper surfaces, through two parallel bodies (fig. 23), whose eye-pieces bring them to a focus in the right and left eyes respectively. The distance between these bodies may be adjusted to the varying distances between the axes of individual pairs of eyes, by adjusting screws at their base, which vary the distance of the lateral prisms from the central. This instrument gives a theoretically perfect representation of a microscopic object in relief, as it would appear if enlarged to the size of its image, and brought to within about 10 inches of the eye ; and its chief practical defect is that, as the two bodies are parallel, instead of being slightly convergent, it cannot be continuously used without an uncomfortable strain. But, as its performance depends upon the accuracy of the seven plane surfaces of the three prisms, and on the correctness of their relations to each other, it is liable to considerable error from imperfections in its construction ; and, as the instrument can only be used for its own special purpose, the observer must be provided with an ordinary single-bodied. microscope for the examination of objects unsuited to the powers of the binocular. This last objection applies also to Professor Riddell's model.

It was for these reasons that Mr Wellborn, fully impressed with the advantages of stereoscopic vision to the microscopist, set himself to devise a construction by which it might be obtained without the drawbacks inevitable in the working of Riddell's and Nachet's instruments; and he soon succeeded in accomplishing this on a plan which has proved not only convenient but practically satisfactory, notwith

It may be fairly objected to Mr Wenham's method (1) that, as the rays which pass through the prism and are obliquely reflected into the secondary body traverse a longer distance than those which pass on uninterruptedly into the principal body, the image formed by them will be somewhat larger than that which is formed by the other set, and (2) that the image formed by the rays which have been subjected to the action of the prism must be inferior in distinctness to that formed by the uninterrupted half of the cone of rays. But these objections are found to have no practical weight. For it is well known to those who have experimented upon the phenomena of stereoscopic vision (1) that a slight difference in the size of the two pictures is no bar to their perfect combination, and (2) that, if one of the pictures be good, the full effect of relief is given to the image, even though the other picture be faint and imperfect, provided that the outlines of the latter are sufficiently distinct to represent its perspective projection. Hence if, instead of the two equally half-good pictures which are obtainable by MM. Nachet's original construction, we had in Mr Wenham's one good and one indifferent picture, the latter would be decidedly preferable. But, in point of fact, the deterioration of the second picture in 2,Ir Wenham's arrangement is less considerable than that of both pictures in the original arrangement of MM. Nachet ; so that the optical performance of the Wenham binocular is in every way superior. It has, in addition, these further advantages over the preceding : - first, the gm-eater comfort in using it (especially for some length of time together) which results from the convergence of the axes of the eyes at their usual angle for moderately near objects ; second, that this binocular arrangement does not necessitate a special instrument, but may be applied to any microscope which is capable of carrying the weight of the secondary body, - the prisnm being so fixed in a movable frame that it may in a moment be taken out of the tube or replaced therein, so that when it has been removed the principal body acts in every respect as an ordinary microscope, the entire cone of rayspassing uninterruptedly into it ; and, third, that the simplicity of its construction renders its derangement almost impossible. Hence it is the one most generally preferred by microscopists who use the long-bodied English model.

For short-bodied Continental microscopes, however, MM. Nachet have devised an arrangement of two prisms, based on Mr Wenham's fundamental idea of deflecting one half of the cone of rays into a secondary body, whilst the other half proceeds onwards without change of direction into the principal body. And it is an interesting feature in this construction that, by a simple change in the position of the dividing prism, the true " orthoseopic" image may be made, by a "conversion of relief," to become " psendoseopic."

The effect of stereoscopic projection may be attained, however, without a double body, by the insertion of a suitably constructed binocular eye-piece into the body of any ordinary monocular microscope. A plan of this kind was first successfully worked out by Mr Tolles (the very able optician of Boston, United States), who interposed a system of prisms similar to that devised by MM. Nachet (fig. 22), but on a much larger scale, between an "erector" (resembling that used in the eyepiece of a day telescope) and a pair of ordinary Huygenian eye-pieces, the central or dividing prism being placed at or near the plane of the secondary image formed by the erector, while the two eyepieces are placed immediately above the lateral prisms, - the combination thus making that division in the pencils forming the secondary (erected) image which it makes in the Naehet binocular in the pencils emerging from the objective.

A stereoscopic eye-piece of a very different construction has been recently devised by Professor Abbe, who, making use, for the division between the two eye-pieces of the rays going to form the first image, of an arrangement of prisms essentially similar to that devised by Mr Wenham for his non-stereoseopic binocular (fig. 27), obtains either an o•thoscopic or a pseudoscopie effect by placing On each eye-piece a cap with a semicircular diaphragm, so as to extinguish half of each of the cones of rays that form the two retinal images. While in one position of the diaphragms true stereoscopic or orthoseopic relief is given, it is sufficient to turn the diaphragms into the opposite position to obtain a pseudoscopic conversion.2 It appears, however, that this arrangement, though possessing points of great interest in relation to the theory of binocular vision, is not likely to supersede the ordinary Wenham prism.

It must be obvious to every one who studies with sufficient attention the conditions under which true stereoscopic relief ean be given that no combination of two dissimilar retinal perspectives can be satisfactory unless the visual pictures represent with tolerable distinctness the features of the object that lie in different focal planes. This is provided for, in ordinary vision, by the power of acconunodation possessed by the eye, which, while focussed exactly to any one plane, can also include in its visual picture (within certain limits) what is either nearer or more remote. Now it seems probable that, as Professor Abbe has urged, this power of accommodation comes into play in microscopic stereoscopy, but there can be DO question that the visual distinctness of the parts of an object lying within and beyond the focal plane, and therefore the completeness of the stereoscopic image, mainly depends upon the "focal depth " of the objective employed, - which, as already explained, is a function of its angular aperture. When, however, objectives of long focus and small aperture are employed in binocular microscopy, although each of the two perspective projections may be fairly distinct throughout; the effect of solid relief will be very inconsiderable, because the pictures are not sufficiently dissimilar to one another, - the ease being exactly analogous to that of the stereoscopic combination of two photographic portraits taken at an angle of no more than a few degrees from each other. Still, with an objective of IA inches focus and an angular aperture of from 15° to 20°, a very distinct separation is made of the focal planes of transparent sections of structures having no great minuteness of detail, - such, especially-, as injected preparations, - the solid forms of their capillary networks being presented to the mind's eye with a vividness that no monocular representation of them can afford. When a 1 inch objective of 20° or 25° is used, the stereoscopic effect becomes much more satisfactory ; so that objects of moderate projection (such as many of the siliceous Polycystina, Diatosnacese, &c.)can be seen in nearly their natural projection, and, if the focal adjustment is made for a medium plane, with tolerable distinctness both of their nearer and remoter parts. With a s inch of 30° or :35°, the stereoscopic relief becomes more pronounced ; but the diminution of the focal depth prevents the several planes of objects in strong relief from being as distinctly seen at the same time. A inch objective of about 40° of aperture, however, affords the most satisfactory results with suitable objects, - full stereoscopic relief being gained without exaggeration, so as to present, e.g., time discoidal diatoms and the smaller Alpeystina in their true forms, whilst their nearer and more remote parts are seen with sufficient distinctness to require only a very slight adjustment of the focus for their perfect definition. Still more minute objects may be well shown by 14,sths and VI objectives whose angular aperture does not exceed 50° ; but it can be shown both theoretically and practically 3 that the dissimilarity of the two perspective projections of objects in relief formed by objectives of any angle much exceeding 40° is such as to exaggerate the stereoscopic effect ; besides which, every enlargement of angular aperture so greatly diminishes the focal depth of the objectives that only those parts of the objects which lie very near the focal plane can be seen with distinctness sufficient for the formation of a good stereoscopic image. Hence, for the purposes of minute histological research, the stereoscopic binocular is (in the present writer's opinion) almost valueless ; since, if any distinct perspective differentiation can be gained with objectives of the short focus and enlarged angle that are most suitable to such investigations, that differentiation will be so great as to produce a highly exaggerated stereoscopic effect. If such objectives be used binocularly at all, they must be so mounted that their back lenses are in very close proximity to the prism ; and the (transparent) object must be illuminated by an achromatic condenser of sufficient aperture to send through it pencils of sufficient divergence to produce the secondary image.

In regard to the advantage derived from the use of the stereoscopic binocular, with the powers, and upon the objects, suitable to produce the true effect of solid form, the writer can unhesitatingly assert, as the result of a long and varied experience, that in no other way could he as certainly or as vividly image those forms to himself, and that in prolonged work upon such subjects he is conscious of a great saving of fatigue, which seems attributable not merely (perhaps not so much) to the conjoint use of both eyes as to the absence of the mental effort required for the interpretation of the microscopic picture, when the solid form of the object has to be ideally constructed from it (chiefly by means of the information obtainable through the focal adjustment), instead of being directly presented to the mind's eye.4 Non-Stereoscopic Binoculars. - The great comfort which is experienced by the microscopist in the conjoint use of both eyes has led to the invention of more than one arrangement by which this can be secured when those high powers are required which cannot be employed with the ordinary stereoscopic binocular. This is accomplished by Messrs Powell and Lea-laud by taking advantage of the fact that, when a pencil of rays falls obliquely upon the surface of a refracting medium, a part of it is reflected without entering that medium at all. In the place usually occupied by the Wenham prism they interpose an inclined plate of glass with parallel sides, through which one portion of the rays proceeding upwards from the whole aperture of the objective passes into the principal body with very little change in its course, whilst another portion is reflected from its surface into a rectangular prism so placed as to direct it obliquely upwards into the secondary body (fig. 26). Although there is a decided difference in brightness between the two images, that formed by the reflected rays being tho fainter, yet there is marvellously littl., loss of definition in either, even when the ,11- inch objective is used. The disk and prism are fixed in a short tube, which can be readily substituted in any ordinary binocular microscope for the one containing the Wenham prism.

Other arrangements were devised long ago by Mr Wenham,, with a view to obtain a greater equality in the amount of light-rays form ing the two pictures ; and he has latterly carried one of these into practical effect, with the advantage that the compound prism of which it consists has so nearly the same shape and size as his ordinary stereoscopic prism as to be capable of being mounted in precisely the same manner, so that the one may be readily exchanged for the other. The axial ray a, proceeding upwards from the objective, enters the prism AIMEE (fig. 27) at right angles to its lower face, and passers prism ABC. By internal reflexion from the former and external reflexion from the latter about half the beam b is reflected within the first prism in the direction eb, while the other half proceeds straight onwards through the second prism, in the direction ca', so as to pass into the principal body. The reflected half, meeting at d the oblique (silvered) surface DE of the first prism, is again reflected in the direction rib', and, passing out of that prism perpendicularly to its surface AF, proceeds towards the secondary body. The two prisms must not be in absolute contact along the plane AB, since, if they were, Newton's rings would be formed ; and much nicety is required in their adjustment, so that the two reflexions may be combined without any blurring of the image in the secondary body.

For the prolonged observation, under high powers, of objects not requiring the extreme of perfection in definition, - such, for example, as the study of the cyclosis in plants, - great advantage is gained from the conjoint use of both eyes by one of the above arrangements.

The optical arrangements on which the working of the compound achromatic microscope depends having now been explained, we have next to consider the mechanical provisions whereby they are brought to bear upon the different purposes which the instrument is destined to serve. Every complete microscope must possess, in addition to the lens or combination of lenses which affords its magnifying power, a stage whereon the object may securely rest, a concave mirror for the illumination of transparent objects from beneath, and a condensing-lens for the illumination of opaque objects from above.

Now, in whatever mode these may be connected with each other, it is essential that the optical part and the stage should be so disposed as either to be altogether free from tendency to vibration or to vibrate together ; since it is obvious that any movement of one, in which the other does not partake, will be augmented to the eye of the observer in proportion to the magnifying power employed. In a badly-constructed instrument, even though placed upon a steady table resting upon the firm floor of a well-built house, when high powers are used, the object is seen to oscillate so rapidly at the slightest tremor - such as that caused by a person walking across the room, or by a carriage rolling by in the street - as to be frequently almost indistinguishable ; whereas in a well-constructed instrument scarcely any perceptible effect will be produced by even greater disturbances. Hence, in the choice of a microscope, it should always be subjected to this test, and should be unhesitatingly rejected if the result be unfavourable. If the instrument should be found free from fault when thus tested with high powers, its steadiness with low powers may be assumed ; but, on the other hand, though a microscope may give an image free from perceptible tremor when the lower powers only are employed, it may be quite unfit for use with the higher. The method still adopted by some makers, of supporting the body by its base alone, is the worst possible, especially for the long body of the large English model, since any vibration of its lower part is exaggerated at its ocular end. The firmer the support of the body along its length the less tremor will be seen in the microscopic image.

The next requisite is a capability of accurate adjustment to every variety of focal distance, without movement of the object. It is a principle universally recognized in the construction of good microscopes that the stage whereon the object is placed should be a fixture, the movement by which the focus is to be adjusted being given to the optical portion. This movement should be such as to allow free range from a minute fraction of an inch to three or four inches, with equal power of obtaining a delicate adjustment at any part. It should also be so accurate that the optic axis of the instrument should not be in the least altered by any movement in a vertical direction, so that, if an object be brought into the centre of the field with a low power, and a higher power be then substituted, the object should be found in the centre of its field, notwithstanding the great alteration in the focus. In this way much time may often be saved by employing a low power as a "finder" for an object to be examined by a higher one ; and when an object is being viewed by a succession of powers little or no readjustment of its place on the stage should be required. A rack-and-pinion adjustment, if it be made to work both tightly and smoothly, answers sufficiently well for the focal adjustment, when objectives of low power only are employed. But for any lenses whose focus is less than half an inch a "fine adjustment," or "slow motion," by means of a screw-movement operating either on the object-glass alone or on the entire body (preferably on the latter), is of great value ; and for the highest powers it is quite indispensable. It is essential that in this motion there should be no "lost time," and that its working should not produce any " twist " or displacement of the image. In some microscopes which are provided with a fine adjustment the rack-and-pinion movement is dispensed with, the "coarse adjustment" being given by merely sliding the body up and down iu the socket which grasps it ; but this plan is only admissible where, for the sake of extreme cheapness or portability, the instrument has to be reduced to the form of utmost simplicity as in figs. 28, 29.

Scarcely less important than the preceding requisite, in the case of the compound microscope, especially with the long body of the ordinary English model, is the capability of being placed in either a vertical or a horizontal position, or at any angle with the horizon, without deranging the adjustment of its parts to each other, and without placing the eye-piece in such a position as to be inconvenient to the observer. It is certainly a matter of surprise that some microscopists, especially on the Continent, should still forego the advantages of the inclined position, these being attainable by a very small addition to the cost of the instrument ; but the inconvenience of the vertical arrangement is much less when the body of the microscope is short, as in the ordinary Continental model ; and there are many cases in which it is absolutely necessary that the stage should be horizontal. This position, however, can at any time be given to the stage of the inclining microscope, by bringing the optic axis of the instrument into the vertical direction. In ordinary cases, an inclination of the body at an angle of about 55 to the horizon will usually be found most convenient for unconstrained observation ; and the instrument should be so constructed as, when thus inclined, to give to the stage such an elevation above the table that, when the hands are employed at it, the arms may rest conveniently upon the table. In this manner a degree of support is attained which gives such free play to the muscles of the hands that movements of the greatest nicety may be executed by them, and the fatigue of long-continued observation is greatly diminished. When the ordinary camera lucidal is used for drawing or measuring, it is requisite that the microscope should be placed horizontally. It ought, therefore, to be made capable of every such variety of position ; and the stage must of course be provided with some means of holding the object, whenever it is itself placed in such a position that the object would slip down unless sustained.

The last principle on which we shall here dwell, as essential to the value of a microscope designed for ordinary work, is simplicity in the construction and adjustment of every part. Many ingenious mechanical devices have been invented and executed for the purpose of overcoming difficulties which are in themselves really trivial. A moderate amount of dexterity in the use of the hands is sufficient to render most of these superfluous ; and without such dexterity no one, even with the most complete mechanical facilities, will ever become a good microscopist. There is, of course, a limit to this simplification ; and no arrangement can be objected to on this score which gives advantages in the examination of difficult objects, or in the determination of doubtful questions, such as no simpler means can afford. The meaning of this distinction will become apparent if it be applied to the cases of the mechanical stage and the achromatic condenser. For, although the mechanical stage may be considered a valuable aid in observation, as facilitating the finding of a minute object, or the examination of the entire surface of a large one, yet it adds nothing to the clearness of our view of either ; and its place may in great degree be supplied by the fingers of a good manipulator. On the other hand, the use of the achromatic condenser not only contributes very materially, but is absolutely indispensable, to the formation of a perfect image, in time case of many objects of a difficult class ; the want of it cannot be compensated by the most dexterous use of the ordinary appliances ; and consequently, although it may fairly be considered superfluous as regards a large proportion of the purposes to which the microscope is directed, whether for investigation or for display, yet as regards the particular objects just alluded to it is a no less necessary part of the instrument than the achromatic objective itself. As a typical example of the simplest form of compound microscope that is suitable for scientific research, - which, with various niodifications of detail, is the one generally employed on the Continent, - the Microscope de dissection et d'observation (fig. 28) of /11. Nachet, especially as constructed for portability (figs. 29-31), seems particularly worthy of description. In its vertical form (fig. 28) the solid foot to which the mirror is pivoted gives support to the pillar F, to the top of which the stage P, having a diaphragm-plate beneath it, is firmly attached. On the top of this pillar the tubular stem A is fitted fn such a manner that it may be removed by unscrewing the large milled head L, - though, when this is well screwed down, the stein stands quite firmly. This stein bears at its summit a short horizontal arm, which carries a strong vertical tube that firmly grasps the " body " of the microscope, while permitting this to be easily slid upwards or downwards, so as to make a "coarse adjustment" of the focus. The "fine adjustment" is made by turning the milled head V, which either presses down the outer tube of the stein, or allows it to be raised by the upward pressure of a strong spiral spring in its interior. By unscrewing the milled head L., the stein A with its arm and compound body can be detached from the pillar ; and, a small light arm H holding either single lenses or doublets being slid into this, a convenient dissecting microscope is thus provided. The only drawback in the construction of this simple model is its not being provided with a joint for the inclination of the body ; but this is introduced into the portable form of the instrument shown in fig. 29, the basal portion of which (fig. 30) can be used, like that of the preceding model, as a simple microscope, and, by a most ingenious construction, can be so folded as to lie flat in a shallow case (fig. 31) that holds also the upper part with the objectives of both the simple arm and the com

A larger model, however, was from the first adopted by English opticians; and, as a typical example of the general plan of construction now most followed both in England and in the United States, the ins-proved JacksonZentmayer micro- , scope of Messrs Ross (fig. 32) may be appropriately selected. The tripod base of this instrument carries two pillars, between which is swung upon a horizontal axis (capable of being fixed in any position by a tightening screw) a solid "limb," with which all the other parts of the instrument are connected, - a plan of construction originally devised by Mr George Jackson. The binocular body, having at its lower end (as in fig. 24) an opening into which either of the Wenham prisms can be inserted, and at its top a rack movement for adjusting the eye Pro. 30. - Nacbet's Portable Dissecting Microscope; on the left as set up for use, on the right as having the stage P turned back upon the joint 0, so as to lie flat on the bottom of the case.

No instrument, in the writer's judgment, is better adapted than this for the highest purposes of microscopical research. It works admirably with every power from the lowest to the highest, and is capable of receiving any one of the numerous pieces of apparatus which have been devised for special researches of various kinds. The detailed description of these not being here admissible, it will be sufficient to indicate the polariscope and the spectroscope as the most important of accessories.

The microscopist has constant need of seine means of taking exact measurements of the dimensions of the minute objects, or parts of objects, on the study of which he is engaged ; and the accuracy of the operation will of course be proportioned to the correctness of the standard used, and the care with which it is applied.

The instruments employed in microscopic micrometry are of two kinds, the measurement being taken in one by the rotation of a fine screw with a divided milled head, whilst in the other a slip of glass ruled with lines at fixed distances gives a scale which forms a basis of computation. Each of these has its advantages and its disadvantages.

The stage-micrometer constructed by Frauenhofer was formerly much used by Continental microscopists, and has the advantage of indicating the actual dimensions of the objects to be measured ; but it has the two special disadvantages that a sufficiently small value cannot be conveniently given to its divisions, and that any error in its construction and working is augmented by the whole magnifying power employed. This instrument has now, however, almost entirely given place to one of those to be next described.

The screw-micrometer ordinarily used in astronomical measurements (see MicuomETER) can be adapted to the eye-piece of the microscope in a manner essentially the same as that in which it is applied to the telescope, - its two parallel threads - of which one is fixed and the other made to approach towards or recede from this by the turning of the screw - being placed in the focus of the eyeglass, and being therefore seen as lines crossing its field of view. The object is so focussed that its image is formed in the same plane ; and, the latter being brought into such a position that one of its ends or margins lies in optical contact with the fixed line, the screw is turned so as to bring the movable line into the like coincidence with the other. But the distance between the lines, as given by the number of divisions of the micrometer, will here be the measurement, not of the object itself, but of its magnified image ; and the value of these divisions, therefore, will depend upon the amplification given by the particular objective used, Thus, suppose each division of the micrometer to have an actual value of -/-0-1-0-uth of an inch, and the visual image to have one hundred times the linear dimensions of the object, the theoretical micrometric value of each division would be -a-6th of TA-06th, or one-millionth, of an inch, - a degree of minuteness, however, not practically attainable. It is necessary, moreover, to determine the micrometric value of the divisions of the micrometer, not only for every objective, but for variations in the conditions under which that objective may be employed, as regards the length of the tube or " body " of the microscope, which is varied not only by the draw-tube, but also, in many cases, in the working of the fine adjustment or slow motion, and also, in the case of the large-angled powers furnished with adjustment for thickness of the covering-glass, for the degree of separation of the front- from the back-glasses of the objective, which makes a very sensible difference in its magnifying power. This determination is made by means of a divided glass stage-micrometer put in the place of the object, so that the lines ruled upon it at fixed intervals shall be projected upon the field of view. The stage-micrometer is usually ruled either to 1000ths of an inch or 100ths of a millimetre; and it is convenient that one of the divisions of its image should be made to coincide exactly with a certain number of divisions of the screw-micrometer. This may be done by lengthening the draw-tube, so as to increase the amplification of the scale until coincidence has been reached ; and the exact amount of this lengthening should be noted, - as should also the precise position of the milled head of the slow motion (if it acts on the objective, instead of on the body as a whole), and of the adjusting screw-collar of the objective itself: Thus, if two lines of the stage-micrometer separated by 1000th of an inch be brought into coincidence with the two threads of the eye-piece micrometer, separated by forty divisions of the screw milled head, the value of each of those divisions is -o-6-oth of an inch. If the above conditions be precisely recorded for each objective used in micrometry, the micrometric value of the divisions remains the same for that objective, whenever it is employed under the same conditions.

The errors to which micrometers arc subject arise (1) from inequalities in the ruling of the stage-micrometer, (2) from irregularities in the screw of the eye-piece micrometer, (3) from " lost time " in its working, and (4) from the thickness of its threads. In order to eliminate the first and second, it is well to determine the relation of the divisions of the two micrometers by the comparison of a considerable number of both ; the third proceeds from an imperfection of workmanship which, if it shows itself sensibly, entirely destroys the value of the instrument, while the fourth can be rectified by the exercise of skill and judgment on the part of the observer. For, if the micrometer is so constructed as to read zero when one thread lies exactly upon the other, its divisions indicate the distance between the axes of these threads when separated ; and the dimensions of any object (such as a blood-corpuscle) lying between their borders will obviously be too great by half the thickness of the two threads, that is, by the entire thickness of one thread. 'When, on the other hand, the measurement is being made (as of the distances of the strife on diatoms) by the coincidence between certain lines on the object and the axes of the threads of the micrometer, the dimensions indicated by the divisions of the screw milled-head will be correct.

The costliness of a well-constructed screw-micrometer being a formidable obstacle to its general use, a simpler method (devised by Mr George Jackson) is more commonly adopted, which consists in the insertion of a ruled-glass scale into the focus of an ordinary Huygenian eye-piece, so that its lines are projected on the field of view. This scale (ruled, like an ordinary measure, with every fifth line long, and every tenth line double the length of the fifth) is fixed in a brass inner frame, that has a slight motion in the direction of its length within an outer frame; and this last, being introduced through a pair of slits into the eye-piece just above the diaphragm, and being made to occupy the centre of the field, is brought exactly into focus by unscrewing the eye-glass as far as may be requisite. When the image of the object to be measured is brought by the focal adjustment of the object-glass into the same plane, a small pushing-screw at the end of the micrometer (whose action is antagonized by a spring at the other end) is turned until one of the long divisions of the scale is brought into optical contact with one edge of the image of the object to be measured, and the number of divisions is then counted to its other edge, - the operation being exactly that of laying a rule across the real object if enlarged to the size of its image. The micrometric value of each division of this eye-piece scale must be carefully ascertained for each objective, as in the case of the screw-micrometer, the error arising from inequality of its divisions being eliminated as far as possible by taking an average of several. The principal point of inferiority in this form of micrometer is that, as its divisions cannot be made of nearly so small a value as those of the screw-micrometer, an estimate of fractional parts of them often becomes necessary, which is objectionable as involving an additional source of error. To meet this objection, Hartnack has introduced the diagonal scale used in mathematical instruments before the invention of the vernier.

Another mode of making micrometric measurements, which for some purposes has considerable advantages, is to employ a stage-micrometer in combination with some form of camera lucida attached to the eye-piece of the microscope, so that the image of its divisions may be projected upon the same surface as that on which the image of the object is thrown. By first using the ruled stage-micrometer, and marking on the paper the average distance of its lines as seen in the central part of the field, and then ruling the paper accordingly, the micrometric value of the divisions so projected may be exactly determined for the objective employed and the distance of the drawing-plane from the eye-piece, - so that., when the image of any object is projected under tire same conditions, the dimensions of that image or of any parts of it can be exactly measured upon the divided scale previously projected, and the true dimensions of the object thus easily ascertained. If, for example, the lines of a stage-micrometer ruled to the thousandth of an inch should, when thus projected, fall at a distance of an inch apart, then the application of an ordinary scale of inches (divided into tenths) to the image of an object projected by the same objective and on the same plane would give its real dimensions in thousandths of an inch, while the tenths of the inch scale would represent a real dimension of as many ten-thousandths. It is often desirable to make such measurements from careful tracings of the outlines of objects, rather than from the visual images, - this plan being especially advantageous when the exact dimensions of many similar objects have to be compared, as in the ease of blood-corpuscles, precise measurements of which are not unfrequently required in judicial inquiries. It was by the use of this method that the late Mr Gulliver made his admirable series of measurements of the average and extreme dimensions of the blood-corpuscles of different animals. And more recently Mr Dallinger has shown, - by first