The Microscope Part 2

[Ill.u.s.tration: Fig. 15.]

[Ill.u.s.tration: Fig. 16.]

"It will be seen by Fig. 15, that when a certain angular pencil A O A'

proceeds from the object O, and is incident on the plane side of the first lens, if the combination is removed from the object, as in Fig.

16, the extreme rays of the pencil impinge on the more marginal parts of the gla.s.s, and as the refractions are greater here, the aberrations will be greater also. Now, if two compound object-gla.s.ses have their aberrations balanced, one being situated as in Fig. 15, and the other as in Fig. 16, and the same disturbing power applied to both, that in which the angles of incidence and the aberrations are small will not be so much disturbed as where the angles are great, and where consequently the aberrations increase rapidly.

"When an object-gla.s.s has its aberrations balanced for viewing an opaque object, and it is required to examine that object by transmitted light, the correction will remain; but if it is necessary to immerse the object in a fluid, or to cover it with gla.s.s or talc, an aberration will arise from these circ.u.mstances, which will disturb the previous correction, and consequently deteriorate the definition; and this effect will be more obvious with the increase of the distance between the object and the object-gla.s.s.

[Ill.u.s.tration: Fig. 17.]

"The aberration produced with diverging rays by a piece of flat and parallel gla.s.s, such as would be used for covering an object, is represented at Fig. 17, where G G G G is the refracting medium, or piece of gla.s.s covering the object O; O P, the axis of the pencil, perpendicular to the flat surfaces; O T, a ray near the axis; and O T', the extreme ray of the pencil incident on the under surface of the gla.s.s; then T R, T' R', will be the directions of the rays in the medium, and R E, R' E', those of the emergent rays. Now if the course of these rays is continued, as by the dotted lines, they will be found to intersect the axis at different distances, X and Y, from the surface of the gla.s.s; and the distance X Y is the aberration produced by the medium which, as before stated, interferes with the previously balanced aberrations of the several lenses composing the object-gla.s.s. There are many cases of this, but the one here selected serves best to ill.u.s.trate the principle. I need not enc.u.mber the description with the theoretical determination of this quant.i.ty, as it varies with exceedingly minute circ.u.mstances which we cannot accurately control; such as the distance of the object from the under side of the gla.s.s, and the slightest difference in the thickness of the gla.s.s itself; and if these data could be readily obtained, the knowledge would be of no utility in making the correction, that being wholly of a practical nature.

"If an object-gla.s.s is constructed as represented in Fig. 16, where the posterior combination P and the middle M have together an excess of negative aberration, and if this be corrected by the anterior combination A, having an excess of positive aberration, then this latter combination can be made to act more or less powerfully upon P and M, by making it approach to or recede from them; for when the three are in close contact, the distance of the object from the object-gla.s.s is greatest; and consequently the rays from the object are diverging from a point at a greater distance than when the combinations are separated; and as a lens bends the rays more, or acts with greater effect, the more distant the object is from which the rays diverge, the effect of the anterior combination A upon the other two, P and M, will vary with its distance from thence. When therefore the correction of the whole is effected for an opaque object with a certain distance between the anterior and middle combination, if they are then put in contact, the distance between the object and object-gla.s.s will be increased; consequently the anterior combination will act more powerfully, and the whole will have an excess of positive aberration. Now the effect of the aberration produced by a piece of flat and parallel gla.s.s being of the negative character, it is obvious that the above considerations suggest the means of correction by moving the lenses nearer together, till the positive aberration thereby produced balances the negative aberration caused by the medium.

"The preceding refers only to the spherical aberration, but the effect of the chromatic is also seen when an object is covered with a piece of gla.s.s; for, in the course of my experiments, I observed that it produced a chromatic thickening of the outline of the Podura and other delicate scales; and if diverging rays near the axis and at the margin are projected through a piece of flat parallel gla.s.s, with the various indices of refraction for the different colors, it will be seen that each ray will emerge separated into a beam consisting of the component colors of the ray, and that each beam is widely different in form. This difference, being magnified by the power of the microscope, readily accounts for the chromatic thickening of the outline just mentioned. Therefore to obtain the finest definition of extremely delicate and minute objects, they should be viewed without a covering; if it be desirable to immerse them in a fluid, they should be covered with the thinnest possible film of talc, as, from the character of the chromatic aberration, it will be seen that varying the distances of the combinations will not sensibly affect the correction; though object-lenses may be made to include a given fluid or solid medium in their correction for color.

[Ill.u.s.tration: Fig. 18.]

"The mechanism for applying these principles to the correction of an object-gla.s.s under the various circ.u.mstances, is represented in Fig.

18, where the anterior lens is set in the end of a tube A A, which slides on the cylinder B containing the remainder of the combination; the tube A A, holding the lens nearest the object, may then be moved upon the cylinder B, for the purpose of varying the distance according to the thickness of the gla.s.s covering the object, by turning the screwed ring C C, or more simply by sliding the one on the other, and clamping them together when adjusted. An aperture is made in the tube A, within which is seen a mark engraved on the cylinder, and on the edge of which are two marks, a longer and a shorter, engraved upon the tube. When the mark on the cylinder coincides with the longer mark on the tube, the adjustment is perfect for an uncovered object; and when the coincidence is with the short mark, the proper distance is obtained to balance the aberrations produced by gla.s.s one-hundredth of an inch thick, and such gla.s.s can be readily supplied.

"It is hardly necessary to observe, that the necessity for this correction is wholly independent of any particular construction of the object-gla.s.s; as in all cases where the object-gla.s.s is corrected for an object uncovered, any covering of gla.s.s will create a different value of aberration to the first lens, which previously balanced the aberration resulting from the rest of the lenses; and as this disturbance is effected at the first refraction, it is independent of the other part of the combination. The visibility of the effect depends on the distance of the object from the object-gla.s.s, the angle of the pencil transmitted, the focal length of the combination, the thickness of the gla.s.s covering the object, and the general perfection of the corrections for chromatism and the oblique pencils.

"With this adjusting object-gla.s.s, therefore, we can have the requisites of the greatest possible distance between the object and object-gla.s.s, an intense and sharply defined image throughout the field from the large pencil transmitted, and the accurate correction of the aberrations; also, by the adjustment, the means of preserving that correction under all the varied circ.u.mstances in which it may be necessary to place an object for the purpose of observation."

In the annexed engraving, Fig. 19, we have shown the triple achromatic object-gla.s.s in connection with the eye-piece consisting of the field-gla.s.s F F, and the eye-gla.s.s E E, forming together the modern achromatic microscope. The course of the light is shown by drawing three rays from the centre and three from each end of the object O.

These rays would, if left to themselves, form an image of the object at A A, but being bent and converged by the field-gla.s.s F F, they form the image at B B, where a stop is placed to intercept all light except what is required for the formation of the image. From B B therefore the rays proceed to the eye-gla.s.s exactly as has been described in reference to the simple microscope and to the compound of two gla.s.ses.

[Ill.u.s.tration: Fig. 19.]

If we stopped here we should convey a very imperfect idea of the beautiful series of corrections effected by the eye-piece, and which were first pointed out in detail in a paper on the subject published by Mr. Varley in the 51st volume of the Transactions of the Society of Arts. The eye-piece in question was invented by Huyghens for telescopes, with no other view than that of diminishing the spherical aberration by producing the refractions at two gla.s.ses instead of one, and of increasing the field of view. It was reserved for Boscovich to point out that Huyghens had by this arrangement accidentally corrected a great part of the chromatic aberration, and this subject is further investigated with much skill in two papers by Professor Airy in the _Cambridge Philosophical Transactions_, to which we refer the mathematical reader. These investigations apply chiefly to the telescope, where the small pencils of light and great distance of the object exclude considerations which become important in the microscope, and which are well pointed out in Mr. Varley's paper before mentioned.

[Ill.u.s.tration: Fig. 20.]

Let Fig. 20 represent the Huyghenean eye-piece of a microscope; F F and E E being the field-gla.s.s and eye-gla.s.s, and L M N the two extreme rays of each of the three pencils, emanating from the centre and ends of the object, of which, but for the field-gla.s.s, a series of colored images would be formed from R R to B B; those near R R being red, those near B B blue, and the intermediate ones green, yellow, and so on, corresponding with the colors of the prismatic spectrum. This order of colors, it will be observed, is the reverse of that described in treating of the common compound microscope (Fig. 12), in which the single object-gla.s.s projected the red image beyond the blue.

The effect just described, of projecting the blue image beyond the red, is purposely produced for reasons presently to be given, and is called over-correcting the object-gla.s.s as to color. It is to be observed also that the images B B and R R are curved in the wrong direction to be distinctly seen by a convex eye-lens, and this is a further defect of the compound microscope of two lenses. But the field-gla.s.s, at the same time that it bends the rays and converges them to foci at B' B' and R' R', also reverses the curvature of the images as there shown, and gives them the form best adapted for distinct vision by the eye-gla.s.s E E. The field-gla.s.s has at the same time brought the blue and red images closer together, so that they are adapted to pa.s.s uncolored through the eye-gla.s.s. To render this important point more intelligible, let it be supposed that the object-gla.s.s had not been over-corrected, that it had been perfectly achromatic; the rays would then have become colored as soon as they had pa.s.sed the field-gla.s.s; the blue rays, to take the central pencil, for example, would converge at _b_ and the red rays at _r_, which is just the reverse of what the eye-lens requires; for as its blue focus is also shorter than its red, it would demand rather that the blue image should be at _r_ and the red at _b_. This effect we have shown to be produced by the over-correction of the object-gla.s.s, which protrudes the blue foci B B as much beyond the red foci R R as the sum of the distances between the red and blue foci of the field-lens and eye-lens; so that the separation B R is exactly taken up in pa.s.sing through those two lenses, and the whole of the colors coincide as to focal distance as soon as the rays have pa.s.sed the eye-lens. But while they coincide as to distance, they differ in another respect; the blue images are rendered smaller than the red by the superior refractive power of the field-gla.s.s upon the blue rays. In tracing the pencil L, for instance, it will be noticed that after pa.s.sing the field-gla.s.s, two sets of lines are drawn, one whole, and one dotted, the former representing the red, and the latter the blue rays. This is the accidental effect in the Huyghenean eye-piece pointed out by Boscovich. This separation into colors at the field-gla.s.s is like the over-correction of the object-gla.s.s; it leads to a subsequent complete correction. For if the differently colored rays were kept together till they reached the eye-gla.s.s, they would then become colored, and present colored images to the eye; but fortunately, and most beautifully, the separation effected by the field-gla.s.s causes the blue rays to fall so much nearer the centre of the eye-gla.s.s, where, owing to the spherical figure, the refractive power is less than at the margin, that the spherical error of the eye-lens const.i.tutes a nearly perfect balance to the chromatic dispersion of the field-lens, and the red and blue rays L' and L" emerge sensibly parallel, presenting, in consequence, the perfect definition of a single point to the eye. The same reasoning is true of the intermediate colors and of the other pencils.

From what has been stated it is obvious that we mean by an achromatic object-gla.s.s one in which the usual order of dispersion is so far reversed that the light, after undergoing the singularly beautiful series of changes effected by the eye-piece, shall come uncolored to the eye. We can give no specific rules for producing these results.

Close study of the formulae for achromatism given by the celebrated mathematicians we have quoted will do much, but the principles must be brought to the test of repeated experiment. Nor will the experiments be worth anything, unless the curves be most accurately measured and worked, and the lenses centered and adjusted with a degree of precision which, to those who are familiar only with telescopes, will be quite unprecedented.

The Huyghenean eye-piece which we have described is the best for merely optical purposes, but when it is required to measure the magnified image, we use the eye-piece invented by Mr. Ramsden, and called, from its purpose, the micrometer eye-piece. When it is stated that we sometimes require to measure portions of animal or vegetable matter a hundred times smaller than any divisions that can be artificially made on any measuring instrument, the advantage of applying the scale to the magnified image will be obvious, as compared with the application of engraved or mechanical micrometers to the stage of the instrument.

The arrangement is shown in Fig. 21, where E E and F F are the eye and field gla.s.s, the latter having now its plane face towards the object.

The rays from the object are here made to converge at A A, immediately in front of the field-gla.s.s, and here also is placed a plane gla.s.s on which are engraved divisions of a hundredth of an inch or less. The markings of these divisions come into focus therefore at the same time as the image of the object, and both are distinctly seen together.

Thus the measure of the magnified image is given by mere inspection, and the value of such measures in reference to the real object may be obtained thus, which, when once obtained, is constant for the same object-gla.s.s. Place on the stage of the instrument a divided scale the value of which is known, and viewing this scale as the microscopic object, observe how many of the divisions on the scale attached to the eye-piece correspond with one of those in the magnified image. If, for instance, ten of those in the eye-piece correspond with one of those in the image, and if the divisions are known to be equal, then the image is ten times larger than the object, and the dimensions of the object are ten times less than indicated by the micrometer. If the divisions on the micrometer and on the magnified scale were not equal, it becomes a mere rule-of-three sum, but in general this trouble is taken by the maker of the instrument, who furnishes a table showing the value of each division of the micrometer for every object-gla.s.s with which it may be used.

[Ill.u.s.tration: Fig. 21.]

While on the subject of measuring it may be well to explain the mode of ascertaining the magnifying power of the compound microscope, which is generally taken on the a.s.sumption before mentioned, that the naked eye sees most distinctly at the distance of ten inches.

Place on the stage of the instrument, as before, a known divided scale, and when it is distinctly seen, hold a rule at ten inches distance from the disengaged eye, so that it may be seen by that eye, overlapping or lying by side of the magnified picture of the other scale. Then move the rule till one or more of its known divisions correspond with a number of those in the magnified scale, and a comparison of the two gives the magnifying power.

Having now explained the optical principles of the achromatic compound microscope, it remains only to describe the mechanical arrangements for giving those principles their full effect. The mechanism of a microscope is of much more importance than might be imagined by those who have not studied the subject. In the first place, steadiness, or freedom from vibration, and most particularly freedom from any vibrations which are not equally communicated to the object under examination, and to the lenses by which it is viewed, is a point of the utmost consequence. When, for instance, the body containing the lenses is screwed by its lower extremity to a horizontal arm, we have one of the most vibratory forms conceivable; it is precisely the form of the inverted pendulum, which is expressly contrived to indicate otherwise insensible vibrations. The tremor necessarily attendant on such an arrangement is magnified by the whole power of the instrument; and as the object on the stage partakes of this tremor in a comparatively insensible degree, the image is seen to oscillate so rapidly, as in some cases to be wholly undistinguishable. Such microscopes cannot possibly be used with high powers in ordinary houses ab.u.t.ting on any paved streets through which carriages are pa.s.sing, nor indeed are they adapted to be used in houses in which the ordinary internal sources of shaking exist.

One of the best modes of mounting a compound microscope is shown in the annexed view (Fig. 22), which, though too minute to exhibit all the details, will serve to explain the chief features of the arrangement.

A ma.s.sy pillar A is screwed into a solid tripod B, and is surmounted by a strong joint at C, on which the whole instrument turns, so as to enable it to take a perfectly horizontal or vertical position, or any intermediate angle, such, for instance, as that shown in the engraving.

This movable portion of the instrument consists of one solid casting D E F G; from F to G being a thick pierced plate carrying the stage and its appendages. The compound body H is attached to the bar D E, and moves up and down upon it by a rack and pinion worked by either of the milled heads K. The piece D E F G is attached to the pillar by the joint C, which being the source of the required movement in the instrument, is obviously its weakest part, and about which no doubt considerable vibration takes place. But inasmuch as the piece D E F G of necessity transmits such vibrations equally to the body of the microscope and to the objects on the stage, they hold always the same relative position, and no _visible_ vibration is caused, how much soever may really exist. To the under side of the stage is attached a circular stem L, on which slides the mirror M, plane on one side and concave on the other, to reflect the light through the aperture in the stage. Beneath the stage is a circular revolving plate containing three apertures of various sizes, to limit the angle of the pencil of light which shall be allowed to fall on the object under examination.

Besides these conveniences the stage has a double movement produced by two racks at right angles to each other, and worked by milled heads beneath. It has also the usual appendages of forceps to hold minute objects, and a lens to condense the light upon them, all of which are well understood, and if not, will be rendered more intelligible by a few minutes' examination of a microscope than by the most lengthened description. One other point remains to be noticed. The movement produced by the milled head K is not sufficiently delicate to adjust the focus of very powerful lenses, nor indeed is any rack movement.

Only the finest screws are adapted to this purpose; and even these are improved by means for reducing the rapidity of the screw's movement.

For this purpose the lower end of the compound body H, which carries the object-gla.s.s, consists of a piece of smaller tube sliding in parallel guides in the main body, and kept constantly pressed upwards by a spiral spring but it can be drawn downward by a lever crossing the body, and acted on by an extremely fine screw whose milled head is seen at N, and the fineness of which is tripled by means of the lever through which it acts on the object-gla.s.s. The instrument is of course roughly adjusted by the rack movement, and finished by the screw, or by such other means as are chosen for the purpose. One very ingenious contrivance, but applied to the stage, instead of the body of the microscope, invented by Mr. Powell, will be found described in the 50th volume of the Transactions of the Society of Arts.

[Ill.u.s.tration: Fig. 22.]

The greater part of the directions for viewing and illuminating objects given in reference to the simple microscope are applicable to the compound. An argand lamp placed in the focus of a large detached lens so as to throw parallel rays upon the mirror, is the best artificial light; and for opaque objects the light so thrown up may be reflected by metallic specula (called, from their inventor, Lieberkhuns) attached to the object-gla.s.ses.

It has been recently proposed by Sir David Brewster and by M. Dujardin to render the Wollaston condenser achromatic, and they have accordingly been made with three pairs of achromatic lenses instead of the single lens before described, with very excellent effect. The last-mentioned gentleman has also projected an ingenious apparatus, called the Hyptioscope, attached to the eye-piece for the purpose of erecting the magnified picture.

The erector commonly applied to the compound microscope consists of a pair of lenses acting like the erecting eye-piece of the telescope.

But this, though it is convenient for the purpose of dissection, very much impairs the optical performance of the instrument.

[Ill.u.s.tration: Fig. 23.]

For drawing the images presented by the microscope the best apparatus consists of a mirror M (Fig. 23), composed of a thin piece of rather dark-colored gla.s.s cemented on to a piece of plate-gla.s.s inclined at an angle of 45 in front of the eye-gla.s.s E. The light escaping from the eye-gla.s.s is a.s.sisted in its reflection upwards to the eye by the dark gla.s.s, which effects the further useful purpose of rendering the paper less brilliant, and thus enabling the eye better to see the reflected image. The lens L below the reflector is to cause the light from the paper and pencil to diverge from the same distance as that received from the eye-gla.s.s; in other words, to cause it to reach the eye in parallel lines.

[Ill.u.s.tration: Fig. 24.]

Dr. Wollaston's camera lucida, as shown in Fig. 24, is sometimes attached to the eye-piece of the microscope for the same purpose. In this instrument the rays suffer two internal reflections within the gla.s.s prism, as will be seen explained in the article "Camera Lucida."

In this minute figure we have omitted to trace the reflected rays, merely to avoid confusion.

[Ill.u.s.tration: Fig. 25.]

[Ill.u.s.tration: Fig. 26.]

[Ill.u.s.tration: Fig. 27.]

Annexed are four engravings of microscopic objects, the true character of which it is, however, impossible to give in wood, and is difficult indeed to accomplish by any description of engraving.

[Ill.u.s.tration: Fig. 28.]

Fig. 25 shows a scale of the small insect called Podura Plumbea, the common Skiptail, magnified about five hundred times. To define the markings on this scale clearly is the highest test of a deep achromatic object-gla.s.s; and this drawing is given rather to explain what the observer should look for, than as a very correct representation. Fig. 26 is a scale or feather of the Menelaus b.u.t.terfly; Fig. 27 is the hair of a singular insect, the Dermestes; and Fig. 28 is a longitudinal cutting of fir, showing the circular glands on the vessels which distinguish coniferous woods. These latter objects may be seen by half-inch or quarter-inch achromatic gla.s.ses.

Opaque objects are generally better exhibited by inch and two-inch gla.s.ses, when a general view of them is required, and by higher powers when we wish to examine their minute structure. In the latter case the light must be obtained by condensing lenses instead of the metallic specula.

Although the reflecting microscope is now very little used, it may be expected that we should mention it. In this instrument, at Fig. 29, the object O is reflected by the inclined face of the mirror M, and the rays are again reflected and converged by the ellipsoidal reflector R R, which effects the same purpose as the object-gla.s.s of the compound microscope. It forms an image which is not susceptible of the over-correction as to color before described, and which therefore becomes colored in pa.s.sing through the eye-piece. This fact, and the loss of light by reflection, will probably always render the reflecting microscope inferior to the achromatic refracting.

[Ill.u.s.tration: Fig. 29.]