Microscope, from μικρός, a small object, and ὀπτικός, to see or examine, is the name of a well-known optical instrument for examining and magnifying minute objects, or the minute parts of large ones. Dr Goring has, in his various works on the microscope, used the word engloscope, from εγγλος, near, and σκοπεῖν, to see; but the old and venerable term is so associated with the history of optical discovery, and is so expressive of the application of the instrument, that we cannot consent to the proposed change.

Single microscopes, in the form of glass globes containing water, were used by the ancients. A magnifying lens of rock-crystal was found by Mr Layard among a number of glass bowls in the north-west palace of Nimroud. Hemispheres of glass, and afterwards lenses, were subsequently used, so that no person has pretended to claim the invention of the single microscope. The compound microscope, consisting of two lenses placed at a distance, so that the one next the eye magnifies the enlarged image of any object placed in front of the other, was invented by Zacharias Zaanst, or his father Hans Zaanst, spectacle-makers at Middelburg in Holland, about the year 1590. One of their 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 VI.

There is probably no branch of practical science which has undergone such essential and rapid improvements as that which relates to the microscope. It has become quite a new instrument in modern times, and it promises to be the means of disclosing the structure and laws of matter, and of making as important discoveries in the infinitely minute world as the telescope has done in that which is infinitely distant.

CHAPTER I.

ON SINGLE MICROSCOPES.

When only one convex lens AB (fig. 1) is used for magnifying objects, the lens is called a single microscope. The object MN to be examined is placed before the lens AB, in its anterior focus; so that the rays which emerge from the lens after refraction by the humours of the eye CD may be parallel, and a distinct and enlarged image MN of the object MN formed on the retina. The simplest form of the single microscope is when the lens is fitted into a rim of brass furnished with a handle, so that when the object is held in the left hand and the lens in the right, it may be examined with facility. If the convex lens is very minute, and has a short focal length, such as from the 10th to the 100th of an inch, it cannot be conveniently used in the hand, and must therefore be either connected with an arm to hold the object, or placed in a firm microscope stand, having a shelf or stage for the object, a screw or a rack and pinion for placing it in the focus of the lens, either by moving the object or the lens, and a larger lens or mirror, or both, for throwing light upon the object. In this form, however complex be its structure, it is still called a single microscope.

The lens which constitutes a single microscope, in order to have all the excellence which art can give it, must consist of a substance perfectly homogeneous, like a fluid without double refraction, or any variation of density. Its figure ought to be that of a plano-convex lens, whose convex surface is part of a hyperboloid, in order to correct completely the spherical aberration. Its surface should be perfectly smooth and highly polished, so as not to disturb the perfection of vision; and the substance of which it is made should have the lowest dispersive power. As it is a great object to obtain high magnifying powers with as little convexity as possible, and a large aperture, substances with high refractive and low dispersive powers are the most suitable for single lenses, such as diamond or garnet, which have no double refraction when well crystallized; or such as ruby, sapphire, topaz, &c., which have double refraction. As flint spar has the lowest dispersive power, it might be used with great advantage when high powers are not wanted, and when the diminution of colour is an object.

Of all the substances we have named, fluids have properties best suited for single microscopes. They possess perfect homogeneity; their surfaces, when made into lenses, are perfectly smooth; and it is possible to mould minute drops of them into a form approaching to that of the hyperboloid. Their defect, however, consists in their not having a high refractive power, in their want of durability, and the difficulty of forming sufficiently minute lenses for producing high magnifying powers. These defects, however, may be overcome by patience and experience; and in proof of this we may state that we have succeeded in forming minute fluid lenses of great excellence.

In the present state of this branch of science, it would be unprofitable to detail the methods of producing microscopic globules of glass, given by Dr Hooke, Father di Torre of Naples, Mr Butterfield, or Mr Slivright; because when they are made after their methods, and in the most perfect manner which these methods will permit, they are of no value compared with lenses of glass when ground and polished to the same focal length.

We shall therefore proceed to describe a single microscope when fitted up in the best form for observation.

Description of a Single Microscope.

The most essential part of this instrument is the lens or single lenses, upon which the value of the microscope depends. The lenses are generally made of plate-glass, and should have focal distances varying from the 1/5th to the 1/30th of an inch. In order that the spherical aberration of these lenses may be the smallest possible, the radii of their two surfaces, when made of plate-glass, should be as 1 to 6; the surface whose radius is 1, or the most convex side, must be turned towards the eye. The lenses thus made are then set in the centre or the lower surface of concave brass caps, a section of one of which is shown in fig. 2.

One of the best modes of fitting up the single microscope Pritchard's is that contrived by Mr Pritchard, which is represented in micro-fig. 3, on a scale about one-third of its real size. It is shown scope, in an inclined position; but it may be used either in a vertical or a horizontal one, according to the convenience of the observer. The body of the instrument rests on a pillar b,

---

1 These methods may be found by the following references—Hooke's Micrographia, Di Torre, Phil. Trans., 1768, p. 246, 1768, p. 67; Butterfield, Phil. Trans., 1678; Slivright, Edin. Phil. Journal, 1829, vol. i, p. 81. supported by three legs, shown at \(a\), and is connected with it by the clip \(f\), being fixed by the pinching screw \(j\). Within the tube \(e\) there slides a tube \(h\), connected by a screw which passes through it to the triangular tube or bar \(i\), carrying the arm \(j\), into which is placed the brass cap \(j\) which carries the lens. This lens is adjusted to the distinct vision of objects placed on the stage \(l\); by sliding the tube \(h\) up or down, and a perfect adjustment is obtained by turning the milled head \(k\). The stage \(l\), which carries the objects, is fitted into the triangular box \(r\) at the extremity of the stem, by means of two pins, and can be removed at pleasure. The spring slider-holder, for holding the sliders in which the objects are placed, is fixed by a bayonet-joint into the stage; and it may be used to hold stops or diaphragms for limiting the field of view. The tube above \(f\) represents an illuminator fixed to the slider-holder. Upon the tube \(e\), two sockets \(d, e\), slide with sufficient spring and friction to keep them in their place. The socket \(d\) carries the reflector \(d\), and the socket \(e\) carries the condensing lens, which is not inserted in the figure.

A section of the stem \(r\) is shown in fig. 4, in order to exhibit the mechanism by which the adjustment is effected. Into the box \(r\), screwed into the top of the stem, is fitted the triangular tube \(ii\), which carries the arm \(j\). In the lower end \(i\) of this triangular tube is a small block with a fine screw working in it, the stem of which turns along with the milled head \(k\) to which it is fixed. The upper end of a spiral spring, shown in the figure, bears against the block \(i\) at the bottom of the triangular tube, while its lower end acts against a stop fixed within the sliding tube \(h\). The method of managing, illuminating, and examining opaque objects with this microscope is the same as that used in the achromatic compound microscope, in the drawing of which it will be more distinctly seen.

The preceding instrument of Mr Pritchard's is intended for general purposes; but as the dissection of botanical and other objects is now a leading object with naturalists, we shall add an account of another microscope, constructed in 1831 by Mr A. Ross, with much skill, for Mr W. Valentine of Nottingham, an eminent vegetable anatomist, who succeeded in dissecting with it under a lens of \(\frac{1}{4}\)th of an inch in focal length.

A perspective view of this microscope is shown in fig. 5. Ross's microscope is supported on a closing tripod \(aaa\), whose feet can be closed together, and are made of hard bell-metal, prevented from springing by edge bars, as seen on the left-hand foot. A firm pillar, which rises from the tripod, carries the stage \(x\), which is fixed on brackets, to give a steady support to the hands of the operator. A capital, fixed to the top of the tube by three screws, has in its axis a triangular hole, into which is fitted a triangular tube, the lower end of which passes through another similar triangular tube fixed to the inside of the instrument. The triangular tube is made to slide up and down by a fixed screw, wrought by a large milled head, which is most judiciously placed at the base of the pillar. At the top and bottom of the fixed triangular tube are fitted two pieces, with triangular holes through them for receiving the triangular bell-metal bar \(s\), which moves up and down in them. This bar carries the arm 10 with the lenses. It is moved up and down, so as to adjust the lenses to distinct vision of the objects on the fixed stage, by the rack and pinion \(t\), when a quick adjustment is required; but when a slow and nicer adjustment is wanted, it is effected by the milled head \(o\). A slit is made in the shaft of the pillar, to allow the neck of the small milled head \(c\) to move up and down; for when the screw is in action by the large milled head \(o\), the triangular tube and the bar move together. The triangular bar is perforated at both ends,—the upper perforation for receiving a conical pin, and the lower for admitting the adjusting screw to preserve the length of the bar. The bearings of the pinion \(t\) are attached to the triangular tube. The bar moves \(\frac{1}{2}\) inch, and the tube \(\frac{1}{2}\) inch, so that

---

1 See Transactions of the Society of Arts, vol. xlviii., where a full description of this microscope, with drawings of all its parts, will be found. we can command an elevation of 3 inches. At the ingenious suggestion of Mr Solly, the screw moved by the milled head o has fifty threads in an inch, and the milled head is graduated into 100 parts, for the purpose of measuring the thickness of any vessel or other object in the direction of the axis of vision. For this purpose the upper surface of the body is brought into distinct vision; the division at which the index or pin of the tripod stands is then observed; and the under surface being in like manner brought into focus by turning the head o, the division is again observed. The number of divisions, which are each 5000ths of an inch, between these two numbers, will indicate, according to Mr Valentine, the space through which the lens has passed, which is the diameter of a vessel.

In this microscope different parts of an object may be brought into the field, either by moving the stage or the lens; a very important requisite in a microscope used for the purposes of discovery. With this view, the large stage is formed of three plates, the lowest of which is fixed to the pillar by the ring l; and, to make it bear the weight of the hands, it rests upon the strong brackets 2, 2. The


under side of this plate is shown in fig. 6; the middle plate (fig. 7) contains two pairs of dovetail slits, 3, 3 and 4, 4, the widest orifice of each being on opposite sides of the plate. The dovetail pieces in 4, 4 screw into the upper side of the upper plate (fig. 8), the points of the screws being shown at 4, 4 in that figure; while the dovetail pieces in 3, 3 are secured to the upper side of the under plate by the screws 3, 3 (fig. 7). The plates are thus moved diagonally, and at right angles to one another, by the adjusting screws 7 and 8 (fig. 8). In the adjusting screw 7 the ball is placed in spring couplings, and fastened to the under side of the upper plate. These screws are judiciously placed, one on each side of the pillar, that the hand may reach them easily and not intercept the light. By turning first one screw, and then the other, or both at once, any part of the object may be brought into the field.

This is not the case, as the refraction of the light issuing from the lower side of the vessel or object is not considered. The right mode is, after having observed the upper surface of an object lying

The arm for holding the lenses is shown at 10 (fig. 5). A conical pin projects from underneath, and fits into a hole made down the triangular bar, as shown at 9 (fig. 8). The lens will therefore have a circular movement in a horizontal plane, and it may be placed at any point in this plane by the action of the rack and pinion at 10. Hence the most complete adjustment can be obtained without any motion of the stage.

The elevated stage for holding the objects is shown at 11 in figs. 5 and 8. A tube screws into the upper plate, and upon this fits the tube 11, carrying the finger-spring, shown in fig. 5. Objects of different thickness are thus kept down upon the plates by the pins sliding in the small pipes. A condensing lens and pincers slide into the sockets 5 or 6 (fig. 5).

The large reflector above a (fig. 5) may be removed, and any other illuminating apparatus substituted.

As the stand and apparatus now described may be used along with all single microscopes, and also with what are called doublets and triplets, we shall now proceed to give an account of the various improvements which the single microscope has undergone.

Between the single lens held in the hand and the one mounted with much of the apparatus of a compound microscope, we may place what has been called the simple microscope, which is nothing more than a single lens mounted on a stand, so that it may be fixed in various positions suited to the purpose to which it is to be applied.

Mr Ross's simple microscope is shown in fig. 9. It consists of a stand A, with a sliding tube, which can be raised or depressed. On the top of this tubular stand is fixed a jointed socket MN, through which a square bar CD slides, carrying at one of its extremities the lens L, the ring of which moves round a joint at C. Lenses of an inch, a half-inch, and a quarter of an inch focus should accompany the instrument, which may be packed into a small space.

**Single Microscopes made of Precious Stones.**

The low refractive power of glass rendered it necessary, when high powers were wanted, to use lenses with excessively short foci, and consequently with very deep curves of precious and very small diameters, so as to admit only a narrow pencil of light into the eye.

Sir David Brewster was the first person who pointed out the value of using other materials for the construction of lenses; and he remarked that no essential improvement could be expected in the single microscope, unless from the discovery of some transparent substance, which, like the diamond, combines a high refractive with a low dispersive

upon glass, remove the object, and observe the divisions when the surface of the glass is seen distinctly; the difference will be the true thickness. Mr Samuel Varley is said to have constructed an instrument on this principle for measuring the thickness of focal lengths; but unless he removed his lens after observing the first surface, his results must have been all erroneous.

*Treatise on Philosophical Instruments*, 1813, pp. 402, 403. power. Having experienced the greatest difficulty in getting a small diamond cut into a prism in London, he did not conceive it practicable to grind and polish a diamond lens; and therefore did not put his opinion to the test of experiment. He got two lenses, however, executed by Mr Peter Hill, an ingenious optician in Edinburgh, the one made of ruby and the other of garnet, and these lenses he found to be greatly superior to any lenses that he had previously used.

Dr Göring, whose zeal and success in the improvement of microscopes has not been surpassed, directed the attention of Mr Pritchard in 1824 to the passages in Sir David Brewster's Treatise on New Philosophical Instruments, respecting the value of the precious stones for single microscopes; and having immediately seen their full force, it was agreed that they should undertake to grind a diamond into a magnifier.

Diamond Lenses.

The history of this attempt is so interesting, that we must give it in Mr Pritchard's own words:—"For this purpose," says he, "Dr Göring forwarded me a small brilliant diamond to begin upon; and it was proposed to give it the curves that in glass would produce a lens of a twentieth of an inch focus. This stone I ground with the proper curves, and polished the flatter side, contrary to the expectations of many whose judgment in these matters was thought of much weight, who predicted that the crystalline structure of the diamond would not permit it to receive a spherical figure. When thus far advanced, fate decreed that I should lose the stone, and my only consolation was, to discover afterwards, that had it been completed, its thickness and enormous refractive power would probably have caused the focus to fall within the substance of the stone.

"Having, however, in this experiment, proved the possibility of working lenses of adamant, I set about another, and selected a rose-cut diamond, in order to form it into a plano-convex lens, and thereby save a moiety of the labour.

"In the progress of working this stone the heat generated by friction, in the course of the abrasion of the diamond, was perpetually melting the cement (shell-lac) by which the flat side was affixed to the tool, and compelled me to seek some means by which it might be prevented. After several trials, I found that when a portion of finely powdered pumice-stone was mixed with the shell-lac, the cement was much stronger, and less liable to melt, than any other similar substance.

"On the 1st of December 1824 I had the pleasure of first looking through a diamond microscope, and it was doubtless the first time this precious gem had been employed in making manifest the hidden secrets of nature. A few days after, I had polished it sufficiently to put it into the hands of Dr Göring, who tried its performance on various objects, both as a single microscope and as the objective of a compound. He states in a letter addressed to me, dated 3rd January 1825, 'that it has shown the most difficult transparent objects I have submitted to it,' and again, 'I can clearly perceive the amazing superiority it will possess when completely finished.' I must, however, inform my readers, that we discovered in this state various flaws in the stone, in consequence of which we abandoned all thought of completing it. In this condition the project remained for about a year, when I determined to resume my attempts; and having worked several stones into lenses, I at last succeeded in obtaining a perfect one. In the course of these labours, a new though not unexpected defect appeared in several lenses, which would have subverted the whole scheme had not the first diamond lens been free from it.

"These lenses, instead of giving a single image like the first, gave a double or triple one. This rendered them utterly useless as magnifiers, and made the defects of soft and hard parts in the same stone, and the small cavities in others, of comparatively trifling consequence. The images exhibited in such lenses overlapped each other, but were never entirely separated, though the quantity of overlapping varied in different specimens.

"It was now evident that these defects arose from polarization, though this stone is described as 'refracting single.' I subsequently learned from Dr Brewster, after I had overcome these obstacles, that this property of the diamond had been observed by him, and an account of it given in the Edinburgh Philosophical Transactions. On referring to his paper, it appears Dr Brewster found that some stones polarized in particular parts, while other portions of the same stone were quite free from any trace of polarity, and thus perfectly adapted to our purpose, as had previously been demonstrated in the first diamond lens.

"Notwithstanding these difficulties, and the consequent expense and labour they entailed on me before sufficiently experienced in working upon this refractory material with certainty, I have now the satisfaction of being able, by inspection a priori, to decide whether a diamond is fit for a magnifier or not; and have now executed two plano-convex magnifiers of adamant, whose structure is quite perfect for microscopic purposes. One of these, about the twentieth of an inch focus, was purchased by the late Duke of Buckingham; the other, in my hands, is the thirtieth of an inch focus, and has consequently amplification enough for most practical purposes." (Microscopic Cabinet, p. 107-111.)

Although it is quite certain that many if not most diamonds possess a doubly-refracting and polarizing structure, owing to their having been irregularly indurated when in a soft state, yet the separation of the images, arising from this structure, is not sufficient to account for the overlapping of the images observed by Mr Pritchard. In order to have this matter investigated, Mr Pritchard sent a bad diamond lens, with two or three images, to Sir David Brewster, who was for a long time perplexed with the difficulties which it presented to him. It occurred to him, however, to examine if the stone possessed a homogeneous structure, as he had observed in amber and gums, which are indurated in a similar manner, a variation in the refractive density capable of accounting for the imperfections of the diamond. In order to do this, he admitted a narrow beam of light into a dark room, and examined by this light the flat surface of the plano-convex lens of diamond with a hand microscope. After getting the diamond into the most favourable position, namely, when the light was reflected as nearly as possible at a perpendicular incidence, he was surprised to see its whole surface covered with thousands of minute bands, some reflecting more and some less light. He at first thought that these bands were the edges of an

---

1 Mr Pritchard informs us (see Edinburgh Journal of Science, No. 1, new series, p. 149, July 1829), that Messrs Randell and Bridge, at the time when Mr Pritchard began his experiments, had many Dutch diamond-cutters at work, and that the foreman, Mr Levi, with all his men, assured him that it was impossible to work diamonds into spherical lenses. The same opinion, he adds, was also expressed by several others, who were considered of standard authority in the art. Mr Pritchard had, contrary to the expectation of many, succeeded in finishing his first lens, it was examined by Mr Levi, who expressed great astonishment at it, and added, that he was not acquainted with any means by which that figure could have been effected.

2 Edinburgh Phil. Trans., vol. viii., p. 157, 1817. See also Geological Transactions, new series, vol. iii., p. 456; and London and Edinburgh Philosophical Magazine, vol. vii., p. 245. infinity of laminae of different reflective, and consequently refractive powers; but having observed that the same bands which reflected most light in one position reflected least light in another, he was driven to the conclusion that all the bands were the edges of veins or laminae whose visible terminations were inclined at different angles not exceeding a few seconds to the general surface. Had this surface been an original face of the crystal, there would have been nothing surprising in its structure; but being a surface ground and polished by art, the phenomenon which it presents is one extremely interesting. The two or three images, therefore, which this lens gave as a microscope were produced by the convergency of the rays to different foci by the differently inclined faces of the laminae.

Similar lines on the cut faces of diamonds have been observed by MM. Trecourt and Oberhauser, who consider them as minute prismatic canals or interstices left during crystallization, and who suppose that they injure the image in consequence of ground-off particles lodging themselves in the orifices of the canals, and which afterwards come out and destroy the polish by the scratches they produce. This explanation is in no way applicable to the phenomenon we have described.

These observations will, we trust, induce opticians to use the diamond more frequently than they were disposed to do when they believed that its imperfections arose from its doubly-refracting structure. In a small lens the doubly-refracting structure, when it does exist, is too small to produce any bad effect; and it is not difficult to discover any defect that may exist in the surface such as we have described above.

As the expense of the diamond, and the labour of working it, are very great, about fifty or sixty hours being necessary to complete a diamond lens with double convexity, it is of the greatest consequence to ascertain beforehand if the substance of the diamond is homogeneous; that is, free from difference of density or double refraction, and if it does not contain any small cavities. The best way is to examine the stone, by cutting two flat faces upon it, unless it is a table or table diamond, which always has two flat faces; but this labour may often be avoided by examining it when plunged or held in a glass trough containing oil of cassia, the fluid which approaches nearest to it in refractive power. This will diminish all the refractions at the irregular surface of the diamond to such a degree as to make any internal imperfections as easily seen as if its substance were plate-glass.

By comparing the indices of refraction of diamond and glass, it may be easily shown that the same magnifying power may be obtained with a diamond lens having its curvature with a radius of 8, as with a glass lens the radius of whose curvature is 3; and as the spherical aberration increases with the depth of curvature or the thickness of the lens, a lens of diamond will bear a much larger aperture than one of glass before indistinctness of vision is produced. Mr Pritchard has given a very useful ocular representation of the relative value of a diamond and a glass lens.

In the annexed figure G is the section of a semi-lens of glass, and D the section of one of diamond, so placed that their principal focus F shall be at the same point. In the diamond semi-lens the marginal rays will intersect the axis at d, and in the glass semi-lens at g; the longitudinal aberration being dF in the diamond, and gF in the glass lens.

In order to obtain a numerical measure of these aberrations, Mr Pritchard computed them from the formula, and found that of the diamond lens to be 4ths of its own thickness, that of the glass lens being 4ths of its thickness; and by taking the thickness of the diamond lens to be 255, while that of the glass is 758, he obtained 4ths of 255 = 109, and 4ths of 758 = 884, and hence it follows that the actual aberration of a diamond lens is only about one-ninth of the aberration of a glass lens of the same power and aperture.

If we suppose the diamond lens to be ground on the same tool with the glass lens, so as to have the same curvature, the same thickness, and the same diameter, the longitudinal aberration of the diamond will be to that of the glass lens as 43 is to 117, or nearly one-third of it; and if we suppose the focal length of both to be 1/6th of an inch, the magnifying power of the diamond lens will be 2133, while that of the glass one will be only 800. In order that a lens of glass may have the same magnifying power as that of the diamond above mentioned, its focal distance would require to be only the 200th part of an inch.

The durability of the diamond lens is also another valuable property, which allows it to be burnished into a disc of metal, and taken out and cleaned without any danger of being scratched. In treating of microscopic doublets and achromatic microscopes, we shall have occasion to recur again to the diamond lens. Some writers have objected to the use of diamonds because they are too costly. For ordinary microscopes, intended solely to amuse or to instruct, they have not been recommended; but if we wish to make great discoveries, to unfold the secrets yet hid in the cells of plants and animals, we must not grudge a diamond to reveal them. If Sir James South, Mr Cooper, and others, have given two or three thousand pounds for a refracting telescope, and if Lord Rosse expended L15,000 on a reflecting one, why may not other philosophers open their purse, if they have one, and other noblemen sacrifice some of their household jewels, to resolve the microscopic structures of the lower world, to unravel mysteries most interesting to man, and secrets which the Almighty must have intended that we should know.

**Sapphire Lenses.**

The ruby and the sapphire are the same substance, differing only in colour. Mr Pritchard has, with his usual success, executed many lenses of sapphire, which, though inferior to those of diamond, are vastly superior to the best executed lenses of glass. When a double convex lens of sapphire and one of plate-glass are ground to the same focus, so as to have the same aperture and magnifying power, their relative curvatures are as 5 to 3, and their thicknesses as shown in the annexed figure, where A is the section of a semi-lens of sapphire, whose focus is at F, and B a section of a semi-lens of glass, having its focus at the same point. This figure points out in the clearest manner another advantage of using the precious stones in place of glass. In small lenses of glass, the thickness of the glass is such that there is no room between its anterior surface and the object for the admission of instruments for dissection, and not even for the thinnest plate of glass, so that it is impossible to use glass lenses of small foci in viewing objects placed in glass sliders. If the preceding figure represents lenses with a focus of 1/6th of an inch, the distance of the glass lens B from F will be little more than 1/6th of an inch, which is less than the thinnest glass.

---

1 See Phil. Trans., 1841, p. 41, for a drawing of the phenomenon.

2 See the last column of the table in page 771, col. 2. In using the sapphire and ruby, or any precious stone which refracts doubly, such as zircon, topaz, &c., for lenses, we are exposed to a very serious defect, arising from the duplication of minute lines, in consequence of the double refraction of these crystals. In order to remedy this defect, the optician endeavours to cut the stone so that the axis of the lens may coincide with the axis of double refraction. This, however, is a difficult task; and, even if it were accomplished, we should not get rid entirely of the duplication of the images, as in all double convex lenses, as well as in plane convex lenses with the plane side turned to the object, the rays cannot pass through the lens in parallel directions, and therefore must suffer double refraction, however small. It may be reduced, however, to the smallest possible amount, and even to nothing; for pencils of rays diverging from a point in the axis, by making the lens plano-convex, and turning the plane side to the eye, as in the annexed figure, where rays issuing from F, and entering the eye parallel at E, must pass through the lens AB in parallel directions, suffering all their refraction at the first or curved surface of the lens. By adopting this form and position of the lens, we may, however, lose more than we gain; for the lens is placed in the position which gives a maximum spherical aberration. When the magnifying power is not very high, the residual double refraction is not injurious; and in proof of this we may state, that we have in our possession a double convex lens of sapphire, executed by Mr Pritchard, which exhibits minute objects with the greatest beauty and precision. The only way, therefore, is to employ precious stones, such as the diamond, the garnet, and the spinelle ruby, which have no double refraction.

Garnet and Spinelle Ruby Lenses.

The garnet is superior in its structure to the spinelle ruby, and the best and purest which we have seen is that which is brought from Greenland, and has a slight tinge of purple. We have used lenses made of this substance by Mr Hill, Mr Adie, Mr Blackie, and Mr Veitch, all of which exhibit minute objects with admirable accuracy and precision; and we can state with confidence, that we have never experienced the slightest inconvenience from the colour of the garnet, which diminishes with its thickness, and therefore nearly disappears in very minute lenses. (See p. 774.)

Single Fluid Microscopes.

Mr Stephen Gray long ago proposed to construct single fluid microscopes with drops of water, which he lifted up with a pin, and deposited in a small hole made in a piece of brass. The drop retained a sort of imperfect sphericity, and showed objects with some distinctness; but it is obvious that the very weight of the drop destroyed its spherical form, even if it had not been disturbed by minute irregularities on the circumference of the aperture in which it was placed.

Sir David Brewster long ago constructed fluid lenses in a different manner, so as to avoid the irregularities above mentioned. He placed minute drops of very pure turpentine varnish, and other viscid fluids, on plates of thin and parallel glass. By this means he formed plano-convex lenses of any focal length; and by dropping the varnish on both sides, he formed double convex lenses, with their convexities in any required proportion. By freeing the glass carefully from all grease with a solution of soda, the margin of these lenses was beautifully circular; and the only effect of gravity, which diminishes with the viscosity of the fluid and with the smallness of the drop, is to elongate the lower lens and flatten the upper one. These lenses were found to answer well as the object-glasses of compound microscopes.

After experiencing the extreme difficulty of obtaining precious stones free of double refraction or difference of making density, and from little cavities and imperfections, as well as the difficulty of giving their surfaces a perfect polish and a correct figure, Sir David Brewster made an extended series of experiments on the formation of minute fluid lenses, which should equal in power and distinctness those made of precious stones. The primary difficulty which was encountered in this attempt was that of depositing a sufficiently minute drop of fluid upon a surface of glass. This arose from two causes: from the difficulty of taking up on the slenderest fibre a minute globule of a fluid of any moderate tenacity, and the still greater difficulty of overcoming its adhesion to the fibre, and laying a portion of it on glass. The first of these difficulties he overcame by a suitable mixture of two fluids, and the second by a mechanical process. Having thus succeeded in obtaining lenses too small to be recognised distinctly by the eye, he next endeavoured to make their figure approximate to the hyperbolic form when the lenses were not of the smallest size; and the results which he obtained were far beyond his expectation. Some of these lenses preserved their perfection for more than a year, and if protected from dust might have been kept much longer. If fluids could be obtained of a high refractive power, and not of a volatile nature, microscopes of extreme perfection might thus be readily constructed.

In order to deposit upon glass a very minute portion of fluid, Sir D. Brewster employed a fibre of spun glass. When slightly dipped into the fluid, the portion which adhered to its extremity, in place of remaining in the form of a small globule, ran along the fibre, so that it could not be laid upon the glass. Upon holding the fibre vertically, and repeatedly knocking the hand which held it upon the thigh, the fluid was gradually made to accumulate at the end of the fibre, so that it could be made to touch the glass surface, and leave a small portion in the form of a plano-convex lens.

The desired result was produced more effectually by fixing the upper end of the fibre in the stand of a microscope, so as to suspend it vertically above the glass plate. By turning the milled head, and making the drop at the end of the fibre descend, or the glass ascend, till they were nearly in contact, it was easy, by a rapid separation of the two after contact, to leave the smallest portion upon the glass.

It is obvious that this operation could not be performed, if the fluid had much tenacity, like Canada balsam in its usual condition. Sir David Brewster therefore tried to obtain a fluid of the proper tenacity, and found that a mixture of castor oil and Canada balsam answered the purpose when carefully incorporated.

With this fluid, and with others, suspended, as shown in fig. 13, from plates of thin parallel glass, he obtained microscopes equal to the glass, or even sapphire, microscopes made by opticians. This, no doubt, arises from three causes,—1. From the perfect homogeneity of the material; 2. From the perfect polish of the surface; and, 3. From the approximation of the figure of the lens to the hyperbolic curve. The form of the curve will obviously vary with the size of the drop and the tenacity of the fluid.

The curvature of the lens may be changed by suspending the drop from convex or concave surfaces, as in

---

1 The form of the lens may be ascertained by taking a highly magnified image of it. With the view of altering the curvature of the fluid lenses, immiscible fluids were used, such as treacle or honey, and castor oil. The dotted line shows (fig. 16) the original castor oil lens, and the horizontally lined lens the form into which it is pulled by the weight of the treacle or honey lens p. The effect of this combination was very good.

In place of the plate CD (fig. 16), we may use a convex lens as in fig. 17, where mn is the castor oil, and o the treacle meniscus.

An achromatic combination may be made as in fig. 18, CD being the glass plate, i a plano-convex lens, ma a concave lens of a highly refractive and dispersive oil, and o a meniscus of treacle or Canada balsam softened.

We may pull down a fluid lens abc (fig. 19) into a hyperboloidal form by the weight of a lens of glass mn. In an experiment thus made there was not a trace of spherical aberration. There is no occasion in this case of a small aperture, as the treacle lens abc excludes all lateral light. The effect of suspending the lens of a minnow at mn was good.

If the fluid lens is too hyperbolic, it may be corrected by a flattened lens mon (fig. 20) placed above the glass plate CD.

**Single Catadioptric Microscope.**

A single lens, by which light is both refracted and reflected, seems at first sight to be something paradoxical. Such a lens, however, which was proposed and used by Sir David Brewster, is shown in the annexed figure, where ABC is a hemispherical plano-convex lens, which, if we use it in the common way, will have a certain magnifying power; but if we use it as shown in the figure, it acts as a double convex lens of the same radius, and has consequently twice the magnifying power. Bisect the semicircle BAC in A, and join AB, AC. If we now place an object at mn, and look into the lens BA at F, we shall see by reflection from the surface BC the object mn, with the same distinctness, and under the same angle, as if we had placed the two lenses AaBd, AaCd, with their plane sides AB, AC together.

Since the light is incident on the reflecting surface BDC at an angle of 45° and upwards, not a ray of it will be transmitted, as it suffers total reflection. The lens thus used, composed in reality of two plano-convex ones, AaCd, AaBd, has less spherical aberration than when used as a whole, ABC, and there is obviously no error from imperfect centering. This lens may be used as the object-glass of a compound microscope; and it will be seen in another section that it possesses other advantages than those which have been mentioned.

**The Grooved Sphere.**

This lens derives its name from its having a deep groove cut round it in the plane of a great circle perpendicular to sphere, the axis of vision. Sir David Brewster was led to its construction by the doublet of Dr Wollaston, which will be described in another section. It consists of a spherical lens or sphere, with a deep concave groove cut round it, so as to cut off the marginal pencils, and thus give a wider field and a more perfect image. It is represented in the annexed figure, where ABDC is a sphere of glass, having the unshaded parts below AC and above BD cut away, in order to prevent rays that fall very obliquely from reaching the eye. The central thickness of the lens may be made so small as to render the spherical and even the chromatic aberration almost insensible. As all the pencils pass through the centre, every part of the image will be equally distinct; a property possessed by no other lens.

This lens, as fitted up by Mr Blackie for the inventor, is shown in the annexed figure; AB being a representation of it when closed, and ABC when open; the lens at A resembling a bird's eye.

Mr Coddington, who entertains a high opinion of the value of this lens, observes: "Besides all this, another advantage appears in practice to attend this construction, which I did not anticipate, and for which I cannot now at all account. I have stated that when a pencil of rays is admitted into the eye, which, having passed without deviation through a lens, is bent by the eye, the vision is never free from the coloured fringes produced by eccentric dispersion. Now with the sphere I certainly do not perceive this defect; and I therefore conceive that if it were possible to make spherical glass on a very minute scale, it would be the most perfect simple microscope, except, perhaps, Dr Wollaston's doublet, than which I can hardly imagine anything more excellent, as far as its use extends; its only defects being the very small field of view, and the impracticability of applying it, except to transparent objects seen by transmitted light. Now, the sphere has this advantage, that whereas it makes a very good simple microscope, it is more peculiarly fitted for the object-glass of a compound instrument, since it gives a perfectly distinct image of any required extent, and that, when combined with a proper eye-piece, it may without

---

1 Phil. Trans., 1830, part i., pp. 69–84. 2 This exception was needless, as the doublet is not a simple microscope, having two lenses placed at a distance. difficulty be employed for opaque objects." We do not rightly apprehend the exact import of these observations. Mr Coddington distinctly asserts that the grooved sphere is the most perfect simple microscope, or the most perfect microscope with one lens; and yet he says in the next paragraph that it is only "a very good simple microscope," being "more peculiarly fitted for a compound instrument."

With regard to the difficulty of making it on a small scale, it is by no means great; for if we can grind and polish its two surfaces, we may readily excavate it round its margin. We have now before us a grooved sphere of garnet 1/4th of an inch radius, executed by Mr Blackie: The focus is almost close to the lens, which in many kinds of observation is a great advantage, and its performance is remarkably fine.

It will be seen in our article on Optics, that when the refractive index of a sphere exceeds 2,000, its focus falls within the sphere. Hence a grooved sphere made of diamond is useless. When made with garnet it is invaluable; and its focus is just thrown so near its surface, that the objects may be laid upon its surface, or pressed against it by a concave surface of the same radius.

A lens of this kind, whether the surfaces have the same or a different radius, provided they have the same centre, may be called a concentric lens, and has valuable properties. One of these, executed upwards of thirty years ago for the writer of this article by Mr Blackie of Edinburgh, has the radii of the two surfaces so adjusted that its anterior focus is on the least convex surface. It is shown in the annexed figure, where C is the common centre of the two surfaces A and BD; the groove round C being cut to the requisite depth.

An equivalent concentric lens may be made by combining two plano-convex lenses, with their plane sides next one another cut separate, the lenses having different sides. One of the lenses may be either a hemisphere or less or greater.

If we call m the index of refraction, then if AC, the radius of the surface A, is m - 1, the radius CB of the surface BD must never exceed unity. When the ratio of CA to CB is as m - 1 to 1, the anterior focus of the lens will be on the surface BD. If the index of refraction m is beneath 2, distinct vision may be obtained by looking into either surface. When the index is 2, the only concentric lens that can be made consists of two hemispheres united, or a sphere. When the index is above 2, distinct vision can be obtained only by looking into, or placing next the eye, the least convex surface.

The Fluid Grooved Sphere.

In order to construct a grooved sphere with fluids, Sir David Brewster adopted the arrangement shown in the annexed figure, where AB is a piece of plate-glass of a circular form, having a groove cut out of its circumference. Two fluid lenses m, n, as nearly hemispherical as possible, are then placed on its upper and under surface by the methods already described. The aberration both from form and colour will be reduced by the groove, as well as by the form of the under lens.

The same effect may be produced by substituting for the piece of glass AB two thin plates of parallel glass, or thin laminae of split topaz ab, cd (fig. 26), separated by a circular plate of metal, with a proper aperture, the three plates being cemented into one by Canada balsam, or any homogeneous cement which may fill the aperture between the glass-plates.

Compound Single Microscopes.

We may give this name to any combination of lenses which acts solely as a single microscope. When we possess single microscopes, we may double or quadruple their power by cutting them into halves, quarters, or more numerous sections, and placing them transversely, as in the annexed figure. In this figure is represented a combination of two semi-lenses ABC, DEF cut from the same lens, so as to form a lens having twice the magnifying power of the original one. If the semi-lens ABC has a greater magnifying power than DEF, in consequence of being the half of another lens more convex, we shall have three different magnifying powers in the same combination—the highest power in the portion EB, a lower power through the portions m, o, and a still lower power through the portions n, p.

A combination of quarters of lenses, having the same properties as those above described, is shown in the annexed figure. The quarter lenses may be combined as in the upper or lower half of the preceding figure, and several of such combinations may be united for optical purposes, and made achromatic by the usual methods.

The preceding method of combining divided lenses enables us to make two or more lenses, or microscopes, or telescopes exactly of the same magnifying power; an effect which cannot be otherwise obtained. (See Stereoscope.)

An Extempore Microscope.

When a magnifying power is wanted for reading any small print or seeing any minute object, and no lens can be got, two bottles filled with water or any other fluid may be crossed, as in the annexed figure, and the object viewed through the middle portion ABCD. Two very small bottles, or two test tubes, crossed in the same manner, will have a considerable magnifying power. Crystalline Lenses of Small Fishes.

The crystalline lens of minnows and small fishes may be taken out of the eye in a state of such perfection, that when used as single microscopes, they give a very perfect image of minute objects. In such lenses, which have an increasing density towards their centre, the spherical aberration is almost wholly corrected. Great care, however, must be taken to make the axis of the lens the axis of vision, to prevent its form from being injured by pressure against the aperture which holds it. The best way is to make a ring at the end of a piece of wire, having its diameter a little greater than that of the lens. A ring of viscous fluid is then made to line the ring of wire, and the lens is suspended in the ring of fluid, some of the fluid encroaching upon its anterior or posterior surface.

Magnifying Power of Single Microscopes.

Having thus described the various kinds of single microscopes, we shall now consider the subject of their magnifying power. When an eye in the prime of life, and neither long nor short sighted, views the minutest object which it can recognise, it will generally place it at the distance of about five inches. When the same object is viewed through a single microscope, the distance at which it is seen is equal to the focal length of the lens; and as the apparent magnitude of objects is inversely as the distances at which they are seen, we have only to divide the distance, five inches, by the focal length of the lens, in order to know its magnifying power, or the apparent magnitude of objects when seen through the lens.

The following table shows the magnifying power of lenses of all focal lengths, from 5 inches up to the 100th of an inch, and is applicable to all lenses, of whatever substance they are made:

| Focal Length | Magnifying Power | |--------------|-----------------| | Inches | | | 5 | 1 | | 2 | 2 | | 3 | 3 | | 4 | 4 | | 5 | 5 | | 6 | 6 | | 7 | 7 | | 8 | 8 | | 9 | 9 | | 10 | 10 | | 11 | 11 | | 12 | 12 | | 13 | 13 | | 14 | 14 | | 15 | 15 | | 16 | 16 | | 17 | 17 | | 18 | 18 | | 19 | 19 | | 20 | 20 |

We have already mentioned the advantages which the precious stones have over glass ones, in having a much less spherical aberration. In order that a glass lens may have the least spherical aberration, its radii of curvature must be as one to six, the flattest side being turned to the object; but this is not the case with bodies of a different refractive power. Mr Coddington, in his Treatise on the Reflection and Refraction of Light, has computed the ratio of the curves when the aberration is a minimum for various indices of refraction from 1·5 up to 2·0, and the amount of the aberration itself in parts of the thickness of the lens. This table is very important in a practical point of view, as will be seen from the observations which follow it.

Table showing the Spherical Aberration of Lenses of Glass and the Precious Stones, and the proper proportion of their Radii when the Aberration is a Minimum:

| Substances | Index of Refraction | Ratio of the Radii of Minimum Aberration | Longitudinal Aberration in parts of the thickness being 10. | |---------------------|---------------------|------------------------------------------|----------------------------------------------------------| | Fluor spar | 1·4 | 1 to 3·6 | 10·96 | | Cryolite | | | | | Glass plate | 1·5 | 1 to 6 | 10·71 | | Oil of almonds | | | | | Castor oil | 1·6 | 1 to 14 | 9·33 | | Honey | | | | | Flint glass | 1·7 | 1 to 9·3 | 6·68 | | Quartz | | | | | Topaz | 1·8 | 1 to 12 | 3·57 | | Oil of essence | | | | | Glass, lead 1, flint 2 | | 1·9 | 1·66 | | Sulphuret of carbon | | | | | Sapphire | | | | | Ruby | 1·9 | 1 to 7 | | | Spinelles ruby | | | | | Garnet | | | | | Glass, lead 2, flint 1 | | 1·9 | | | Sulphate of lead | | | | | Glass, lead 2, flint 1 | | 1·9 | | | Zircon | | | | | Calomel | 2·0 | 1 to 5 | 0·62 | | Sulphur | | | | | Phosphorus | | | | | Glass, lead 3, flint 1 | | | |

It appears from the preceding table, that when the refractive index is between 1·4 and 1·6 and a little more, but less than 1·7, the second surface of the double convex lens must be convex, in order to have the least spherical aberration; but that when the index is a very little above 1·6, the second surface must be plane, and when the index is nearer 1·7 than 1·6 the second surface must be concave, in order to make the aberration a minimum, and this concavity, in the case of zircon and sulphur, is so much as −5, so that in diamond it must be nearly −3; so that we must sacrifice a great deal of magnifying power in order to obtain this advantage in diamond; but the sacrifice will be well bestowed, for such a lens will be almost wholly free of spherical aberration.

Notwithstanding the difficulty of the task, we would earnestly direct the attention of artists to the subject of grinding plano-convex lenses of a hyperbolic form for single microscopes. The smallness of the lens must increase the difficulty; but in this case the effect may be accidentally obtained, as it is often done in giving a parabolic and an elliptical form to specula. Mr Potter has given, and put to the test of experiment, a method of obtaining any curve derived from revolution, by giving a particular form to the grinding and polishing tools. (Edin. Jour. of Science, new series, No. 12.)

CHAPTER II.

DESCRIPTION OF MICROSCOPIC DOUBLETS AND TRIPLETS.

Under this chapter we propose to describe all combinations of lenses in which two or more are placed in contact, and trip or at such a distance that no image is formed between them. Wollaston's Periscopic Doublet.

The earliest proposal of a doublet lens was that which Dr Wollaston made (Phil. Trans. 1812, p. 375), under the name of a periscopic microscope. The following is his own description of it:—"The great desideratum," says he, "in employing high magnifiers, is sufficiency of light; and it is accordingly expedient to make the aperture of the little lens as large as is consistent with distinct vision. But if the object to be viewed is of such magnitude as to appear under an angle of several degrees on each side of the centre, the requisite distinctness cannot be given to the whole surface by a common lens, in consequence of the confusion occasioned by oblique incidence of the lateral rays, excepting by means of a very small aperture, and proportionate diminution of light. In order to remedy this inconvenience, I conceived that the perforated metal which limits the aperture of the lens might be placed with advantage in its centre; and accordingly I procured two plano-convex lenses ground to the same radius, and applying their plane surface on opposite sides of the same aperture, in a thin piece of metal (as is represented by a section, fig. 30), produced the desired effect, having virtually a double convex lens, so contrived that the passage of oblique pencils was at right angles with its surface, as well as the central pencil. With a lens so constructed, the perforation that appeared to give the most perfect distinctness was about one-fifth part of the focal length in diameter; and when such an aperture is well centered, the visible field is at least as much as 20° in diameter. It is true, that a portion of light is lost by doubling the number of surfaces; but this is more than compensated by the greater aperture which, under these circumstances, is compatible with distinct vision."

Periscopic Sphere.

In the preceding passage Dr Wollaston describes only a double convex periscopic microscope, consisting of two plano-convex lenses; but he does not take the case where these two lenses are hemispheres, and consequently where the doubly convex one which they form is a sphere. When the lenses are not hemispheres, the pencils are not concentrical, and the rays from different parts of the object do not each suffer the same species of refraction as they do when passing through a sphere, so that every part of the field is not equally distinct. It is obvious also that Dr Wollaston did not think of filling up the central aperture with a fluid of the same refractive power as the lens, in order to remove the loss of light from the double number of surfaces, which he mentions as a defect in his microscope.

The construction of a periscopic sphere proposed by Sir David Brewster combines these two properties. The lenses, whether they are hemispherical or not, must be so placed that their convex surfaces form part of the same sphere, as shown in the annexed figures.

In fig. 31 the plano-convex lenses AB, CD may be cemented to a piece of plate-glass mn, of such a thickness in one direction as to complete the sphere, and of such a diameter in the direction mn as to form a suitable contraction of the aperture.

In fig. 32 the space between the two unequal lenses may be filled up, as in the figure, by two pieces of plate-glass AmnB, CmnD, between which is a plate of brass, or of thin black paper, containing a suitable aperture in the centre of the lenses. Here there are six surfaces within the sphere; but by uniting them with a proper cement, the whole becomes a single sphere, in which there is no perceptible loss of light.

In fig. 33 lenses of unequal size and thickness are combined either with a plate of glass or a fluid between them of the same refractive power as the glass, and the apertures may be placed on the plane surfaces AB, CD.

In fig. 34 two convex lenses may be combined into a sphere, the intermediate portion being filled up with a fluid of the same refractive power. This may be readily done by cementing each lens on the end of a brass or glass tube ab, and introducing the fluid by an aperture.

In uniting these lenses, it is obviously necessary that the convex outer surfaces should be exactly of the same curvature and of the same kind of glass. The best way of effecting this is to grind a thick lens ABC, either greater or less than a hemisphere, and then to bisect it at AD, and out of the portions ADB, ADC to form two plano-convex lenses ABE, ACF, or two double convex lenses AEBG, AFCH. The outer surfaces of these two lenses will belong accurately to the same sphere. The perfect similarity of the inner surfaces is of less consequence, as all refraction by them is wholly removed by the cement if it has the same refractive power.

By these different steps Sir David Brewster was led to the idea of the grooved sphere, or the lens already described under the head of single microscopes, in which the aperture is contracted by excavating the sphere all round in one of its great circles.

Periscopic Achromatic Spheres.

If, in the construction shown in fig. 36, in place of making the fluid op of the same refractive and dispersive power as the two lenses, we make it such as to correct the colour of these lenses, we shall obtain an achromatic sphere, as proposed by Sir David Brewster; and the compound lens may be still farther improved as a microscope by attaching, either by cement or not, to the back of the first lens AB a convex speculum of silver or steel for illuminating the object, the contracted aperture being the hole in the centre of the speculum. The concave fluid lens is shown at op; and such a curvature must be given to the convex reflector mn that it may reflect parallel or diverging rays upon the object.

---

1 Edinburgh Philosophical Journal, 1820, vol. iii., pp. 74-77; and Prichard's Treatise on Optical Instruments, in the Library of Useful Knowledge, p. 41, § 66. Mr Coddington thus treats of the preceding contrivance:

"An achromatic sphere may be constructed by interposing between two crossed lenses (double convex ones), in opposite positions, a concave lens of a medium more highly dispersive than that of the lenses, adjusting the curvatures so that the outer surfaces of the crossed lenses shall be portions of the same sphere, and that the interior surfaces shall exactly fit into each other.

"In such a system, we may consider the effect to be the same as that of an entire sphere of the same medium as the two lenses diminished by that of a concave lens having for its refractive ratio that which exists between the two media in question.

"Thus, if \( \mu_1 \) be the ordinary index of refraction for the convex lenses, \( \mu_2 \) for the concave one, \( r : s = 1 : 1 \) the ratio of the dispersive powers, \( r \) the radius of the sphere \( s \), \( \sigma \) those of the internal surfaces, we must have

\[ \left( \frac{\mu_2}{\mu_1} - 1 \right) \left( \frac{1}{s} + \frac{1}{\sigma} \right) = 2 \frac{\mu_2 - \mu_1}{\mu_1} \frac{1}{r} = \pi : 1 ; \]

whence it follows that \( \frac{1}{s} + \frac{1}{\sigma} = 2 \pi \frac{\mu_2 - \mu_1}{\mu_1} \frac{1}{r} \).

For example, let \( \mu_1 = 1.5 ; \mu_2 = 1.65 ; r = 1.25 \).

Then \( \frac{1}{s} + \frac{1}{\sigma} = \frac{1}{4} \cdot \frac{5}{5} \cdot \frac{1}{r} = \frac{1}{1.25} \).

If the first internal surface be plane, or \( s = \infty \), we have in general \( \sigma = \frac{1}{2} \frac{\mu_2 - \mu_1}{\mu_1} r \); or, in this particular example, \( \sigma = 1.25 \), or \( \sigma : r = 6 : 5 \)."

**DOUBLET OF NO ABBERRATION.**

So long ago as 1668, a doublet was described in the *Philosophical Transactions*, in which a large and flat field was obtained. This subject, however, was never investigated with care till Sir John Herschel took up the subject in 1821. The doublet, made of glass, which Sir John proposes for obtaining perfect distinctness in microscopical observations, is shown in the annexed figures 37, 38, the convex sides being turned to the eye when the doublet is used as a microscope, and to the sun when it is used as a burning-glass. The following are the radii and focal length of these lenses:

| Focal length of the first lens | Fig. 37 | Fig. 38 | |-------------------------------|--------|--------| | Radius of its first surface | + 5833 | + 5833 | | Radius of its second surface | + 5833 | + 5833 | | Focal length of the second lens | + 17829 | + 5777 | | Radius of its first surface | + 3888 | + 2954 | | Radius of its second surface | + 6291 | + 8128 | | Focal length of the combined lenses | + 6407 | + 3474 |

"Whether we ought or ought not," says Sir John, "to aim at the rigorous destruction of rays parallel to the axis, the use to which the lens is to be applied must decide. In a burning-glass it is of the highest importance. A slight consideration will suffice to show, that the difference of temperatures produced in the foci of a double convex lens of equal radii, and one of the same focal length, but of the best form, must be very considerable. In order to try whether even the latter might not be improved by the shortening of the focus, and the superior concentration of the exterior rays, by applying a correcting lens of one of the forms above calculated, in spite of the loss of heat in passing through a second glass, I procured two lenses to be figured to the radii assigned in the first column of the foregoing table. They were about three inches in aperture, and when combined as above described, the aberration was almost totally destroyed, and probably would have been so completely had the index of refraction proper to the glass been employed instead of that adopted in our calculation for brevity. Their combined effect as a burning-lens appeared to me decidedly superior to that of the first lens used alone, and there is therefore good reason to presume that the effect of the other construction, which, with the same loss of heat, affords a much greater contraction of the focus, would be still better; and I regret not having tried it in preference.

"In eye-glasses and magnifiers, if we would examine a minute object with much attention, as a small insect, or (when applied to astronomical purposes) if we would scrutinize the appearance of a planet, a lunar mountain, the nucleus of a comet, or a close double star, where extent of field is of less consequence than perfect distinctness in the central point, too much pains cannot be taken in destroying the central aberration." (*Phil. Trans.* 1821, p. 246-248.)

Mr Pritchard has executed some of these doublets for the object-glasses of compound microscopes, "for which," he says, "they answer remarkably well, but their angle of aperture is small compared with combinations of double achromatics." (*Microscopic Cabinet,* p. 163.)

**Herschel's Perisopic Doublet.**

We owe also to Sir John Herschel the construction of Herschel's perisopic doublet with a very large field of moderate perisopic distinctness. "In spectacles," says he, "reading-glasses, doublet-magnifiers of moderate power, and eye-glasses for certain astronomical purposes, the correction of the aberration in the centre of the field may be sacrificed with little inconvenience. By far the best perisopic combination I am acquainted with consists of a double convex lens of the best form, but placed in its worst position (radii as 6 to 1) for the lens next the eye, and a plane concave whose focal length is to that of the other as 2:6 to 1, or as 13 to 5, placed in contact with its flatter surface, and having its concavity towards the object, as in the annexed figure, for the farthest; yet for destroying the aberration of rays parallel to the axis nothing can be worse. In fact, our formula gives for the aberration in this construction 22°02', or about 22 times what the best single lens of equal power would give; yet on accidentally combining two such lenses in this manner, I was immediately struck with the remarkable extent of oblique vision, with the absence of fatigue, on reading some lines with a power much beyond that of the natural eye, and with the freedom from colour at the edges of the field, arising from the opposition of the prismatic refractions of the two solids; an advantage which a single meniscus does not possess." The focal length of the compound lens which Sir John tried was 1'84 of an inch. The field of tolerably distinct vision extended fully 40' from the axis, and the letters of a book might be read, and the forms of objects distinguished, with management, as far as the 75th degree. In using such a combination the lenses should be very thin, and the eye applied as close as possible. Plano-Convex Doublet.

A doublet of much simpler construction, and with its spherical aberration greatly diminished, has also been proposed by Sir John Herschel. It is represented in the annexed figure, and consists of two convex lenses of equal focal lengths, the convex sides being placed in contact, and the eye and object opposite the plane sides. In this case the aberration will be only 0.6028. But if we make the focal length of the first to that of the second as 1 to 2.3, the aberration will be reduced to 0.2481. In order to have an idea of the value of such a doublet, we shall give the series of aberrations for single lenses, as investigated by Sir John Herschel:

| Aberration | |------------| | Plano-convex, plane side first | 4.2 | | Plano-convex, convex side first | 10.81 | | Doublet | 1.567 | | Best form of a single lens | 1.00 | | Doublet of two equal plano-convex lenses | 0.6028 | | Doublet of two plano-convex lenses with their focal lengths as 1 to 2.3 | 0.2481 | | Doublet of garnet, with suitable focal lengths | 0.08 |

As these calculations are made for glass, the advantage of such a doublet made of garnet or sapphire must be much greater. In a garnet the minimum aberration takes place when the form of the lens differs very little from that of plano-convex; and as it is then to that of glass as 35 to 107, the aberration will be only about 0.08, or next to imperceptible.

Wollaston's Doublet.

The consideration of the Huygenian eye-piece for astronomical telescopes suggested to Dr Wollaston the probability that a similar combination should have a similar advantage, of correcting both achromatic and spherical aberrations, if employed in an opposite direction as a microscope. With this view, he took two plano-convex lenses, the ratio of whose focal lengths was as 3 to 1, and he placed them as in the annexed figure, so that the distance of their plain surfaces was from 1.5 to 1.5 times the focal length of the smallest. The plane sides of the lenses are towards the object. The advantage of the first lens having its plane side next the object is, as Dr Wollaston states, that if it should touch a fluid, the view is not only not impaired, but improved, whereas a double convex lens would require to be taken out and cleaned. The following excellent observations on this doublet are made by Pritchard:

"Having mounted some plano-convex lenses of the relative foci named by Dr Wollaston, in such a manner that the distances might be varied at pleasure, I was surprised to find that after the doublet was adjusted by trial, so as to obtain the maximum of distinctness, the distance between the lenses did not accord either with the rule given by Huygens, or that of Dr Wollaston. Supposing that I had not got the combination intended by Dr Wollaston, I procured several doublets made by different artists, and to my astonishment found they agreed with my own, and therefore presumed the Doctor was mistaken in the distance by the thickness of the lenses and the minuteness of the space between them. The distance which appeared to me essential to obtain the best effect, is the difference of the focal length of the two lenses, making a proper allowance for their thickness. The proportion of the foci of the two lenses may be varied ad libitum. All that is requisite in this respect is, that the difference must be greater than the thickness of the anterior lens, while it may be observed (in high powers), that the greater the difference between their two focal lengths the more space will be left in front; and as this is of great practical importance, they should never be less than as 1 to 3. I have made some very good ones, differing as much as 1 to 6. . . . The following details are necessary to insure their goodness:

First, The convex surface of each lens must be truly spherical. If this is not obtained, it will be in vain to procure a good doublet, however beautifully the lenses may be polished or accurately adjusted. From this circumstance I have found globules perform very well, providing they are free from air-bubbles, which, however, is rarely the case. It should be observed, that a slight scratch on their surface is trifling compared to air-bubbles; for the latter not only stop the light, but, by the reflection around the edges of each bubble, produce considerable fog or glare.

Second, The distance between the lenses is the next point of importance; its adjustment is best accomplished by trial, mounting the lenses in such a manner that their distance can be varied at pleasure, and capable of being turned round, so as to adjust the centering. When this is obtained, they should be fixed so that their distance and position cannot be altered. This is necessary to regard, as I have sometimes spent whole days in re-adjusting a doublet that had been separated to examine the lenses singly.

Third, The stop or diaphragm, for limiting the aperture in these combinations, should be placed immediately behind the anterior lens. From the difference of the situation of the stop in the various doublets I have examined, it will appear that their makers did not know that the field of view depended upon the plane of the stop. I have found, that when the stop is situated close behind the anterior lens, no other is required, and the field is enlarged without sensibly augmenting the aberration. On this account the lenses of the finest doublet, when used singly with the same aperture as combined, has so much aberration and distortion that distinct vision cannot be obtained, even with the most rigid adjustment of the focus. From the difficulty of procuring a flat surface, some makers have worked the anterior surface of the lens next the object concave; these lenses do not possess any advantage in point of performance, not even to compensate for loss of power from the negative side."

Mr Pritchard remarks, that when the lens next the object is a jewel, the performance of the doublet is improved; but that he has not observed any advantage when both lenses are gems. This must be a mistake; for lenses of any gem, that are superior to glass ones when acting singly, must, if suitably combined, be superior also when united. In proof of this, we have a garnet doublet before us, executed by Mr Blaikie, the performance of which is quite remarkable. The lenses are made of Elie garnets, and their convex sides are placed towards each other. The radius of the smallest lens near the object is \( \frac{1}{9} \)th of an inch, and that of the other \( \frac{1}{9} \)th of an inch. Its magnifying power is very high, exceeding greatly that of the semi-jewel doublet made by Mr Pritchard, with a sapphire lens \( \frac{1}{9} \)th of an inch focus, combined with a glass lens \( \frac{1}{9} \)th of an inch focus.

On Fluid Doublets.

Dr Wollaston's doublet, as shown in fig. 41, may be fluid imitated with great facility by placing two plano-convex doublets, fluid lenses of different sizes upon plates of parallel glass. In such an arrangement it is necessary in the fluid, as well as in the glass doublet, to have the axes of the lenses perfectly coincident; a result which, by the method already referred to, may be more accurately effected in the fluid one.

**Pritchard's Triplet.**

Upon the same principle as the doublets, Mr Pritchard constructed triplets, the third or posterior lens having a longer focal length than the two others. This combination requires much more precision in the adjustment, and more attention in the centering. Mr Pritchard remarks, that, "when perfected, they amply repay the pains bestowed upon them, in the accuracy with which they exhibit the most difficult lined objects, though it is to be regretted that neither these nor the doublets of deep power will show pleasantly cylindrical bodies of large diameter, such as a large mouse or bat's hair." Having long made use of one of Mr Pritchard's triplets, we can amply confirm the account which he has given of the excellence of this combination. Mr Blackie has executed for us a triplet, the centre lens of which is garnet, the posterior one of quartz, and the anterior one of flat glass. It is a very powerful combination, and performs admirably.

Sir David Brewster has made triplets, in which two of the lenses are fluids and the third a solid, and some in which they are all fluids.

A very simple method of fitting up doublets and triplets, or even single lenses, has been proposed by Dr William Gairdner of Edinburgh, and executed by Mr Bryson.

In this instrument a Wollaston's doublet A is fixed at the end of a handle AB. A ring C is attached to the end of a bent brass stem CD, which is secured to the handle AB at D. This ring contains a disc of thin glass, on either side of which objects may be placed for examination; fluids on the outside, and other objects on the inside of it. By means of a milled head M, the screw of which passes through the handle and acts upon the arm CD, the observer is enabled to bring the objects into the focus of the doublet. This little instrument has been recommended by botanists, physiologists, and medical practitioners.

**Single Achromatic Microscope.**

In many of the doublets which we have already described, the chromatic aberration is partially, and sometimes greatly corrected, but still not to such a degree as to entitle them to the name of achromatic. The great improvement which has taken place in the art of grinding and polishing small lenses, has enabled the optician to execute double and triple achromatic lenses having a diameter so small as from 4th to 1/8th of an inch. Mr Pritchard has made them of the latter size with an angle of aperture of 65°. These lenses may be advantageously used in single microscopes where very high powers are not required, or when they cannot be applied, though it is usual to employ them as the object-glasses of compound microscopes, as we shall afterwards see.

Sir David Brewster has executed achromatic lenses, both double and triple, by combining a fluid concave lens with one or two convex lenses of the precious stones or glass. When the lenses are double, the fluid lens is of course a meniscus in which the concavity predominates, as it is impossible to form a fluid lens doubly concave.

**Single Achromatic Fluid Microscope.**

A single lens of glass, or of any of the gems, having a high refractive and low dispersive power may be made achromatic, or the colour much corrected, by suspending a fluid concave lens M upon a double convex lens L, as in fig. 43; CD being a plate of metal, or if the solid lens L is plano-convex, it may be cemented upon a plate of glass as in fig. 44. In order to increase the correcting power of the fluid lens M, we may make it doubly concave as in fig. 45; or AB may be a plano-convex lens with its plane side uppermost.

**Fluid Achromatic Doublets.**

A fluid achromatic doublet may be made by placing a suitable fluid mm between the lenses, as in the annexed figures, in which all the lenses may be fluids, provided mm and the other fluids be immiscible.

When M, L are of glass or precious stones, they may be set in brass plates.

**Single Reflecting Microscopes.**

Single reflecting microscopes are not much in use. They consist of a concave metallic speculum of a short focal length, so that any minute body placed in its focus will be seen magnified. The form of the speculum should of course be parabolic. Such a microscope is principally useful for looking at one's own eye, or any part of it not far from the pupil. In these cases no image is formed, as the rays enter the eye parallel.

The following ingenious contrivance for a fluid reflecting Gray's microscope we owe to Mr S. Gray (Phil. Trans. 1697, No. 258, p. 539). Having taken a small globule of quicksilver, and dissolved it in a menstrum of 10 parts of water and 1 of nitric acid (aquafortis), he dipped the end of a stick in this solution, and rubbed with it the inner circle of the ring A, so as to give it a mercurial tincture. This ring is made of brass, and is about the 30th of an inch thick, having its mean diameter not exceeding 3ths of an inch. When the inner surface of the ring wetted with the solution has been wiped dry and laid upon a table, pour a drop of quicksilver within it, and when this drop is gently pressed with the ball of the finger it will adhere to the ring, and when cleansed with a hare's foot will form a correct speculum. If the ring and speculum are now taken up and carried horizontally, and laid on the margin of the hollow cylinder B, the mercury will become a concave reflecting speculum, in consequence of its upper surface sinking down by gravity. The cylinder B rests upon a pillar with a screw on its outside, and supported by the base D. A stage, ECFG, may be moved up and down, so as to place the object, which is fixed at G, in the focus of the concave speculum. CHAPTER III.

ON COMPOUND MICROSCOPES.

A compound microscope is an instrument in which a distinct and enlarged image of an object is formed by an object-glass or a speculum, and this enlarged image again magnified by one or more eye-glasses.

There is every reason to believe, that the earliest compound microscopes which were used by Zanzs and Galileo, consisted of a convex lens for an object-glass, and a concave one for an eye-glass, like the telescope which was at that time in use.

Fontana in 1646 used two convex lenses; Dr Hooke three, and Eustachio Divini four; the two next the eye being plano-convex, and placed in contact, with their convex sides towards each other, to give a high power and a large and flat field. In 1691 Phillip Bonanni used a compound microscope with three lenses, and added to it an illuminating apparatus with two lenses.

The reflecting compound microscope was first suggested by Sir Isaac Newton, and its construction varied and made more complex by Dr Barker and Dr Smith of Cambridge. The simple contrivance of Sir Isaac has in modern times been greatly improved by Amici, Potter, Tulley, Cuthbert, and Dr Goring.

The Common Compound Refracting Microscope.

The principle of the common compound microscope with two lenses will be understood from the annexed figure, where MN is a minute object placed in the focus of the object-glass AB, or rather a little farther from it than its principal focus. An image of this object will be formed at mn, at some distance behind AB, the distance nA increasing as AM diminishes. The size of the image mn will be to that of the object MN as nA is to AM, their distances from the lens AB. If we now view this magnified image mn through an eye-glass EF, so placed that mn is in its principal focus, we shall again magnify it in the inverse proportion of Ef to the distance at which the eye sees minute objects most distinctly, which is about five inches. The object MN is thus doubly magnified, so that if nA is six times AM, and the lens EF has a focal length of half an inch, the magnifying power will be $6 \times \frac{5}{2} = 60$. While the lenses are the same, the magnifying power may be increased to any extent by increasing the distance between the lenses EF and AB; but the object becomes indistinct as the magnifying power increases, so that it is not advisable to make the distance nA more than five, six, or seven inches; or calling f the focal distance of the eye-glass, D = AM, d = nA, and A the distance at which we see objects distinctly, then this magnifying power M will be $M = \frac{d}{D} \times \frac{A}{f}$.

In this arrangement of lenses the field of view is small, and therefore we cannot see the whole of many small objects at one view. In order to remedy this, a large lens, called the amplifying glass, is placed between the image and the object-glass, as shown in fig. 49, where mn is the image formed by AB alone; but in consequence of the interposition of GH, it is contracted into m'n', and this con-

tracted image is magnified by the eye-glass EF. In order to widen the field still farther, and make it flat, two plano-convex lenses have been placed at E, F, having their convex sides in contact. In order to find the magnifying power when the lens GH is used, we must multiply the magnifying power, as obtained by the preceding formula, by the quantity $\frac{L}{\phi}$, $\phi$ representing the focal length of the lens GH and L = $\frac{d}{\phi - \delta}$, $\delta$ being the distance between the first and second glasses, and d the distance between the first and third glasses.

Dr Goring prefers the following method of finding the magnifying power of these microscopes. Measure the aperture of the object-glass and call it a, the diameter AM = f, and having measured with a micrometer scale the diameter of the usual pencil of rays before they enter the eye, call it d; then $a : f = d : F$, F being the focal length of a single lens having the same power as the compound microscope. But the magnifying power m of a lens F is $\frac{A}{F}$. Hence the magnifying power M of the compound microscope will be

$$M = \frac{Aa}{fF}.$$

In the construction of this microscope some attention is requisite in adjusting the apertures of the object-glasses employed. The smaller they are, the less will be the spherical and chromatic aberration of the object-glass, but the less will be the light. When a plano-convex lens about half an inch focus is used, its plane side should be towards the object, and its aperture limited to $\frac{1}{8}$th of an inch.

A compound microscope is sometimes so constructed that it can be used on a single microscope stand. This is done by screwing the lower end of the body round the object-glass into a projecting arm at the top of the stand. When the body is unscrewed and removed, a single lens or a doublet or triplet may be screwed into the same place, and the moveable stage, with the slider and object, brought near the single lens, just as if it had been the object-glass of a compound microscope. (See fig. 3.)

Dr Goring's Improvement on the Object-Glass of the Compound Microscope.

When the compound microscope does not require to have a high power, a compound object-glass of two lenses may be advantageously employed. Dr Goring (Quart. Jour., vol. xvii., p. 202) has contrived the combination shown in the annexed figure, where A is a plano-convex lens, with its flat side next the object, having its focal distance about one-half or two-thirds that of the plano or double convex lens B. A stop D is placed in the posterior focus of the object-glass A. Mr Pritchard remarks, that when the focal length of A "is not less than half an inch, this combination has been employed with considerable advantage, both as regards distinctness and aperture."

Mr Coddington's Improvement on the Eye-Glasses of the common Compound Microscope.

The improvement suggested by Mr Coddington on the eye-pieces of compound microscopes is shown in fig. 51.

---

1 Observations circa viventia, quae in rebus non viventibus repertantur. The object of the contrivance is to fulfill the condition proposed by Huygens in his excellent telescope eyepiece; namely, to have the refraction of the pencils divided between the two lenses, and to produce the greatest possible flattening of the field. Mr Coddington found that the most proper form of the lenses was that shown in fig. 52, where the two eye-glasses consist of a meniscus A next the eye, and a double equi-convex lens B, while the field-glass is composed of two meniscuses C, D. Mr Coddington, however, informs us that he "found no sensible error arise from the substitution of plano-convex lenses for the meniscus-glasses, which are difficult and expensive to form." He remarks also, that theory indicates "a farther flattening of the field to be made by separating the eye-glasses a little, which requires the distance of the first eye-glass from the field-glass to be diminished by about half as much;" but he did not perceive any improvement arising from this alteration in practice, and therefore he does not recommend the change. The object-glass which Mr Coddington uses in this microscope is the grooved sphere proposed by Sir David Brewster.

In his Treatise on the Eye and Optical Instruments Mr Coddington has proposed a different combination for the eye-glasses and the field or amplifying glass. Supposing the distance between the object-glass and field-glass to be 1 inch, the focal length of the field and eye-glasses 1 inch each, and the distance between the field-glass and nearest eye-glass 1 inch, he finds the distance of the two eye-glasses to be 4th of an inch. He finds also, "that all indistinctness arising from the oblique refractions will be corrected when the field-glass is convexo-convex, nearly convexo-plane, the first eye-glass convexo-convex (the flattest side next the eye, radii as 3 : 1), and the second eye-glass a meniscus (the most convex side next the eye, radii as 1 : 5)."

Taking another case, he supposes the distance of the object-glass from the field-glass to be 2 inches, and the eye-glasses to be in contact, as in fig. 52; then "it appears that for the achromatism we must have the distance between the field-glass and the second eye-glass 1 inch." Then the field-glass must be convexo-plane nearly; the first eye-glass equi-convex, and the second eye-glass a meniscus with the radii as 1 : 5.

Dr Goring, who examined one of the instruments constructed on these principles, states, that both the chromatic and spherical aberration of the objective part was wholly untouched, and that the eye-piece, consisting of four glasses, was achromatic. He adds also, that nothing can surpass the beauty of the field of this microscope for extent of flatness. Now we think that Dr Goring has mistaken Mr Coddington, who never pretended to correct the spherical and chromatic aberration of the object-glass. He considers the chromatic and spherical aberration of the grooved sphere, which is the object-glass he uses, as reduced to very small quantities, by leaving only a small channel in its axis for the passage of the rays. Whatever the residual aberration may be, Mr Coddington is not answerable for it, as his object was merely to make the other part of the microscope good, which, according to Dr Goring, he has succeeded in doing.

In accurate investigations with the microscope the instruments above described are of little use, and have been completely superseded by the compound achromatic microscope.

**Compound Achromatic Microscope.**

Although the achromatic microscope has only recently come into use as an effective and superior instrument, yet it can scarcely be considered as a new one. Every person knew that achromatic object-glasses were most desirable in the compound microscope. So early as 1776 Euler proposed to employ them in compound microscopes; but so late as 1821 M. Biot considered their introduction as out of the question, from the impracticability of making achromatic lenses as small as those which the microscope requires!

In 1823 M. Selligues and Dr Gorin were both occupied with the subject, the former having employed MM. Chevalier, two excellent opticians in Paris, and the latter Mr Talley, to execute small achromatic object-glasses. It is to M. Selligues, however, in so far as we can learn, that we are indebted for the new and happy idea of making the object-glass consist of four achromatic compound lenses, each consisting of two lenses. This idea is the actual source of the superiority of the achromatic microscopes; and in proof of this we may state, that Professor Amici, who had early been following out the old idea of a single achromatic object-glass, abandoned his attempts in 1815, but afterwards successfully resumed them by adopting M. Selligues' plan of the superposition of several object-glasses.

In M. Selligues' instrument the focal length of each object-glass was 18 lines, its diameter 6 lines, and its thickness at the centre 6 lines. In that of Amici the focal length of each was about 6 lines; and MM. Chevalier have executed them having only 2 lines in focal length. More recently, however, Mr Pritchard has surpassed all these artists, by making them of one-sixteenth of an inch in focal length.

From this brief historical detail we shall proceed to give a more minute account of the lenses executed by these different individuals, for which we are indebted to Mr Jackson Lister, whose able memoir on this subject is, as we shall see, one of the most valuable contributions to the science of the microscope that has for a long time appeared.

The achromatic object-glasses of M. Selligues' microscope made by MM. Chevalier, consisted of a plano-concave lens of float-glass, and a double convex one of crown or plate glass, with their inner curves cemented together by a mixture of mastic and turpentine, to remove the reflection of the interior surfaces, and prevent the introduction of dampness. Four of these lenses, of from \( \frac{1}{2} \) to \( \frac{1}{4} \) of an inch in focal length, were made to screw before each other, so as to be used either all together, or any of them individually, in the usual manner, like the object-glasses of a compound microscope. The aberration of colour was thus corrected in a considerable degree, but the glasses were fixed in their places, with their convex sides towards the object, which is their worst position; and in consequence of this the spherical aberration was enormous, and was distinctly seen, even with the small aperture to which it was necessary to reduce them.

Notwithstanding this defect, the grand idea of the combination was acquired; and M. Chevalier having observed the mistake committed by M. Selligues, made them of less focal length, and more achromatic; and turning the concave lens to the object, he produced in 1825 an instrument far above that of M. Selligues. His deepest glasses were four-tenths of an inch in focal length; and in his first microscope two such compound lenses were combined for his highest power.

The date of Fraunhofer's achromatic microscopes is not known. Many years ago the writer of this article ordered Fraunhofer an achromatic object-glass from Fraunhofer for a large microscope, for the purpose of making a particular class of observations; but at that time he seems not to have made any compound lenses to be combined after the manner of Salligues. Mr Robert Brown (Phil. Trans., 1830, p. 188) obtained a series of five such object-glasses from Utzschneider, whose focal lengths are from 1'8 to 0'43 of an inch.

When Professor Amici visited London in 1827, he brought with him some compound object-glasses, which performed very well; and Mr Lister subsequently learned from him that he had executed a combination of 2'7 lines in focal length, and 2'7 lines in aperture, which greatly excels the former.

Among the most successful improvers of the achromatic microscope we must rank Mr Jackson Lister, who has discovered some curious and valuable properties of these lenses that have escaped the notice of the most skilful analysis. Mr Lister has investigated the subject entirely as a matter of observation, and therefore his results are more likely to have a higher practical value.

Mr Lister takes as the basis of a microscopic object-glass two conditions: 1. That the flint-glass shall be plano-concave; and 2. That it shall be joined by some cement to the convex lens. The first condition obviates the risk of error in centering the two curves; and the second diminishes by nearly a half the loss of light from reflection, which is very great at the numerous surfaces of a combination of compound object-glasses.

Now Mr Lister has found that in every such compound lens which he has tried, whether the flint-glass was Swiss or English, with a double convex of plate-glass, which has been rendered achromatic by the form given to the outer curve of plate-glass, the ratio between the refractive and dispersive powers has been such that its figure has been correct for rays issuing from some point in its axis not far from the principal focus on its plane side; and these rays either tend to a conjugate focus within the tube of the microscope, or emerge nearly parallel.

If AB represents such an object-glass, let us suppose that it is free from spherical and achromatic aberration for a ray FDEG radiating from F, then the angle of emergence GEH will be about three times as great as that of incidence FDL. If the radiant point is now made to approach the lens, the angles of incidence and emergence will approach to equality, and the spherical aberration produced by the two will bear a less proportion to the opposing error of the single correcting curve ABC, and hence in this case the rays will be over-corrected for such a focus.

As F continues to approach the lens, the angle of incidence continuing to increase, it will exceed that of emergence, which has been in the meantime diminishing, so that the spherical aberration produced by the two outer surfaces will recover their original proportion. When F has reached this point F" (at which the angle of incidence does not exceed that of emergence so much as it had at first come short of it), the rays will again be free from spherical aberration. If F" comes still nearer the lens, or is carried beyond F in the opposite direction, the angle of incidence in the former case, or of emergence in the latter, becomes disproportionately effective, and in either case the aberration exceeds the correction, or the rays are under-corrected. Hence Mr Lister gives the following rule:

"That in general an achromatic object-glass, of which the inner surfaces are in contact, or nearly so, will have on one side of it two foci in its axis, for the rays proceeding from which the spherical aberration will be truly corrected at a moderate aperture; that for the space between these two points, its spherical aberration will be over-corrected; and beyond them either way, under-corrected."

Mr Lister found also, "that when the longer aplanatic focus is used, the marginal rays of a pencil not coincident with the axis of the glass are distorted, so that a coma is thrown outwards, while the contrary effect of a coma directed towards the centre of the field is produced by the rays from the shorter focus." These interesting results obviously furnish the means of destroying both aberrations in a large focal pencil, and of thus surmounting what has been hitherto the chief obstacle to the perfection of the microscope. And when it is considered that the curves of its diminutive object-glasses have required to be at least as exactly proportioned as those of a large telescope, to give the image of a bright point equally sharp and colourless, and that any change made to correct one aberration was liable to disturb the other, some idea may be formed of what the amount of that obstacle would have been. It will, however, be evident, that if any object-glass is but made achromatic, with its lenses truly worked and cemented, so that their axes coincide, it may with certainty be connected with another possessing the same requisites, and of suitable focus, so that the combination shall be free from spherical error also in the centre of its field.

For this the rays have only to be received by the front glass B, from its shorter aplanatic focus f', and transmitted in the direction of the larger correct pencil f'A of the other glass A. It is desirable that the latter pencil should neither converge to a very short focus, nor be more than very slightly, if at all, divergent; and a little attention at first to the kind of glass used will keep it within this range, the denser flint being suited to the glasses of shorter focus and larger angle of aperture. If the two glasses, which in the diagram are drawn as at some distance apart, are brought nearer together (if the place of A, for instance, is carried to the dotted figure), the rays transmitted by B in the direction of the larger aplanatic pencil of A, will plainly be derived from some point (Z) more distant than f', and lying between the aplanatic foci of B; therefore (according to what has been stated) this glass, and consequently the combination, will then be spherically over-corrected. If, on the other hand, the distance between A and B is increased, the opposite effects are of course produced.

In combining several glasses together, it is often convenient to transmit an under-corrected pencil from the front glass, and to counteract its error by over-correction in the middle one.

Slight errors in colour may, in the same manner, be destroyed by opposite ones; and, on the principles described, we not only acquire fine correction for the central ray, but, by the opposite effects at the two foci in the transverse pencil, all coma can be destroyed, and the whole field rendered beautifully flat and distinct. (Phil. Trans., 1830, p. 199.)

Compound Achromatic Microscopes with Solid and Fluid Lenses.

In 1812 a very simple method was employed by Sir David Brewster for making both single and compound fluid achromatic microscopes. Almost all objects are seen to the greatest advantage when immersed in a fluid, even the microscope finest test objects, such as the scales of the Podura. Having placed the object on a piece of glass, he put above it a drop of an oil having a greater dispersive power than the single lens, or than the concave lens which formed the object-glass of the microscope. The lens was then made to touch the fluid, so that the surface of the fluid was, as it were, formed into a concave lens. Now if the radius of the outward surface of this lens was such as to correct the dispersion, we have here a perfect achromatic microscope, both simple and compound. The best way is to over-correct the colour of the plate-glass lens by the fluid, and then to reduce the dispersion of the fluid by mixing it with one of less dispersive power. This will be understood from the annexed diagram, where AB is an unequally convex lens, the flattest side of which is plunged in the fluid mn, placed in a watch-glass CD. The object c is placed at mn, and the dispersion of the concave surface of the fluid compensates that which is produced by the lens. All errors of centring are here removed, and also the loss of light at the touching surfaces of solid lenses. If AB is a single microscope, the object mn will be placed in its principal focus, and the emergent parallel rays will enter the eye; but if it is the object-glass of a compound microscope, an image will be formed a few inches behind AB, by withdrawing AB a little from mn, or placing the object a little without its principal focus. We have already had occasion to describe an achromatic grooved sphere, but in the process of achromatizing it, the sphere loses in a very small degree its valuable property of refracting in the very same manner all the pencils that enter the eye. This property, however, may be preserved in the bird's-eye sphere by the achromatic method which we have now described.

Let AB (fig. 56) be the grooved sphere, and CD the watch-glass containing the fluid; it is obvious that every ray which passes through the centre of the sphere will enter and quit it perpendicularly, without suffering any refraction. The same mode of achromatizing the sphere AB may be adopted with a solid concentric concave lens of flint-glass or other substance, or the sphere may be placed between two such concentric lenses. The greater the dispersion of the flint-glass, the nearer must the outer surface CD approach to AB. By these means the grooved sphere may be rendered perfect, both as a single microscope and as the object-glass of a compound one.

The principle above described may be applied to a system of object-glasses like those of Selligues' microscope. Let A, B, E (fig. 57) be three convex lenses, so placed at the end of the tube of a compound microscope, that the highly dispersive fluid in the watch-glass CD will enter between the glasses A, B, and E. The concave lenses of fluid will over-correct the three lenses A, B, and E; but if a very deep curvature on the outside of A is not sufficient to compensate this over-correction, it may be effected by a suitable lens at F. If the three lenses are made of the precious stones, with a high refractive power and a low dispersive one, the concave fluid lenses will not over-correct them.

If, as Dr Blair did in his aplanatic fluid object-glasses for telescopes, we use muriatic acid in the form of butter of antimony, and containing a due quantity of metallic particles, for the fluid, and crown-glass for the lenses, the secondary colours will be completely corrected, and an instrument of the most superior kind produced. If a permanent and portable aplanatic object-glass is preferred, the butter of antimony may be placed between a meniscus and a plano-convex lens of crown glass, as in the annexed figure, where o is the object, CD a meniscus of crown-glass, AB a plano-convex lens, and mn a concave lens of the fluid. This construction of the object-glasses of compound microscopes is much more easily applicable in the case of the microscope than in that of the telescope. In the latter case the colour of the fluid, the changes which it undergoes by time, and the difficulty of retaining it, are objections of considerable amount; but in the case of the microscope, the colour of the fluid disappears owing to its small thickness, and it may be retained by capillary attraction alone, and renewed as often as we choose.

Since these observations were published, the compound Recent achromatic microscope has undergone great improvements in the hands of Pritchard, Ross, Powell, Messrs Smith and the micro-Beck, M. Nachet, MM. Oberhauser, and Professor Amici scope. of Florence. These great improvements, by which the compound achromatic microscope has been brought to such a high degree of perfection, were no doubt owing to the spirit of competition excited by the London and Paris Exhibitions.

In the Crystal Palace of 1851, Mr Andrew Ross, Messrs Smith and Beck, and M. Nachet of Paris, were the leading competitors. Mr Ross and Messrs Smith and Beck received council medals, and M. Nachet a prize medal. The instruments of the first two artists were of first-rate quality, and those of M. Nachet were superior to those of all foreign opticians. The following tables show the relative angles of aperture and focal lengths of the object-glasses exhibited by the competitors:

**Mr Ross's Object-Glasses in 1851.**

| Focal Lengths | Angles of Aperture | |---------------|-------------------| | 1 inch | 27 degrees | | 0 1/2 " | 60 " | | 0 3/4 " | 113 " | | 0 1/2 " | 107 " | | 0 1/4 " | 135 " |

**Messrs Smith and Beck's Object-Glasses in 1851.**

| Focal Lengths | Angles of Aperture | |---------------|-------------------| | 0 1/2 " | 45 degrees | | 0 3/4 " | 70 to 75 " | | 0 1/2 " | 60 " | | 0 1/4 " | 100 to 105 " |

**M. Nachet's Object-Glasses in 1851.**

| Focal Lengths | Angles of Aperture | |---------------|-------------------| | 0 1/2 " | 88 degrees | | 0 3/4 " | 108 " | | 0 1/2 " | 134 " |

Mr Ross intended to exhibit in Paris object-glasses of a still higher order than those which we have mentioned, and he would thus have found himself in competition with his eminent rivals Messrs Smith and Beck, and M. Nachet. He was prevented, however, by the pressure of business from exhibiting the new object-glass which he had prepared for that purpose; and Messrs Smith and Beck, who had no English rival, carried off the microscopic prize by receiving a medal of the first class. Although the microscope of M. Nachet was not equal to that of the English artists, it had such a high degree of merit that a medal of the same value was adjudged to him.

MM. Oberhauser of Paris exhibited an excellent achro- Mr Pillischer's microscope with an achromatic object-glass half an inch in focal length, and of such excellence that a medal of the second class was awarded to him. Mr Pillischer also exhibited what he calls a lenticular microscope, for examining urinary deposits at the bedside, which has been highly spoken of by the late Mr Golding Bird and Mr Quekett.

Mr Pillischer's "students' microscopes" were remarkable, not only for their cheapness, but the excellence of their construction. The following is a list of the angles of aperture and prices of his object-glasses:

| Focal Lengths | Angles of Aperture | Prices | |---------------|-------------------|--------| | 2 inches | 14 degrees | L2 2 | | 1 | 26 | 2 2 | | 0 1/2 | 60 | 4 0 | | 0 1/4 | 90 | 5 0 | | 0 1/8 | 109 | 5 0 |

The following table contains a description of the achromatic object-glasses which Mr Ross intended to exhibit:

**Mr Ross's new Object-Glasses in 1855.**

| Object-Glasses | Angles of Aperture | Magnifying Powers with four Eye-Visors | Prices | |---------------|-------------------|----------------------------------------|--------| | | | A | B | C | D | | | 2 inches | 12 degrees | 20| 30| 40| 60| L3 0 0 | | 1 | 15 | 60| 80| 100|120| 3 10 0 | | 1 | 22 | 60| 80| 100|120| 3 10 0 | | 0 1/2 | 65 | 100|120|180|220| 5 5 0 | | 0 1/4 | 85 | 220|350|500|620| 5 5 0 | | 0 1/8 | 125 | 220|350|500|620| 7 10 0 | | 0 1/16 | 135 | 320|510|700|910| 10 0 0 | | 0 1/32 | 150 | 400|670|900|1200|11 0 0 | | 0 1/64 | 170 | 650|900|1250|2000|18 0 0 |

Messrs Smith and Beck sent two achromatic microscopes to the Paris Exposition, namely, one of their very best instruments, and another of an entirely new construction, to which they gave the name of "The Educational Microscope."

The first of these microscopes differed very little from the one which they exhibited in 1851 at the Crystal Palace. It had, however, object-glasses of a shorter focus and greater angular aperture, as is shown in the following list:

| Focal Lengths | Angles of Aperture | |---------------|-------------------| | 1 1/2 inches | 13 degrees | | 0 1/2 | 27 | | 0 1/4 | 90 | | 0 1/8 | 110 | | 0 1/16 | 120 |

The Educational Microscope exhibited by Messrs Smith and Beck is an instrument of great value, and from its low price and excellence it cannot fail to have an extensive sale. With object-glasses of one inch and a quarter, and apertures of 22° and 75°, its price, packed in a case, is only £1.10, and the additional apparatus, including one Lieberkühn, a Wenham's parabolic reflector, a Wollaston's camera lucida for drawing, and a polarizing apparatus complete, with prisms of selenite, amount only to £1.5 additional.

Since the middle of 1855 no fewer than 100 of these educational microscopes have been sold, and two-thirds of this number had the additional apparatus.

The following were the object-glasses which M. Nachet exhibited in 1855, and which were much admired by the jury:

| Series | Focal Lengths | Angles of Aperture | Prices | |--------|---------------|--------------------|--------| | No. 3 | 1 inch | 75° | L2 10 0 | | No. 4 | 1 " | 90 | 2 10 0 | | No. 5 | 1 " | 95 | 3 3 0 | | No. 6 | 1 " | 110 | 4 0 0 | | No. 7 | 1 " | 125 | 5 5 0 | | No. 8 | 1 " | 165 | 7 5 0 |

With these two last object-glasses M. Nachet states that there is no test-object too difficult to be resolved when it is plunged in Canada balsam.

When the jury of Class VIII. were comparing the rival fine microscopes, Professor Amici of Florence, distinguished by scope and ingenuity in optical inventions, showed a microscope which exhibited certain striae in test-objects better than any of the instruments under examination. This superiority was produced by the introduction of water between the object and the object-glass; but as Professor Amici was not an exhibitor, the jury was not called upon to adjudicate to him a medal.

This microscope was of small dimensions compared with those with which it was compared, and shows how much may be effected by the ingenuity and optical knowledge of an observer like Professor Amici, thoroughly acquainted with optics. We have seen at Florence, in Professor Amici's studio, instruments of his construction which exhibit distinctly the lines in certain objects which have hardly been seen by other instruments; and we are convinced that it is only by a preparation of difficult objects by the observer himself, by illuminating them properly, and by optical processes which the optician neither knows nor pretends to know, that great discoveries are to be made.

In a work like this we cannot find room for an account of the achromatic microscope in the various forms in which it has been constructed. Every artist has shown much ingenuity in the construction of different parts of the instrument and in the adaptation of it to different objects of research, and the naturalist will be the best judge of the size and nature of the instrument which he wishes to employ. We shall therefore content ourselves with describing one of the earliest achromatic microscopes, namely, that of Mr Pritchard; the latest, and what we believe to be the best, namely, that of Mr Andrew Ross; and some forms of the instrument which possess special advantages.

**Pritchard's Compound Achromatic Microscope.**

This instrument is represented in fig. 59 as fitted up by Mr Pritchard. All its parts are so distinctly shown in the figure that they require no description, especially as the uses of most of the parts have been described in a former chapter. Fig. 59 is a perspective view of the instrument in its most convenient position for examining transparent objects by reflected light. The stops and condensing illuminator, which are seen under the stage, should be removed when particular objects are to be examined. When test-objects are to be viewed by direct light the instrument can be turned round.

In Mr Pritchard's instrument the following are the dimensions and powers of the lenses for a complete microscope:

| Sidereal Focal Length in parts of an inch | Angle of Aperture | Magnifying Powers in Diameters by a standard of 5 inches | |------------------------------------------|------------------|-------------------------------------------------------| | 1 | 16° | 60 to 100 | | 0 1/2 | 21° | 100 to 350 | | 0 1/4 | 42° | 240 to 500 | | 0 1/8 | 63° | 500 to 1100 | | 0 1/16 | 63° | 900 to 3000 | Of these object-glasses, that whose focal length is 4th of an inch appears to be the most perfect and useful.

Without depreciating the fine instruments of Smith and Beck, and Powell and Lealand, which evince great ingenuity, and have many new and admirable properties, the microscope of Mr Ross must be regarded as the finest hitherto constructed.

Mr Andrew Ross's Compound Achromatic Microscope.

The great achromatic microscope of Mr Andrew Ross, in its most perfect and recent form, is shown in fig. 60.

The body of the microscope AB rests upon a massive stand so constructed as to prevent any perceptible tremor in the object under examination. The transverse arm m into which it is screwed at m, is fixed by a screw E to the top of a strong flat bar, in the back of which is a rack into which works a pinion moved by the milled head M, which gives the coarse adjustment for bringing the body of the microscope into focus. Another milled head on the opposite side enables the observer to do the same thing with his left hand. The fine adjustment, for obtaining distinct vision of the object, is effected by the milled head C, which acts upon the tube at B, into which the object-glasses are screwed, one turn of it giving a motion of the 300th of an inch. On the top of the two pillars P, P is fixed a horizontal axis D, which passes nearly through the centre of gravity of the microscope, and upon which it turns, so that it may be placed at any angle whatever to the horizon. The stage S for holding the object, and the apparatus beneath it for modifying the light to illuminate the object, are most ingeniously constructed. The two rectangular or traversing motions of the stage are produced by the two milled heads below B. The secondary stage at T, for condensing and modifying the light reflected from the mirror V, receives all the requisite motions from the milled heads shown in the figure. In the cylindrical tube of which it is composed is placed the achromatic condenser and one of the polarizing prisms or rhombs, and other pieces of apparatus which are often required in particular researches.

The compound achromatic microscope may be considered as having nearly attained to perfection, while the practical of the optician confines himself to the use of flint and crown-glass microscope lenses with spherical surfaces. It is hardly possible, however, that so noble an instrument, by which so much knowledge has yet to be acquired, will long remain in its present imperfect state.

The writer of this article has long ago, and repeatedly, urged upon the optician the necessity of constructing both telescopes and microscopes upon the aplanatic principle discovered by Dr Blair, a principle much more easily applied to small than to large object-glasses. Science has fully performed her part in showing how the colours of refracted light, both primary and secondary, may be corrected, but neither public liberality nor private enterprise has been called forth to put in practice her methods. Even in the case of the primary colours opticians have declined to take the trouble of making each lens of their eye-pieces achromatic, and, with one exception, they seem not even to have attempted to correct the errors of the secondary spectrum. The time, however, has now come to make this attempt; and we have no doubt that before the close of the century we shall have—what Dr Blair neither anticipated nor proposed to have—each lens of our optical instruments per- The employment of fluids of various dispersive powers gives the artist a wider range in his experimental researches, but even if he limits himself to the use of different kinds of glass and transparent minerals, we have no doubt of his ultimate success. This attempt has been boldly and so far successfully made by Professor Amici of Florence, who has actually constructed microscopes in which there are solid lenses of various refractive and dispersive powers. These microscopes are now made for sale; and an account of them has been recently published by M. Achille Brachet of Paris, who has added in Italian M. Amici's own account of his invention.

**Description of Amici's Compound Achromatic Object-Glasses.**

Amici's achromatic object-glasses contain seventeen achromatic object-glasses, which are arranged in six series, and marked in the following manner:

| Series I | Series II | Series III | Series IV | Series V | Series VI | |----------|-----------|------------|-----------|----------|-----------| | A | B | C | D | E | F |

The equivalent focal distances, apertures, magnifying powers, &c., are given in the following table:

| Series | Equivalent Focal Distance, Millimetres | Aperture | Magnifying Powers | Value of one part of the Objective Micrometer | |--------|--------------------------------------|----------|-------------------|---------------------------------------------| | No. I | 22-82 | 26° | 100 | 0-0325 | | No. II | 8-47 | 37 | 257 | 0-0121 | | No. III| 4-27 | 70 | 535 | 0-0061 | | No. IV | 3-22 | 57 | 577 | 0-0056 | | No. V | 3-50 | 77 | 650 | 0-0050 | | No. VI | 1-74 | 160 | 1310 | 0-00248 |

The two series Nos. I. and II. are used for transparent objects when illuminated with the Lieberkühn or perforated silver speculum, and for opaque objects when illuminated by Professor Amici's spherical prism, which throws the light down upon the object. When the objects are very small, and either opaque or transparent, and placed between two plates of glass, they may be illuminated by light reflected very obliquely from the spherical prism placed below them, and they are seen on a dark ground when the prism gives an obliquity greater than the angle of aperture of the object-glass employed. In the series No. I., for example, where half the angle of aperture is 13°, if the lower illuminating spherical prism is more than 13° distant from the optic axis, none of the refracted light will reach the eye, and the object will radiate only the light which its surface is capable of reflecting. This mode of illumination, which often produces an excellent effect, may be used with the series No. VI.

The series No. IV. is used for naked transparent objects, or when they are not covered with a plate of glass,—at least with one not very thin.

The series No. V. is used for transparent objects covered with a plate of glass 0-86 of a millimetre thick, of which there is a dozen. If a plate thicker than this—a millimetre, for example—is used, the object will be seen less distinctly.

The series Nos. III. and VI. are constructed on a new principle, which renders the image more clear and distinct, and does not require any correction of the error which the common system introduces, owing to the different thicknesses of the plates of parallel glass which cover the object. This advantage is obtained by immersing in a drop of distilled water the last lower surface of the series III. and VI. This operation is performed in the following manner:—Let AB be a plate of glass, beneath which is the object C. With the point of a wet hair pencil place a drop of water D on the outer surface of the object-glass N. The drop will remain adhering to it when the series is put upon the microscope. By putting another drop C on the upper surface of the plate AB, and bringing the two drops together, a parallel plate of water will be placed between the object-glass and glass plate AB, the two surfaces between which it lies having been carefully cleaned to remove any grease which may prevent the water from adhering to the surfaces of the glass. It is supposed that the object C is under the plate AB, in contact with it, and dry; but it may be immersed in another fluid contained between two plates of glass.

The series No. III. is used for all preparations preserved between plates of glass whose thickness is a millimetre, and may be also used for looking at objects immersed in water without the interposition of glass, such as aquatic plants, living infusoria, &c., &c.

The series No. VI. is used in the same manner as No. III., but being very powerful, it requires to be delicately managed. In this series the objects are placed on a piece of wood with a conical aperture in its centre, covered with a plate of glass one-fourth of a millimetre thick. Its profile is shown in the annexed figure, in which the object placed under C adheres to the glass, and the two drops of water D, E are united. It is necessary to mention, that as the equivalent focal distance of the series is 1-74 millimetre, the distance between the inferior lens and the object will be 0-4; and as the thickness of the plate of glass is one-fourth of a millimetre, or 0-25, the distance between the object-glass and the glass plate—that is, the thickness of the plate of water—will be only 0-15, a distance so small that the greatest care is necessary in finding the object, in order that the very thin glass may not be broken. If this does happen, we must substitute another of the same thickness, as measured by the spherometer.

The series may also be used for any other thickness of glass less than 0-4, and down to zero, that is, when there is no glass over the object placed in water; but the effect is the best when the thickness of the glass is 0-25, as in this case the achromatism is perfect, even at the obliquity of $\frac{160^\circ}{2} = 80^\circ$ with the optical axis, in which case we can see strie or parallel lines whose distance is equal to $\frac{1}{300}$ th of an inch.

If the object to be examined is in a fluid, such as the globules of blood, take a fragment of thin glass, a line or two in diameter, and place upon it the blood; it will, when put in contact with the plate on C, adhere to it by attraction, and retain its fluidity for many hours.

If we have occasion to look at any object with No. VI., when it is covered with very thin glass, or when it is in water, without the interposition of glass, the vision will be improved by removing the object-glass U, and leaving the series formed as in fig. 65.

Professor Amici is of opinion that no object-glass hitherto constructed has a power as great as his series No. VI.; and considering the distance (about 0·4) which is left between the object-glass and the object, with an aperture of 160°, he thinks he has given a proof of the superiority of the principle he has invented.

Professor Amici has not described the principle here referred to, nor mentioned the transparent substances of which his object-glasses are composed. He merely tells us that Nos. I. and II. are constructed with four different refractive and dispersive substances; Nos. III., IV., and V., with five; and No. VI. with six such substances.

In illuminating transparent objects Professor Amici uses only a single lens of flint-glass or rock-crystal, and maintains the strange opinion, contrary to theory as well as to the experience of every practical optician, that achromatic illumination is not necessary.

**Professor Amici's Pocket Achromatic Microscope.**

This portable microscope, which we have found very useful, is shown in the annexed figure, where AB is the body of the microscope, 2½ inches long, sliding into the tube BC, ¾ths of an inch in diameter. The tube BC screws into the double plate of brass EDG, 2½ by 1½ inches, which acts as a spring, and may be opened or shut by the screw-nut S, for the purpose of moving the stage or object-holder MN towards or from the object-glass. This stage is a spring which holds the object-plate firm by pressure; two pins mm, at the lower end of each arm N, M, sliding through holes in the plate EDG. When the object-plate is placed between MN and EP, and fixed by pressing the two plates together, the tube may be held horizontally, and distinct vision obtained by the motion of the body AB in the tube BC, and by the finer motion given by turning the screw-nut S, which shuts or opens the spring DEF, and places the object nearer or farther from the object-glass.

When it is desired to hold the microscope vertically, the object is illuminated by a rectangular prism Pp attached to an arm pq, which slides in a little spring tube fixed in the plate EDG. The side of the prism next the object-glass is convex, for the purpose of condensing the rays which fall upon it.

**The Microscopic Finder.**

Professor Amici has referred, in the description of his series No. VI., to the great difficulty of finding the object and placing it on the point of sight, and to the great danger of breaking the thin glass of the object-plate, owing to the distance between it and the object-glass being only 0·15 of a millimetre, or the 1/8th part of an inch. A microscope, indeed, requires a finder as much as a telescope; but, in so far as we know, no person has attempted to give it one.

We obviously cannot with advantage attach a second microscope to the principal one, as is done in the telescope; but the object may be gained in a simpler and more effective manner. When the observer is using his highest power both of object-glass and eye-piece, and loses sight, as he frequently does, of the object, or part of an object, under examination, he often finds it extremely difficult to bring it again into the field of view. Owing to the uneasiness of almost every microscopic stand, he will seldom succeed by taking the lower powers, bringing the object into the centre of the field, and then replacing the higher powers with which he has been viewing it. But even if this method were successful, the labour which it imposes is intolerable. Sir David Brewster has therefore proposed the following method, and found it perfectly successful:—A concave lens of a greater focal length than the equivalent focal length of the object-glass is slipped upon the tube of the object-glass, or brought in front of it when withdrawn from the object. The magnifying power may be thus reduced in any required degree, the field of view enlarged, and the object brought into the centre of the field; the concave lens is then withdrawn, and when the instrument has been readjusted without any movement of its parts, the object will be found within the field.*

Various methods have been described for finding the object by means of scales, horizontal and vertical, applied to the slides; but however valuable these may be, the apparatus cannot be called a Microscopic Finder, which should form an integral part of the instrument.

**Nachet's Multocular Microscopes.**

M. Nachet, of whose microscopes we have already spoken in high terms, has adapted the microscope for anatomical demonstrations, so that two or three persons may see at the same time the result of microscopical dissections, by constructing two microscopes—a double and a triple one. By means of the first, one person can examine the progress and result of a dissection which is performed by another person; and by means of the second, two persons can enjoy this advantage.

In the microscope for two persons this result is obtained by placing above the object-glass a prism P (fig. 67), the section of which is an equilateral triangle. The rays from the object-glass, shown in the figure by the letter ab, ab', entering the lower face of the prism perpendicularly, the two halves of the pencil are reflected in opposite directions from the other faces of the prism at angles of 45°, and thus enter the two separate tubes, in each of which they form an image of the object. These images are in a certain sense erect; but in order to seem in exactly their natural position, in which case alone the ann-

---

* See Brewster's Treatise on Optics, p. 486, edit. 1853. * Opticians will adopt various modes of applying and withdrawing the concave lens. tomist can use his scalpel, a prism is placed in each tube between the former prism and the eye-pieces, so that their planes of reflection are perpendicular to those of the other prisms. By this means the images are perfectly erect, and the demonstrator can proceed with his work without fatigue or difficulty. If the demonstrator and observer should have eyes of different focal lengths, the adjustment is effected by moving the eye-piece to or from the object-glass.

When the microscope is constructed for three persons, the pencil of rays from the object-glass is divided by three prisms placed in the same plane, and whose reflecting faces, if brought together, would form a triangular pyramid. The pencil from the object-glass is then divided and directed into three separate tubes, in which three prisms erect the three images, and place them in their natural position. This instrument is shown in the annexed figure.

M. Nabet has also constructed the instrument for the use of four persons.

**Nabet's Binocular Microscope.**

The idea of a binocular microscope can hardly be called an invention, if constructed on the same principle as the binocular telescope with two object-glasses as well as two eye-glasses. The additional expense of such an instrument will not be repaid by any advantage which it is supposed to possess. An instrument of this kind was constructed by Père Cherubin about 1670; but in so far as we know, no other binocular microscope has been made.

In 1851 Professor Riddell, of the university of New Orleans, devised and constructed a binocular microscope with the view "of rendering both eyes serviceable in microscopic observations."

"Behind the objective," says Professor Riddell, "and as near thereto as practicable, the light is equally divided and bent at right angles, and made to travel in opposite directions by means of two rectangular prisms which are in contact by their edges somewhat ground away; the reflected rays are received at a proper distance for binocular vision upon two other rectangular prisms, and again bent at right angles, being thus either completely inverted for an inverted microscope, or restored to their first direction for the direct microscope."

Sir Isaac Newton seems to have been the first person who described a reflecting microscope. He communicated reflecting his plan to Oldenburg in 1679, as shown in the annexed diagram, where AB is a concave speculum, O the object, F the place where an image of it is formed, and CD an eye-glass for magnifying it. In another letter to Oldenburg, dated 14th July of the same year, he refers to another improvement on microscopes, which is to "illuminate the object in a darkened room, with the light of any convenient colour, not too much compounded;" for by that means the microscope will, with distinctness, have a deeper charge and larger aperture, especially if its construction be such as I may hereafter describe." We are not aware that this idea was ever further developed by its author.

**Mr Potter's Improvement upon it.**

Mr Potter has recently proposed "a new construction Potter's of Sir Isaac Newton's microscope," principally with the improvement of removing the difficulty of illuminating the object. His first construction was for opaque objects; and in order to illuminate them, he cut a large circular aperture abe in

---

1 The use of Maltocular instruments was proposed by Sir David Brewster in 1822. (See Edinburgh Philosophical Journal 1822, vol. vii., p. 327; and Coddington's Elementary Treatise on Optics, p. 133.)

2 Brewster's Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton, vol. i., p. 212.

3 Edinburgh Journal of Science, Jan. 1832, No. 11, p. 61. the tube, between the object and the speculum; but the light which fell on the sides of the tube occasioned a good deal of indistinctness in the field of view. This defect, however, was completely removed by lining all the lower parts of the tube with black velvet. Mr Potter found it advantageous to concentrate the light on those objects that required it by a large lens at d. For transparent objects he applied a lens, as shown at e. Its convergent beam is reflected on the object placed at the end of the wire ah, by means of a small diagonal mirror in the axis of the tube, and inclined to this axis 45°. By this means a very strong light may be thrown through and past the object. By means of movable caps to cover the opening abc, and the lens e, all interference of foreign light is prevented; and without altering the position of the object, both methods of illumination may be successively adopted. Mr Potter attaches his objects to thin brass wires a, stuck into wooden handles h, and these pins pass through a slit cut into a small piece of cork attached to the sliding-piece g, which at the same time carries the lens e and the plane mirror, the whole of which are moved by the small arm connected to the crank, as at i. The adjustment of the object to the focus of the mirror is effected by turning a nut attached to the pivot on which the crank is fixed.

In the microscope used by Mr Potter he employs a speculum 1 inch in diameter, with a focal length of 1½ inch; and he generally makes the distance between the object and the image from 12 to 14 inches.

The size of the speculum allows him to place an insect or other object of ¼th of an inch square in the tube, without any perceptible bad effect resulting from it.

When Mr Potter had adjusted the illuminators in the manner which we shall afterwards have occasion to describe, he "saw quite easily what are called the diagonal lines on the scale from the wing of the white cabbage butterfly, which has been proposed as a difficult test-object by Dr Goring; and it is such a one as those who have only seen the stronger longitudinal striae or scales from the wings of moths and butterflies have little idea of." Mr Potter was also able to resolve a delicate blue tissue in the web of a spider called the Clubiona atroz, into its component fibres.

The great size of speculum used by Mr Potter arises from his being able to give all specula a true ellipsoidal figure, so as to remove the spherical aberration. We have in our possession two of Mr Potter's instruments, one of them with a spherical and the other with an ellipsoidal mirror. The quantity of light and the defining power of the latter are unusual in such instruments.

Amici's Reflecting Microscope.

This instrument is shown in section in figure 72, where a is a small ellipsoidal speculum about 1 inch in diameter, and 2½ths in focal length. The object is placed on a stage mn, below the tube of the microscope, and the rays which issue from it fall upon a small speculum b inclined 45° to the axis of the ellipsoidal speculum, in the same manner as if the object had been placed in the tube as far to the right hand of the small mirror as it is below it. An image of this object is of course formed in the other focus of the ellipsoidal speculum, and may be viewed by a single or double eye-piece, as in other compound microscopes. Professor Amici, however, uses a negative eye-piece, consisting of two plano-convex lenses A, B.

The new and peculiar part of this instrument is the use of the small speculum, which allows the object to be placed without the tube, and illuminated with the utmost facility.

Amici's Second Reflecting Microscope.

At the end of his Memoir, in the Acts of the Italian Society, on his first reflecting microscope, the author informs us that he had constructed another cataleptic one in 1813, which was more efficacious, and in which the aperture of the concave speculum was six lines, and its focal length eight lines, with an angular aperture of 44°. This form of the instrument is shown in the annexed figure, in which AB is the concave speculum, CD the plane speculum inclined 45° to the optic axis, and m a hole in its centre through which the rays from the object F pass to the speculum AB, from which they are converged upon CD and reflected to a focus at f, where they are received by the eye-piece at E. By polishing the speculum CD on the outside, opaque objects might be illuminated by the light which it may be made to reflect.

M. Vicenzo Amici, the son of the professor, has proposed to modify this construction, as shown in the annexed figure, where ABDC is a rectangular parallelopiped of glass, the curved surface of which, AB, is spherical or elliptical, and well polished and silvered. On the middle of CD a small cylinder of glass P is cemented with Canada balsam, the outer surface of which is concave, having its centre at F. The rays from the object at F enter the cylinder without refraction, and after reflection from AB and CD, as in the preceding figure, are conveyed to a focus at f, as in fig. 73.

Another form of this instrument which we have seen, is shown in the annexed figure, where ABDC is a cylinder of glass whose base AB is silvered, and has an unsilvered portion mn with its centre of concavity at F. The rays from the object at F pass without refraction to CD, part of which, pq, is silvered; and being reflected again from AB, they pass... through the unsilvered portion \( C_p \), \( D_q \) to their convergence as before at \( f \), fig. 73, and enter the eye-piece \( E \).

**Dr Goring's Improved Reflecting Microscope of Amici.**

Mr Cuthbert, an ingenious London optician, constructed one of Amici's instruments, the speculum having \( \frac{1}{2} \) inch of aperture, and a focal length of 3 inches, and the body of the microscope being about 1 foot long. Dr Goring and he having tried it on the test-objects which the doctor had newly introduced, found its performance unsatisfactory. Dr Goring therefore recommended that the speculum should be only half an inch in focal length, and the body 4 or 5 inches long. Mr Cuthbert accordingly finished a pair of metals \( \frac{1}{8} \)ths of an inch in focal length, and only \( \frac{1}{8} \)ths in diameter. Their excellent performance induced Dr Goring and Mr Pritchard to turn their attention to the improvement of the instrument; and, as Mr Cuthbert\(^1\) has been able to execute perfectly ellipsoidal metals, having an aperture equal to their sidereal focal length, or \( \frac{1}{4} \), and of so small a diameter as \( \frac{1}{8} \)ths of an inch, they have produced an instrument of a superior kind.

This microscope is represented in fig. 76, where it is seen to rest on a tubular pillar, its body being held by a split socket. The pillar is screwed on a solid cruciform stand, to one of the legs of which an adjusting screw is applied, to produce steadiness. The body moves round a cradle-joint at the top of the pillar, and may be firmly fixed at any degree of inclination. The body of the microscope is shown at \( a \), the eye-tube at \( d \), and the eye-piece, which is a Huygenian one, at \( e \). The focal lengths of the interior glasses of the eye-pieces, of which there are usually three, are \( \frac{1}{8} \)ths, \( \frac{1}{8} \)ths, and \( \frac{1}{8} \)ths of an inch. The tube containing the specula is shown at \( b c \). The triangular bar which carries the illuminating reflector, the stage, and the apparatus for adjustment, is shown at \( f \), and is soldered to the neck of the body. The mirror \( k \) is plane on one side, and has a plaster of Paris surface on the other. The stage \( l \) is a combination of rack and screw work, wrought by two concentric milled heads at \( m \). The smallest of these moves the object in the direction of the body, and the other in an opposite direction. The stage can be lifted out of the triangular socket \( g \), which carries the adjusting screw \( i \) for obtaining distinct vision, and the clamping screw \( h \).

When the body and stand are used for a compound achromatic microscope, a tube containing the compound object-glasses below it, increasing in diameter from the object, is screwed into the body at \( b \), in place of the tube \( b c \). A rectangular prism, shown in dotted lines, reflects the pencils that pass through the object-glasses along the axis of the tube \( b c \) to the eye-piece \( e \).

The following sets of metals are made for the reflecting microscope:

| No. | Solar Focus | Angle of Aperture | Distance between Object and Tube | |-----|-------------|------------------|--------------------------------| | 1 | 2 inches | 13° | \( \frac{1}{2} \) inch | | 2 | 1 | 18° | \( \frac{1}{2} \) inch | | 3 | \( \frac{1}{2} \) | 27° | \( \frac{1}{2} \) inch | | 4 | \( \frac{1}{2} \) | 36° | \( \frac{1}{2} \) inch | | 5 | \( \frac{1}{2} \) | 41° | almost 0 inch | | 6 | \( \frac{1}{2} \) | 55° | |

The metals Nos. 1, 2, and 3 are those most useful for examining opaque objects. No. 3 is excellent also for all kinds of transparent objects. No. 5 can scarcely be used for opaque objects, as it leaves almost no space between the tube and the object for allowing the latter to be illuminated. No. 6 cannot be used at all for opaque objects, but is especially intended for the most difficult class of transparent test-objects.

**Dr Smith's Reflecting Microscope.**

Having constructed one of Sir Isaac Newton's microscopes in 1738, Dr Smith of Cambridge observed that the reflecting colours of objects were much more beautiful and natural than in refracting microscopes. He found that objects were very distinct and sufficiently light when the microscope had the following dimensions:

- Focal length of the speculum: 24 inches. - Diameter of ditto: 1 inch. - Focal length of the plano-convex eye-glass: 24 inches. - Ratio of the distance of the object from the focus of the speculum to the focal distance of the speculum: 1 to 19.

Finding that, in order to obtain a high magnifying power, the speculum required to be very concave and small, he contrived another microscope with two reflecting spherical surfaces of any size, but so related to each other that the second reflection should correct the aberration of the first.

Dr Smith's microscope is shown in fig. 77, where AA is a concave spherical speculum, having its polished surface inwards. The rays from an object \( o \) placed in the slider \( m n \) will be reflected from the concave speculum AA upon the convex CC, and will have a distinct and magnified image of it formed before the convex eye-glass \( E \), by which it will be magnified still more. This instrument, in short, is nothing more than the Cassegrainian telescope converted into a microscope, with this difference only, that in the telescope distinct vision is obtained by moving the convex mirror, whereas in the microscope it is obtained by a motion of the eye-glass. Dr Smith constructed one of these microscopes, which he found to perform "nearly as well in all respects as the very best refracting micro-

---

\(^1\) The process by which Mr Cuthbert was able to accomplish this difficult task is similar to that by which he gave truly hyperbolic figures to the mirrors of small Gregorian telescopes, with three inches of aperture and five inches of focal length. Microscope.

The writer of this article has one of them now before him, which performs wonderfully well, though both the specula have their polish considerably injured. It shows the lines on some of the test-objects with very considerable sharpness.

The following are the dimensions, &c., of Dr Smith's reflecting mirror, as given by himself:

| Dimension | Value | |------------------------------------------------|---------| | Focal length of both specula | 10000 | | Distance of the centres of both specula | 16558 | | Distance of the image from the centre of the concave speculum | 1337 | | Focal length of the eye-glass | 1497 | | Distance of the eye behind the eye-glass | 479 | | Diameter of the eye-hole | 0190 | | Distance of the object from the centre of the convex speculum | 0626 | | Length of the concave speculum | 1549 | | Arch of the convex speculum | 45049 | | Distance of the stop s from the object | 04545 | | Diameter of the stop s | 0038 | | Diameter of the hole in the concave speculum | 0143 | | Diameter of the hole in the convex speculum | 0049 | | Magnifying power, the focal length, &c., of the eye being 8 inches | 300 times |

The dimensions of the instrument in our possession is very different:

| Dimension | Value | |------------------------------------------------|---------| | Diameter of the concave speculum | 217 inches | | Focal length | 217 | | Diameter of the hole in it | 0375 | | Diameter of the convex speculum | 103 | | Diameter of the hole in it | 010 | | Diameter of stop | 013 | | Distance of stop from hole in convex speculum | 067 | | Distance of specula | 380 | | Focal length of doubly-convex eye-glass | 017 |

Sir David Brewster's Reflecting Microscope.

Notwithstanding the excellence of Professor Amici's microscope, we are convinced that it is not the peculiarity in its construction which constitutes it a different instrument from Newton's. This peculiarity is a disadvantage, and we consider the instrument as recommended solely by its possessing an ellipsoidal speculum with a large angle of aperture. The only advantage which can be ascribed to the instrument is a more convenient mode of illumination; but this advantage, whatever be its amount, is purchased at great sacrifices. 1. The whole instrument is an awkward-looking piece of mechanism, with its triangular bar and all its appendages. 2. It cannot be used in the vertical position, which we consider a defect. 3. By the use of the small reflecting speculum, one-half of the whole light is lost. 4. With small concave specula, such as those 3/8ths of an inch in diameter, opaque objects cannot be illuminated.

The construction which has been proposed by Sir David Brewster to remedy most of these defects is shown in the annexed figure, where ABC is the body of the instrument, which screws at its lower end C into the horizontal projecting arm DE of the stand, either of the achromatic microscope or the single microscope; so that we get rid of all trouble about the objects placed at mn, and their mode of illumination, as everything concerning them is the same as in other microscopes. This is certainly a great advantage; for neither naturalists nor amateurs are disposed to purchase and use two sets of the extensive apparatus necessary for holding, moving, and illuminating microscopic objects. At the lower end C of the body, where the objective glasses of the common compound microscope and the achromatic object-lenses are placed, is a small tube abed, at the lower end of which is fixed the concave speculum cd, perforated with a very small hole at its centre, and with its concave surface upwards. Above it is the plane speculum s, fixed by a slender arm to the side bd of the small tube, and having its diameter a little greater than the perforation in the speculum cd. This little tube abed screws into the arm DE, as if it were a microscopic doublet or single lens; and the body ABC may either screw upon the outside of this tube, or, what is better, upon a stronger piece of tube forming part of the arm DE. A concave illuminating reflector h, for opaque objects, may screw on the back of the speculum cd, or the speculum itself may be made thick, and ground and polished on both sides, so that while one side illuminates the objects, the other magnifies them.

It is obvious that rays proceeding from an object at mn will be reflected from the plane speculum s, upon the concave speculum cd, exactly as if the objects were placed at r, as far above s as mn is below it, and an image of it would be formed in the other focus of the ellipsoid, r being the one focus, if the rays were not intercepted by the eye-piece AB, by which the image is farther magnified. By this mode of construction, the whole of the reflecting microscope, in place of having a separate stand and separate apparatus costing a large sum of money, is comprehended in the little tube abed, and may be considered as a reflecting object-speculum, forming part of a general microscope, furnished with single lenses, doublets, and compound achromatics.

By the means now described are removed all the defects which we enumerated as belonging to Amici's combination, except the third, which is one of such importance that it is of consequence to consider how far it is capable of being remedied. Sir David Brewster has proposed to get rid of this loss of light by placing the object mn, as in Amici's instrument, outside of the tube, but inclined to its axis, and refracting its rays upon the speculum cd, by means of an achromatic prism e, in a manner analogous to his method of producing a similar effect in the Newtonian telescope. The faces of this prism are equally inclined to the axis of the microscope and the axis of the pencil issuing from the point of the object under examination. As the prisms of plate and flint glass which compose e are cemented by a substance of nearly the same refractive power, there will be no farther loss of light than what is reflected at the two surfaces. A socket may be placed at D for holding an illuminating lens, or any other apparatus for opaque objects. But in order to avoid the incumbrance and expense of separate stands and apparatus for this as well as Amici's form of the instrument, we would propose that a strong piece of tube should be inserted in the opening, above mn, to screw into the upper side of the projecting arm, as shown in fig. 78; or a solid screw attached to the upper side of the tube, a little to the right hand of C, and above the opening, might screw into the lower end of the projecting arm DE. In these cases the object at mn will be placed on the ordinary stage, and illuminated in the common manner; but it will

---

1 Treatise on Optics, edit. 1853, p. 494. (See also article Optics.) be necessary to have a counterpoise at D, to balance the weight of the body ABC.

Those who are acquainted with the principle of the Cassegrainian telescope, and of Dr Smith's compound microscope, will readily see that the reflecting microscope, with the perforated speculum, may be converted into a more compound reflector, analogous to Dr Smith's, by making the little speculum s (fig. 78) convex, the figures of d and s being made hyperboloids.

CHAPTER IV.

ON POLARIZING MICROSCOPES.

The use of polarizing microscopes is to observe and exhibit structures and phenomena which are invisible with the common microscope.

These microscopes were first used by Sir David Brewster, upwards of forty years ago, in his experiments on the structure of Apophyllite, Amethyst, and Analcime, and other mineral bodies; and also in his examination of various animal and vegetable organizations. In employing the single microscope for these purposes, he cemented plates of agate and tourmaline with Canada balsam to the plane side of a plano-convex lens, and thus analyzed the polarized light, by means of which the peculiar structure was rendered visible. In other cases he preferred for the analyzer an achromatized prism of calcareous spar, in which one of the images only was visible, or one in which he had extinguished one of the images by a particular process, which he has described.

When considerable magnifying power was necessary, or when the structure was to be drawn by an artist, he used the compound microscope, in which the light was polarized and analyzed by various means, accommodated to the nature of the structure to be examined.

Single Polarizing Microscope.

The simplest and most useful polarizing microscope is a hand one, such as AB, containing a convex lens A. It is to be held in the right hand, as in fig. 80, and a plate of light reddish-brown tourmaline (or of the artificial tourmalines, viz., plates of the sulphate of iodoquinine, discovered by Dr Herapath), fixed above the lens, either temporarily by a little bit of soft wax, or cemented to it by Canada balsam. The last method has the advantage of preventing the loss of light by reflection from the first surface of the tourmaline, and removing any imperfection of polish that it may have. It would be advisable, indeed, to construct the microscope with two plano-convex lenses, and to place the tourmaline between them, joining it to both by Canada balsam, so that there would be no loss of light or imperfection of vision produced by the surfaces of the tourmaline.

The position of the plate abed should be such, that when it is held as in the figure, the polarized light, which is to illuminate the object, should be unable to pass through it. This polarized light may be obtained either from light reflected at an angle of 56° from a plate of black glass, or from a bundle of plates of crown or flint glass, or mica (properly placed), or by transmission through a bundle of such plates, or from one of the images of a rhomb of calcareous spar.

When this light is obtained, the observer holds the microscope AB in his right hand, and examines through it the object in his left hand, turning AB slightly round, so as to bring it into the position in which it refuses to transmit any of the polarized light which passes through the object, and towards which, of course, the observer's eye is directed. When this is done, the peculiar structure of the object will depolarize or alter the polarization of part of the incident light; and this light, being no longer polarized, will pass through the plate of tourmaline to the eye, and exhibit on a dark ground, and in luminous and often beautifully coloured lines, the structure of the body.

If the body is transparent, and not flat, it may be advantageously placed in a little glass trough containing water or oil, or a fluid of the same refracting power as the body, so that the polarized light may be made to pass through it in all directions, and exhibit its entire structure.

When the shape and surface of the body present no difficulties, the best method is to stick it by a transparent cement, or simply to place it upon a plate of tourmaline held in the left hand. The observer thus carries the polarizer and the object in his left hand, and in his right the magnifier and the analyzer.

When a second plate of tourmaline is not at hand, the object may be placed upon a rhomb of calcareous spar, above one of the images which that rhomb forms of a circular aperture on its lower or farther side, the light of the other image being stopped out by a piece of water.

When a small lens is needed, and strong light can be commanded, the magnifier and the analyzer may be united in one by making the magnifying lens of tourmaline.

When microscopic doublets or triplets are used, the plate of tourmaline may be placed between two of the lenses, and cemented to the plane side of any of the plano-convex lenses.

Compound Polarizing Microscope.

The simplest form of the compound polarizing microscope is to make the eye-glass into an analyzer, in any of the ways described for a single lens, the proper position of the plate of tourmaline being readily found by the motion of unscrewing the eye-glass. The polarizer is also a plate of tourmaline, laid on the slider-holder, and having the object laid upon its upper surface. If the polarizer is laid down in any accidental position, the proper position of the analyzer will be found by a slight unscrewing of the eye-glass. The best method is to place the small polarizing piece of tourmaline (which need not be larger than an object which fills the field of the microscope) between two pieces of glass, with Canada balsam interspersed. In this way a compound microscope may be converted into a polarizing one, fit for any researches, at the expense of a few shillings.

When tourmaline cannot be obtained, the light may be polarized by one or more plates of glass, placed on the illuminating mirror so that their surface may be inclined 34° to the axis of the microscope, and the analyzer may be a chip of black, blue, or any other kind of glass, having the reflection from its second surface removed by grinding, or by a few drops of black wax. If this chip is placed on the brass ring above the eye-glass so as to turn with that ring, and so that its surface is inclined 34° to the axis of the microscope, the observer, by looking into a little reflector, will see the object under examination when the plane of this analyzing plate is at right angles to the plane of the polarizing plate.

When the compound microscope is fitted up with Nicol's prisms, and for the express purpose of exhibiting structures by polarized light—which we believe was first done by Henry Fox Talbot, Esq.—one of these prisms is fixed between the illuminating mirror and the slider-holder, to polarize the light, and another similar prism is placed above the eye-glass to analyze it. The last prism, however, is very inconvenient, as it contracts unpleasantly the field of view; and it is therefore necessary to substitute for it a plate of tourmaline, as already described; or, what is much better, as Sir David Brewster suggested, is to screw the analyzer into the lower end of the body of the microscope, immediately behind the object-glass.

The expense of constructing a Nicol's prism, the difficulty of making the one next the eye perfectly colourless, and the risk of a change taking place in the cement which unites the two parts of it, renders it desirable to have a simple, cheap, and durable substitute for it. The polarizer which has been employed by Sir David Brewster in his experiments on elliptical polarization, and on the action of crystallized surfaces upon light, where tourmaline could not be used owing to its colour, was a single rhomb of calcareous spar, with its natural surfaces, having thin plates of colourless glass cemented to them by Canada balsam, which removes any imperfection of surface, and at the same time protects the surfaces from any accidental injury, or from the deterioration of the polish, which arises from frequently cleaning them. This rhomb ABCD had a circular aperture a, placed upon its lower surface, and of such a diameter that it just separated the two images b, c, seen from above. This rhomb may be placed either beneath the slider-holder or upon it, and by sticking a piece of wafer upon any one of the images b, c, and leaving the other exposed, and placed exactly beneath the aperture of the object-glass, we have the most perfect polarizer that can be constructed. The object to be examined may, if necessary, be laid above the circle b.

By this construction of the polarizer we obtain another advantage; we may so adjust the size and distance of the pencils b, c that both of them may be included in the field of view, and by placing one of the objects to be examined above b, and another of the same above c, we may observe them at the same instant under their opposite colours, if the depolarized light is coloured, which it generally is.

These rhombs may be made even out of rhombs crossed with veins, which multiply the images, because the multiplied images are at too great a distance from the principal ones to be visible. This is a peculiar advantage, as it is often very difficult to get good pieces of spar free from this composite structure.

This method of constructing a polarizing rhomb enables us to take advantage of the two lateral images, which accompany the two principal images in crystals crossed by one vein. These lateral images, m, n, are distant from one another, and from the principal images b, c; and as each of them consists of light wholly polarized in one plane, we have only to bring one of them under the aperture of the object-glass to have an admirable polarizer, without being at the trouble of stopping out any of the other pencils.

The images m, n are much less bright than the principal ones b, c; but this is really of no consequence, as we can obtain any degree of light we choose in the microscope, either by the condensation of artificial, or the use of solar light.

When the vein by which these lateral images are formed is above a certain thickness, their light is white; but they are most frequently coloured; and the observer who understands the cause of these colours may make this coloured pencil of great service in microscopical observations. If he uses a rhomb which gives to m a green of the second order, it will contain none of the extreme violet and blue rays, and none of the extreme red; so that it affords a more homogeneous pencil than if it were white light, and thus improves the performance of a microscope that is not achromatic.

He may in like manner use tints which give the red extremity or the blue extremity of the spectrum, or, even when the tint is divisible by the prism into periodical bands, he may absorb the least luminous of these bands, and create a homogeneous pencil of polarized light of inestimable value, in particular researches and with particular microscopes.

But, independent of these advantages, the method of using a lateral pencil m has the great advantage of not requiring much thickness in the rhomb. A Nicol's prism, and a rhomb in which the two principal images b, c are used, must be about an inch thick in order to be efficacious; but the distances mn or mb are the same at all thicknesses, so that we can use rhombs for this purpose which are quite useless for any other.

It is scarcely necessary to add, that similar rhombs in which either the principal images b, c, or the lateral ones m, n, are used, may also be employed for the analyzer. For this purpose a thin plate, in which m or n is white, is peculiarly applicable, as it enables us to see at once the whole field of the microscope.

CHAPTER V.

ON SOLAR AND OXYHYDROGEN MICROSCOPES.

The solar microscope is a well-known popular instrument, for exhibiting on a white screen, in a dark chamber, magnified images of minute objects, illuminated by the condensed light of the sun. As the sun cannot often be commanded in our climate, this instrument may be considered as having fallen into disuse; but the discovery of the lime-ball light by Mr Drummond amply supplies the place of the great luminary, in so far as the microscope is concerned. The instrument has accordingly been revived under the name of the oxyhydrogen microscope, and is now a favourite public exhibition.

The solar microscope was proposed by Dr Lieberkühn in 1738; and early in 1739, when he paid a visit to London, he exhibited an instrument of his own construction to several members of the Royal Society, and to Mr Cuff, Mr Adams, and other London opticians.

This microscope is nothing more than a convex lens, in front of which, a little farther from it than its principal focus, is placed a microscopic object, the rays of the sun being reflected in a horizontal line, and condensed by a lens. This will be understood from figure 83, where CD is the convex lens, E the object placed before it, and AB the illuminating condenser. An enlarged image of E will be formed on the right hand of CD, upon a wall or

---

1 This ingenious prism, consisting of two pieces of calcareous spar cemented together so as to transmit only one image, derives its name from its inventor, the late William Nicol, Esq., of Edinburgh, and is of great use in all experiments on the polarization of light, particularly where the colour of tourmaline would interfere with the phenomena to be observed.

2 The most interesting objects for the polarizing microscope are minute crystallizations of all kinds, but particularly composite minerals, such as apophyllite, amethyst, analcime, and a large class of crystals to which the name of "circular" has been given, and an account of which will be found in a paper in the Edinburgh Transactions, vol. xx., p. 60, 1853.

---

We have recently (May 1857) seen these methods of using rhombs in place of Nicol's prisms successfully adopted by Professor Amelot in his achromatic microscopes, and we are satisfied that those who have once employed them, either for the purposes of research or amusement, will never use any other pieces of apparatus. screen, and the size of the enlarged image will be to that of the object as the distance of CD from the screen or wall is to CE, the distance of the object from the lens. Dr

Fig. 83.

Lieberkühn's solar microscope had no mirror for reflecting the sun's rays into the tube, so that it could only be used for a few hours, when the tube could be conveniently pointed to the sun. The improvement of adding a mirror was made by Mr Cuff, who constructed the instrument in a very superior manner. Dr Lieberkühn subsequently fitted up the solar microscope to show opaque objects; but the method which he employed is not known. Since the time of Mr Cuff the solar microscope has undergone many improvements. Mr Benjamin Martin added greatly to the value of this instrument by fitting it up both for opaque and transparent objects, in the manner shown in figs. 84 and 85. In fig. 84 it is shown as fitted up for opaque objects. The body ABCDEF has the part ABCD of a conical, and the part CDEF of a tubular form. A large convex lens, corresponding with AB in fig. 83, is placed at AB, at the end of the conical tube ABCD, which screws into the square plate QR, which is fastened to a window-shutter opposite a hole of at least the size of the lens AB, by means of the screws e, d. Upon the square plate QR there is a movable circular plate abc. To this circular plate is attached the silvered glass mirror NOP, placed in a brass frame, which moves round a joint PP, and which may be placed in any position with regard to the sun, so as to reflect his rays into the tube ABCD by means of rackwork and pinions at Q and R. The pinion Q moves the circular plate abc (to which the mirror NOP is fixed) in a plane perpendicular to the horizon, while the nut R gives it a motion in an opposite plane. The light introduced by this mirror falls upon the lens AB, which throws it in a condensed state upon any object in the tube. But before it reaches the opaque object it is received by a mirror M, placed in the box HILX, which reflects the condensed light back upon the face of the object E (fig. 83) next to the lens CD. This mirror is adjusted to a proper angle by the screw S.

Above the body ABEF is seen the part VK, which carries the sliders or objects, and the object-glass or lens CD (fig. 83). The tube K slides within the tube V, and V again slides into the box HILX. These tubes carry each a magnifying lens. The inner tube K is sometimes taken out of the other V, seen within the box, and used alone. The sliders and objects are introduced into a slit or opening at H. The brass plate to the left of H is fixed to a tube h, by means of a spiral wire within the tube, which presses the plate against the side of the box HILX, so that the sliders, when placed in the opening, are pressed against the side of the box.

In using this microscope, the sun's rays are first made to pass along the tube ABCD by the nuts Q and R. The box for opaque objects, HILX, is then slid by its tube G into the tube EF. The slider containing the object, having its face to be examined turned to the right hand, is then pushed into the opening at H, till the object is in the centre of the tubes V, K. The condensed light falling upon the mirror M is then thrown back on the face of the object of the slider, and the door ki shut. Upon a white paper screen or cloth, from 4 to 8 feet square, and placed at the distance of from 6 to 10 feet from the window, the observer, in the room made thoroughly dark, will see on the screen a magnified representation of the object, which may be rendered distinct at different distances of the screen, by pulling out or pushing in the tubes V, K containing the convex lenses. As the sun is constantly moving, its rays must be kept in the axis of the tubes by now and then turning the nuts Q and R.

When the microscope is to be used for transparent objects, the box HILX, with its tube G and other appendages, is removed, and the apparatus shown in fig. 85 substituted for it. This is done by sliding the tube Y of fig. 85 into the tube EF of fig. 84. A slider containing the magnifying lens is then slipped through the opening at n, and a second condenser may or may not be inserted in the opening at h. The slider with the object is then placed in the opening m, and when its magnified picture falls upon the screen, it is adjusted to distinctness by turning the milled nut O.

The picture formed by a solar microscope being in Dr Robison's opinion "generally so indistinct that it is fit only for amusing ladies," he proposed to use as an object-glass the achromatic eye-piece of four lenses, constructed by Mr Ramsden for telescopes. Having made the experiment, he found the image "perfectly sharp," and recommended this application "to the artists, as a valuable article of their trade."

A much simpler method, however, of correcting the defects of the microscope, is to use compound achromatic lenses, which were first suggested by Mr Benjamin Martin.

Another mode of improving the instrument was proposed in 1812 by Sir David Brewster, who has described a new solar microscope which can be rendered achromatic. The method of doing this is shown in the diagram (fig. 83), where AB is the condensing lens, and CD the object-glass, cemented firmly into one end of a tube mCDn, which has a tubular opening at E, while the other end of the tube has a circular piece of parallel glass cemented upon it. The tube mCDn is then filled with water, or any other fluid, and the object, when placed upon a slider or held in a pair of forceps, is introduced at the opening E into the fluid. The mechanism for producing these effects is easily conceived. By the instrument thus constructed, imperfectly opaque and corrugated objects, rendered transparent, and extended by the fluid medium, may be examined in this microscope, though incapable of being used in any other. Objects may be even dissected in the aqueous tube. Nay, objects preserved in spirits might be exhibited by immersing the bottle, if it is small, in the trough or tube mCDn.

But the most important purpose effected by this form of the instrument is, that it can be rendered perfectly achromatic by using a fluid of higher dispersive power than the glass lens CD, and making the interior curvature of the side CD, which touches the fluid, of that degree of convexity which will convert the fluid into a concave lens capable of correcting the colour of CD. The lens CD may be made most advantageously of fluor spar, which, from its low dispersive power, might form an achromatic combination with water.

Although, in so far as we know, metallic specula have never been regularly fitted up as a reflecting solar microscope for use, yet every person familiar with, and in the habit of using specula and lenses, must have made the experiment of forming magnified images both in solar and artificial light, with small concave specula. The perfection of these images cannot be doubted; and it has often appeared to us surprising that the optician did not avail himself of such a combination for a solar microscope. Neither the Newtonian nor the Amici form of the instrument offers facilities for this purpose. Sir David Brewster has therefore proposed to employ his form of the reflecting microscope for a solar and oxyhydrogen instrument. Its facilities for this purpose are very great, and there can be little doubt that it will be practically successful, and will be as superior to other solar microscopes as the best reflecting compound microscope is to the ordinary compound microscopes. Dr Goring made an experiment with the Amici microscope; but he obviously considers it as not likely to succeed, remarking, that "after all that could be done, a refractor would be sure to beat it hollow; therefore," says he, "I shall take my leave of the subject, as I cannot conscientiously recommend such an instrument." It is no wonder that this experiment failed, because Dr Goring seems to have used the whole of the Amici microscope, eye-glasses and all, as the magnifier in the solar microscope, and therefore it could not be considered as a reflecting solar microscope, being in fact as much a refracting one. The construction to which we have above referred is shown in the annexed figure, where AB is the illuminating lens, throwing the condensed rays of the sun upon a transparent object mn. The rays from this object falling upon the small speculum e, are reflected to the deep concave speculum cd, so placed that the image is formed at MN on a screen at some distance behind it, distinct vision being obtained either by moving the object or the speculum.

For opaque objects this form of the instrument is peculiarly adapted. The parallel rays of the sun, falling upon the deep speculum cd, are condensed by it and thrown on the inner face of the object mn, of which a magnified image is formed, as before, at MN. A greater condensation of light may be obtained by using the lens AB, so that the speculum cd shall receive its convergent beam before the rays reach their focus and complete their convergency.

In this construction we have the disadvantage of two reflections, belonging also to the Amici form; but this may be considered as compensated by the image being without the tube, and more under our command. Though this is true in the compound microscope, yet the advantage of having the object outside the tube is of less consequence in a solar microscope. To avoid therefore two reflections, and two mirrors with their relative adjustments, Sir David Brewster has proposed to construct the reflecting solar microscope in the manner shown in the annexed figure, where cd is the perforated concave speculum, saw the object in one of its foci, and MN the magnified image in its other focus. The object mn, placed on a slider passing through an opening in front of the speculum, is illuminated as an opaque object by the lens AB, whose refracted rays are farther condensed by a lens placed in the aperture of the speculum. This form of the solar microscope is therefore singularly adapted for opaque objects; and as the whole of the effect of the instrument is produced by a single reflection from a single surface, it is the simplest optical instrument in existence. In order to throw light upon mn as a transparent object, the rays must pass through it in an opposite direction from the side MN, and this may be done by the very same method given by Mr Potter, and represented in fig. 71.

The simplicity and practical value of this instrument will be immediately recognised by comparing it with the complex opaque box, which in all solar microscopes is a necessary appendage for opaque objects. See fig. 84.

Dr Goring's Solar Camera Microscope.

Dr Goring has described in the Micrographia a very complete solar microscope, which has the property of exhibiting the image on a horizontal curved surface, placed in a darkened camera, at which two or more persons can look at the same time. It is, to a certain extent, a new instrument, but can also be used like the common solar microscope in a darkened room.

This instrument, with all its parts, is shown in figs. 88, 89, 90, and 91; fig. 88 being a geometrical elevation of the instrument, one-tenth of the real size, the various parts being represented as if formed of transparent matter. A strong framework A of wood rests upon four legs, having a large hole in it, into which the instrument is fixed with two

---

1 See Treatise on New Philosophical Instruments, p. 401, for an account of the advantages of examining objects immersed in fluids. 2 Dr Goring states that a friend of his had constructed a solar microscope with metals on the Amici principle, and without a body or eye-glass, which exhibited a variety of test objects in a highly satisfactory manner.

---

Dr Goring calls this instrument a "solar microscope," while he gives the name of "solar microscope" to the same instrument when used in a dark room in the common way. The introduction of the image into a camera becomes thus the reason for changing a microscope into an eyepiece. The word eyepiece, however appropriate it may be as a companion to the word telescope, is quite inapplicable to any kind of solar microscope. screws FF. The frame is large enough to protect the observer from the solar rays. A long plane mirror B is fixed to an arm C, which moves round a pin fixed to the side of the mirror frame, and also round a joint attached to a strong round wire E, which slides backwards and forwards in the tube D, having a spring within, and a pinching nut to fix it in its place. The inclination of the mirror is varied by pulling out or pushing in the wire E; and another motion of the mirror is produced by the action of the milled head G on a rack and pinion. A common illuminating lens, five inches in diameter and one foot in focal length, is placed at H. Dr Goring recommends an achromatic lens (which would be a very expensive appendage), though he says that he has never used one. The main body of the microscope is conical, having a bayonet catch at L to receive the rest of the instrument, viz., the tube carrying the stage and rack-work. This tube 11 moves within the conical one by means of the milled head M and rack and pinion N. The end of this tube is closed, and an ordinary slider-holder O is fixed to it. On the inner side of the stage, near N, is fixed a condensing lens, about one and a half inch in diameter and two inches in focal length, which, by means of a sliding wire passed through a hole in the stage, can be moved from one side of the tube to the other, and also made to approach or recede from the stage. A second tube PPP (fig. 90), slit open at the sides, is screwed into the tube in which the stage moves; and into this tube the optical part is made to slide, the object-glass being placed at K. Dr Goring here remarks that "the focus may of course be roughly adjusted, by sliding the body backwards and forwards in its containing tube, before it is attached to the camera, fig. 89; but when this has been done, it must of course remain immovable. I look upon it," he continues, "as a principle in the solar microscope, that the magnifier or object-glass should not be moved, but always remain at a fixed distance from the illuminator." Perhaps we do not distinctly understand the import of this passage; but we apprehend that the magnifier or object-glass may be, nay, must be, moved in any way that is necessary to produce distinct vision upon the screen, whatever be its distance; and that the essential condition is, that the distance of the illuminator and the object shall be invariable, the object being, if possible, accurately situated in the focus, unless where a slight deviation is necessary to prevent its destruction by the concentrated heat of the solar rays.

The end of the tube q is now pushed into another piece of tube at R, fig. 89, which communicates with a conical tube of brass, "having a rectangular prism, with its reflecting side silvered," or a plane metal adjusted at its head S, so as to throw down the image to the bottom of the box or camera, where it is to be received on paper (at T), or on a surface of plaster of Paris duly curved to suit its shape. The camera WWXX is constructed with windows V, V, to permit two persons to view the picture on the table T. Two pieces of wood W, W, carved out to fill the slope of the upper part of the face, are placed as in the figure (one of them is shown in the annexed figure). Dr Goring adds that "he has found it necessary to exclude the breath from entering the camera, as it dims the eye-glass of the enigroscope, and thus spoils the image;" but he does not mention whether this is the object of the pieces of carved wood, or whether they are used to keep extraneous light.

---

1 See Edinburgh Journal of Science, No. 9, new series, p. 85; and our chapter on the Illumination of Microscopic Objects. from the eye, which, in so far as the figure indicates, does not appear to be the case.

The sides U, U of the camera may be removed at pleasure, to allow the observer to draw the picture on the table, the light being excluded by some black drapery, while the hand passes through a suitable opening in it. Dr Gorring recommends that the whole of the interior of the conical brass tube and camera should be well blacked, or lined with black silk velvet.

In applying this instrument to opaque objects, the opaque box, shown in fig. 90, is applied to the conical tube in fig. 76 by means of the bayonet catch at L. A plane mirror R, adjusted by the screw S, throws the light of the illuminator to the object O placed in the conjugate focus of the eye-glass K, by means of the milled nut M and screw T, which causes the stage and the object to approach to or recede from the lens K. The stage is formed by a piece of cork covered with black velvet. PP is the tube into which the body q of the microscope is inserted, as in fig. 76.

This instrument may be converted into a common solar microscope by unscrewing and removing the tube PP, and placing a simple object-glass in an appropriate mounting at M. The whole apparatus is then removed from the frame A, and screwed to a window-shutter in the usual way.

On the Oxyhydrogen Microscope.

The great popularity of the public exhibitions made with this instrument has turned the attention of opticians and amateurs to its improvement. Mr Pritchard has written a long and interesting chapter of nearly fifty pages on the subject of solar and oxyhydrogen gas microscopes, in the Micrographia, already referred to, and has given a most popular and minute account of all the details of the instrument. These details, to which we must refer our readers, do not belong to an article like the present; and we shall content ourselves with explaining what an oxyhydrogen microscope is, and how the optical apparatus of a solar microscope may be readily converted into that of an oxyhydrogen one, and vice versa.

An oxyhydrogen gas microscope differs from a solar one chiefly in this, that a brilliant light obtained by igniting a ball of lime the size of a pea (hence called the pea or lime light, or more appropriately the Drummond light, from its inventor, the late Mr Drummond) with oxyhydrogen gas, is substituted in place of the solar rays. This enables us to enjoy the amusement of the solar microscope apparatus in all weathers and at all hours of the day.

As the lime-ball light, however, is at our elbow, it sends forth diverging rays; whereas the rays of the sun are parallel. A very beautiful principle, already referred to in our article Micrometer, enables us to give the simplest construction for this purpose. Let AB (fig. 92) be the illuminating lens of the common solar microscope, throwing the parallel rays ef of the sun upon the object mn, and let the whole instrument be in perfect adjustment; then, without moving or changing any part of it, we may convert it into an oxyhydrogen microscope, where the light diverges from the lime-ball L, simply by placing in front of AB another lens CD, whose focal length is equal to the distance of the lime-ball light L from the lens AB. The oxyhydrogen microscope will then have its objects at mn illuminated in precisely the same way as they were by the sun's rays. The two lenses CD, AB, should be in contact, the space in the figure being left only to show the parallel rays ef. Now, as L is the focus of the lens CD, the converging rays ef will be parallel, and consequently will be refracted by AB exactly as if they had been the rays of the sun.

If the instrument had been made originally as an oxyhydrogen microscope, with a large and deep lens at AB, which would be required to refract rays diverging from L to mn, then we might convert the instrument into a solar microscope, by simply placing a concave lens in front of AB, whose focal distance is equal to the distance of L from AB. This concave lens will give such a divergency to the parallel rays of the sun that they will have their focus at mn.

Our readers will find the most ample details respecting the gas apparatus, and the method of managing and using the instrument, in Mr Pritchard's Micrographia.

Notwithstanding the precautions to prevent an explosion of the oxygen and hydrogen employed in this apparatus, we would recommend to Mr Pritchard, and those who may construct such instruments, to use a common oil or gas lamp supplied with oxygen gas, such as Sir David Brewster some years ago recommended as a safe substitute for the lime-ball light, when it was proposed to use the latter for lighthouses. This oxygen lamp, equally safe and brilliant, has been tried with success at the Trinity House, and will, we are confident, be soon in universal use, not only in lighthouses, but wherever strong lights are required.

On the Apparatus for Dissolving Views.

By employing two microscopes similar to the oxyhydrogen microscope, but of a larger size, the interesting optical apparatus for illusion of dissolving views is produced. In order to ad-dissolving views, objects four or five inches square, condensing lenses 8 views, or 10 inches in diameter are necessary. The views to be employed are painted on glass with much more care and minuteness than those employed in the magic lantern. The following is the method of causing one picture to dissolve and pass gradually into another. The two microscopes are placed near each other, and at the distance of 20 or 30 feet from a white screen for receiving the images. The position of the microscopes is then adjusted so that each throws the image of the picture placed in it on the same part of the screen. When this is obtained the microscopes are fixed, and in front of them an apparatus like that in figure 93, where A and B are the front openings of the two microscopes, and CD and EF two dark screens moveable upon the centres m, n, and capable

---

1 In using this and all other optical instruments where perfect vision is either agreeable or essential, we would recommend the use of the Greenland snow spectacles, cut, to suit the individual, from a plaster of Paris cast of the eyes, nose, and brow.

2 Mr Potter found black velvet to be superior to any other blacking for the interior of his reflecting microscope, and we have used it successfully in the solar telescope in observing the extreme red rays of the spectrum. (Edin. Jour. of Science, No. 11, p. 62, new series.)

3 Mr Drummond heated the lime-ball with three flames of a spirit-of-wine lamp. It may be done even with one flame urged upon the ball by a blowpipe of oxygen gas. of moving up and down on the vertical rod GH. These screens are fixed in front of the openings A, B, and close to them. In the position of the dark screens, shown in the figure, the view in the microscope A will alone be seen on the white screen; but if we push up the joint m the upper edge Ew of the screen EF will obstruct part of the light which illuminates the view, and the view will become fainter and begin to dissolve. At the same time the under edge D of the screen CD will rise also, and allow the image of the view in the microscope B to appear very faintly, and mixed up with the image of the other view on A. As EF rises, and causes the view in A to dissolve, CD will rise, and cause the view from B to be brighter and more distinct. By continuing the upward motion of m, the view from A will gradually dissolve till it disappears altogether, while the view from B will gradually become more and more distinct till it obliterate the view from A. By causing m to descend the reverse will take place, the view from B now dissolving till it is obliterated by that from A.

Another very ingenious method of exhibiting dissolving views is to include two views in the same piece of paper, so that when you see the piece of paper by reflected light you see distinctly one of the views like an ordinary painting or engraving; but when you look through the paper, you see the other view by transmitted light. This piece of paper is placed at the wide end of a conical tube, at the other end of which is a convex lens to magnify it. On the upper side of the wide end of the tube, a lid like that in the stereoscope opens and shuts, so that when open it throws light upon the face of the piece of paper containing the view to be seen by reflected light, and, when shut, the eye sees the picture to be seen by transmitted light. On the lower side of the wide end of the tube is another lid which opens and shuts. When shut it prevents the transmission of light, which would interfere with the view of the picture seen by reflected light. Now, the two lids are so connected by a wire that as one opens the other shuts, the one being completely open when the other is completely shut. By this means the picture seen by reflected light gradually dissolves till it is obliterated by a transmitted picture, and vice versa. The pictures for this apparatus are circular, and are very nicely executed by Parisian artists. A larger apparatus, which contains rectangular pictures about 8 inches by 6, has been constructed under the name of the Polyorama Pantoptique. A variety of natural effects, such as the motions of ships, &c., rainbows, fire, &c., may be produced by two, three, or more lanthorns. A trioptic lanthorn, in which one light is made to produce the effect of two or three lanthorns, has been described by Mr Beechey. Microscopes are inserted in apertures at proper angles in the sides of the lanthorn, and three-sided prisms are used to reflect the rays to the screen. Photography now supplies us with beautiful drawings of all classes of objects for the instruments described in this chapter.

CHAPTER VI. ON THE ILLUMINATION OF MICROSCOPIC OBJECTS.

The methods of illuminating microscopic objects that have been long in use have been described in the preceding chapters. They consist in throwing light upon the object, either by means of a mirror or a lens, or both combined; but the nature of the light employed, the magnitude of the pencil, its condition with regard to parallelism, divergency, or convergency, and the diameter of the pencil employed, or the direction in which it falls upon the object, people have never been discussed as matters of science, although objects, upon these the performance of the finest instrument essentially depends.

In so far as we know, the most important of these topics was pressed upon the notice of the scientific reader by Sir David Brewster, in the year 1820; and in order that the progress of improvement in this essential branch of the art of making discoveries with the microscope may be understood, we shall quote his observations on the subject:

"The art of illuminating microscopic objects is not of less importance than that of preparing them for observation. No general rules can be given for adjusting the intensity of the illumination to the nature and character of the object to be examined; and it is only by a little practice that this art can be acquired. In general, however, it will be found that very transparent objects require a less degree of light than those that are less so; and that objects which reflect white light, or which throw it off from a number of lucid points, require a less degree of illumination than those whose surfaces have a feeble reflective force.

The following rules may be laid down respecting the Rules for illumination of microscopic objects, and the method of viewing them:

1. The eye should be protected from all extraneous light, and should not receive any of the light which proceeds from the illuminating source, excepting that portion of it which is transmitted through or reflected from the object.

2. Delicate microscopical observations should not be made when the fluid which lubricates the cornea of the observer's eye happens to be in a viscid state, which is frequently the case.

3. The figure of the cornea will be least injured by the lubricating fluid, either by collecting over any part of the cornea, or moving over it, when the observer is lying on his back, or standing vertically. When he is looking downwards, as into the compound vertical microscope, the fluid has a tendency to flow towards the pupil, and injure the distinctness of the vision.

4. If the microscopic object is longitudinal, like a fine hair, or consists of longitudinal stripes, the direction of the lines or stripes should be towards the observer's body, in order that their form may be least injured by the descent of the lubricating fluid over the cornea.

5. The field of view should be contracted, so as to exclude every part of the object excepting that which is under immediate examination.

6. The light which is employed for the purpose of illuminating the object should have a small diameter. In the daytime it should be a single hole in the window-shutter of a darkened room, and at night it should be an aperture placed before an Argand lamp.

7. In all cases, and particularly when very high powers are requisite, the natural diameter of the light employed should be diminished, and its intensity increased by optical contrivances.

8. When a strong light can be obtained, and indeed in almost every case, homogeneous light should be thrown upon the object. This may be done either by decomposing the light with a prism, or by transmitting it through a coloured glass, which has the property of admitting only homogeneous rays."

* See Brande's Journal, vol. ii., p. 127. In the same article Sir David Brewster has described "a new method of illuminating objects in the solar and the lucernal microscopes." "The great defects," says he, "which still attach to the solar and lucernal microscopes, arise from the imperfect method of illuminating the objects. The method suggested by Epinus, and employed almost universally by opticians, of reflecting the light concentrated by a lens upon the objects, by means of a plane mirror, is good enough as far as it goes; but in consequence of the light arriving from one direction only, the surface of the illuminated object is covered with deep shadows, and the intensity of illumination is by no means sufficient when the power of the instrument is considerable. We propose, therefore, that in the solar microscope the sun's light should be reflected by a very large mirror through four apertures, A, B, C, D (surrounding the tube T), each of which is furnished with an illuminating lens. The four cones, if condensed, are then received before they reach their focus, each by an inclined mirror, which reflects them upon the object; the distance of the lens from the mirror, added to the distance of the mirror from the object, being always less than the focal length of the illuminating lens. In the lucernal microscope it would be desirable to place an Argand lamp opposite each of the apertures A, B, C, D. By these means the light would fall upon the surface of the object in four different directions; a high degree of illumination would be obtained for very dark objects; and by shutting illumination up one or more of the four lenses, or parts of them, we shall be enabled to find the particular direction of the light which is best suited for developing the structure which it is the object of the observer to discover."

Although the focus of the illuminating rays should always fall upon the object, for the reasons already assigned, yet in the preceding method, applied to the solar microscope, a deviation from this rule becomes necessary, for two reasons—1st. Because, if the focus of the illuminating lens fall exactly upon the object it might burn it, or destroy it by corrugation; and, 2dly, In the ordinary illuminating lenses, the diameter of the focal spot, or image of the sun, is not sufficient to cover the whole object, or to give a sufficient luminous field around it. For these reasons it is recommended in the preceding extract to place the object a little way within the focus of the illuminator, that is, between the illuminator and its focus. But if the object is such that it cannot be injured by the solar heat, and if the illuminator is sufficiently large to give a focal spot capable of filling the field of the microscope, then the object should be placed in the solar focus of the illuminator.

After a lapse of nearly ten years, the subject of microscopic illumination was discussed by Dr Wollaston, in his paper on the Microscopic Doublet, published in the Phil. Trans. for 1829. This eminent philosopher, whose ingenuity never failed in executing in the best manner whatever he attempted, was then on his deathbed; and this, among other papers, was published without that complete revision which its author would otherwise have given it.

"The state of my health," says Dr Wollaston, "induces me to commit to writing rather more hastily than I have been accustomed to do, some observations on microscopes; and I trust that, in laying them before the Royal Society, they will meet with that indulgence which has been extended to all my former communications.

This is the earliest suggestion of oblique illumination for developing structures.

"In the illumination of microscopic objects, whatever light is collected and brought to the eye beyond that which is fully commanded by the object-glasses, tends rather to impede than to assist distinct vision.

My endeavour has been, to collect as much of the admitted light as can be done by simple means to a focus in the same plane as the object to be examined. For this purpose I have used with success a plane mirror to direct the light, and a plano-convex lens to collect it; the plane side of the lens being towards the object to be illuminated."

These two principles of illumination, the first of which is the same as the first and fifth of the rules already given, though not so fully developed, and the second of which is founded upon a mistaken principle, have been carried into effect by Dr Wollaston in the following manner—

"T, U, B, E represents a tube about 6 inches long, and of such a diameter as to preclude any reflection of false light from its sides; and the better to insure this, the inside of the tube should be blackened. At the top of the tube, or within it at a small distance from the top, is placed either a plano-convex lens UT, or one properly curved, so as to have the least aberration, about 1/32th of an inch focus, having its plane side next the object to be viewed; and at the bottom is a circular perforation A, of about 1/32th of an inch diameter, for limiting the light reflected from the plane mirror R, and which is to be brought to a focus at a, giving a neat image of the perforation A, at the distance of about 1/32th of an inch from the lens UT, and in the same plane as the object which is to be examined. The length of the tube, and the distance of the convex lens from the perforation, may be somewhat varied. The length here given, 6 inches, being that which it was thought would be most convenient for the height of the eye above the table, the diameter of the image of the perforation A must not, excepting with lower powers than are here meant to be considered, exceed 1/32th of an inch.

The intensity of illumination will depend upon the diameter of the illuminating lens and the proportion of the image to the perforation, and may be regulated according to the wish of the observer.

The lens UT, or the perforation A, should have an adjustment by which the distance between them may be varied, and the image of the perforation be thus brought up to the same plane as the object to be examined.

For the perfect performance of this microscope, it is necessary that the axis of the lenses, and the centre of the perforation A, should be in the same right line. This may be known by the image of the perforation being illuminated throughout its whole extent, and having its whole circumference equally well defined. For illumination at night, a common bull's-eye lantern may be used with great advantage.

Supposing the plano-convex lens to be placed at its proper distance from the stage, the image of the perforation may be readily brought into the same plane with the object, by fixing temporarily a small wire across the perforation with a bit of wax, viewing any object placed upon a piece of glass upon the stage of the microscope, and varying the distance of the perforation from the lens by screwing its tube until the image of the wire is seen distinctly at the same time with the object upon the piece of glass.

In the preceding passages we have extracted every one of Dr Wollaston's observations in reference to his method of illuminating microscopic objects, so that the reader will be enabled thoroughly to understand it.

This method of illumination was highly commended by optical writers. Dr Goring considered it as most effective, and enumerates it among the inventions which founded a new era in the history of the microscope; and he elsewhere states, that "there is no modification of daylight illumination superior to that invented by Dr Wollaston."

The marked difference between the methods of illumination proposed by Dr Wollaston and Sir David Brewster induced the latter to publish, in 1831, a paper, "On the Principle of Illumination of Microscopic Objects." In this paper the mistake committed by Dr Wollaston is clearly pointed out. The rays which Dr Wollaston throws upon the object, in place of being rays actually converged to a focus, as he himself says they ought to be, are rays which diverge from a focus situated between the object and the lens. He makes the focal point of the circular margin of the perforation fall upon the object, without considering that the rays which pass through that perforation do not diverge from it, and therefore cannot be collected in the conjugate focus corresponding to the perforation. In Dr Wollaston's diagram (Phil. Trans., 1829, plate ii., fig. 1), the rays which are incident on the mirror R are actually drawn as parallel rays; and it is quite clear that he meant them to be parallel rays issuing from the bull's-eye lantern which he recommends. But if we suppose that a common flame is used, the error is just of the same nature. It is a distinct image of the flame that should be thrown upon the object; and hence the perforation A should be placed close to the flame,—the source of light and the illuminated object forming the conjugate foci of the lens. After explaining this principle, Sir D. Brewster adds in the same paper:—

"I have no hesitation in saying, that the apparatus for illumination requires to be as perfect as the apparatus for vision; and on this account I would recommend that the illuminating lens should be perfectly free of chromatic and spherical aberration, and that the greatest care be taken to exclude all extraneous light, both from the object and from the eye of the observer."

At the meeting of the British Association at York in 1831 the preceding methods were communicated to Mr Potter, who was then engaged in inquiries with the reflecting microscope, and who had used only the common method of illuminating his objects. The effect which he obtained by it, is thus described:—"I am indebted to Dr Brewster for information on the necessity of having the focus of the illuminating lens for transparent objects to fall exactly upon the object, when great nicety of vision is required. Having adjusted my microscope carefully on this point (see our figure 71, where the object is seen in the focus of the illuminating rays), I saw quite easily what are called the diagonal lines on the scale from the white-cabbage butterfly, which has been proposed as a difficult test-object by Dr Goring; and it is such a one as those who have only seen the stronger longitudinal striæ on scales from the wings of moths and butterflies have little idea of." By the same means Mr Potter's instrument "showed him easily, not only the striæ on the scales of the wing of the small house-moth,

but also the diagonal lines." Mr Potter afterwards applied his microscope, and the new method of illumination, to "a much more difficult object than those just referred to." This object is the broad bluish band first noticed in the web of the spider, the Clubiona atrax. "There can be no doubt," says Mr Potter, "that this blue band consists of lines produced by the spider, and woven into the delicate tissue. To demonstrate these fibres, however, is a work for an expert microscopist provided with a first-rate instrument. So critical a defining power is required, at the same time with a large quantity of light, that I doubt much whether any compound refracting microscope, even the best achromatic, will ever show the construction of this web on a transparent object. When viewed in this manner through good common compound microscopes, the blue band can scarcely be perceived at all with a moderately high power. It is better seen as an opaque object by the light of the sun, and it was on this method that I discovered it, when highly illuminated and highly magnified, to be covered very regularly and closely with white spots. This was sufficient information that it was of a uniform texture; but as there is always in such a light a strong display of irradia-

It is found in the crevices of old walls, and may be recognised by its irregular fleecy-looking web.

Mr Prichard received from Mr Potter a specimen of this web; but though he detected the blue bands, yet, as the specimen was not a recent one, he was unable to perceive "the complete structure of a regularly woven net." (List of 2000 Microscopic Objects, pp. 6, 7.) may be made in any azimuth. A doublet \(AB, CD\), of no aberration, and having a focal length of from half an inch to an inch, is then placed in the tube, with a rack and pinion, or any other adjustment, to bring its focus for parallel rays \(F\), or its conjugate focus for diverging rays, accurately to a point in the plane \(mn\), and upon the object lying in that plane, for examination. A short way below it is placed a metallic speculum (not a silvered glass one), which receives parallel or diverging rays, entering the tube at \(ST\), and reflects them upon the doublet \(ABCD\). This speculum should be of pure virgin silver, notwithstanding its liability to tarnish, and should be wrought with the same care as the plane speculum of a Newtonian telescope; or it might be a rectangular prism of good homogeneous glass, acting by total reflection. This part of the illuminator forms part of the microscope. The other part of the illuminator, which is detached, is no less essential. It consists of the flame \(S\), which should be as bright and small as will give the necessary quantity of light after condensation. As close to it as possible is placed a stand for holding a screen, with different circular apertures, and a variable rectilineal aperture. If a stronger light is required than can be obtained from the plane \(S\), its light must be condensed into a parallel beam \(SL\) by another doublet of no aberration, \(A'B'C'D'\) the flame \(S\) being in its anterior focus.

The illuminator, as now described, is adapted to homogeneous light, either as obtained from a monochromatic lamp, or by means of coloured glasses, or from the prismatic spectrum; but if we employ common light, the doublets \(ABCD, A'B'C'D'\) must be achromatic. We have mentioned above a variable rectilineal aperture. This is a most essential accompaniment for giving perfection to the vision of lined objects. The aperture should be made to form every possible angle with a vertical line, and should be opened and shut by means of a screw till as much light is introduced as is necessary to obtain a perfect view of the object. The image of the slit, which is close to the flame, must be thrown upon \(mn\), so as to be parallel with the lines of the object, or to form any angle with them. When the objects are circular, circular apertures are preferable to any other.

We have already stated that no light should reach the eye, either from the field of the microscope or any other source. For this reason it would be desirable to have circular and rectilineal apertures of different sizes, to be placed immediately beneath \(mn\), so as to allow no part of the field to be seen, excepting that which is occupied by the object, or part of it, under examination.

The above apparatus being provided, let us suppose that the observer is called to examine some structure very difficult to be resolved, such as the blue band of the Clubiona atror, or the structure and nature of the lines and test-objects. We omit at present the consideration of the preparation of the object and the eye of the observer, and also the nature of the light which he is to use, as these will be separately considered; and confine ourselves to the use of the illuminator. The object is first placed on a piece of thin colourless parallel glass, or film of topaz or sulphate of lime, near its middle, and the microscope is directed to it, so that it can be seen distinctly in the ordinary way. Put the illuminator in its place, and set the proper aperture close to the small plane. Adjust the doublet \(ABCD\) by its screw or pinion till a distinct image of the aperture \(GH\) is seen in the field; and, by means of the apertures below \(mn\), any stronger or unnecessary light may be still more completely excluded. If the structure is not rendered sufficiently distinct by this process, it will be proper to try the effects of oblique illumination by inclining the axis \(FL\) of the illuminator to the plate \(mn\), and observing carefully the effects which it produces in different azimuths. If all these means are insufficient, we must have recourse to new auxiliaries,—to monochromatic light, if the microscope is not achromatic, or to monochromatic illumination, if it is achromatic; and we must prepare both the eye and the object, the one for exhibiting and the other for viewing to the best advantage the structures which we are anxious to develop.

As the method of illumination which we have described has been neither understood nor appreciated by some writers on the microscope, the following observations may be useful:

—If we examine with a polarizing microscope certain minute fibres which depolarize light, we shall, with high powers, see them very indistinctly, owing chiefly to the fringes formed by diffraction; but if we examine them when the field is dark and the fibres alone luminous, they will be seen with great distinctness, and unaccompanied with fringes. The reason of this is, that no light passes by their edges, so that no diffraction fringes can be formed either within or without their image. They are seen as if they were self-luminous. In like manner, a fine wire made red hot, if examined in a dark field, will be unaccompanied with fringes. Hence it appears that if we can converge light upon a transparent object so that the points of convergence or the foci of the rays fall upon the object, the light will, as it were, radiate from the parts of the object which they illuminate as if they were self-luminous; and consequently there will be no diffraction fringes. The light, therefore, must be either achromatic or monochromatic. Hence it follows that a common lens which has different foci for the different colours of the spectrum, and also for different parts of its surface, is unfit for microscopic illumination.

These views have been adopted by the most distinguished opticians, as well as by the most eminent observers, and all the finest instruments are accompanied with an achromatic condenser or illuminator.

This method of illumination was, as we have already stated, proposed by Sir David Brewster in 1831, and used by Mr Potter in the same year. It was more fully described by the inventor in this work in 1837, and in his separate Treatise on the Microscope published in the same year; and yet the very same apparatus was communicated to the Academy of Sciences in Paris as a new invention, by M. Dujardin, and published in September 1838. It can hardly be expected that foreigners should be acquainted with every English invention, and we have no doubt that M. Dujardin had not seen the books to which we have referred; but it is discreditible to the science of England that the authors and compilers of English treatises on the microscope should continue to ascribe to M. Dujardin an invention which has not only been used in their own country for 25 years, but distinctly described in English works, easily accessible, and well known in the scientific world.

Before we conclude this chapter we must gratify the reader with an account of Mr Wenham's very ingenious

---

1 This contrivance, though published twenty years ago, has been recently brought forward as a new invention by Mr Solit in the Quarterly Microscopical Journal, 1855, vol. iii., p. 88. 2 Such specula may now be made by the observer himself by the beautiful method of depositing a layer of silver upon glass, invented by Mr Power—a method which M. Foucault has applied with great success to the construction of specula for reflecting telescopes. We have had occasion to see at the Imperial Observatory at Pulkowa two excellent specimens constructed by M. Foucault, one 18 inches, and another about five feet in focal length. 3 If the axis of the microscope is placed horizontally, or even with some obliquity, we may dispense with this speculum altogether, and direct the tube at once to the illuminating flame.

---

1 These views are successfully explained in the Phil. Mag., 1848, vol. xxxii., p. 161. 2 See also the Phil. Mag., 1848, vol. xxxii., p. 163. 3 Comptes Rendus, &c., Sept. 10, 1838, tom. vii., p. 620. method of illuminating opaque microscopic objects when object-glasses of very high power are employed. It is impossible to apply a Lieberkühn to objects covered with a plate of glass, and equally so to throw upon the object reflected light sufficient to illuminate it. Mr. Wenham has therefore conceived the ingenious idea of illuminating the object by light that has suffered total reflection from the interior of the upper surface of the thin glass which covers the object. The method of doing this is shown in the annexed figure, where \(aa\) is the surface of the plate of glass viewing the sun's disc, to work with homogeneous light; but in microscopes, where the quantity of light is in our power, it is perfectly practicable to make that quantity so great that all the yellow or red rays which it contains may give sufficient light for microscopical observations. This insulation of homogeneous light may be effected in three ways; first, by a monochromatic lamp, as proposed and constructed by Sir David Brewster; secondly, by the absorption of coloured media; and thirdly, by the prism.

1. The monochromatic lamp is shown in the following figure, where \(AB\) is a lamp having its globe \(A\) filled with diluted alcohol, which descends gradually through the tube \(C\) into a thin platinum or metallic cup, in which it burns. A strong heat is kept up by a spirit-lamp inclosed in a dark lantern, and when the diluted alcohol is inflamed, it will burn with a fierce and powerful yellow flame. If the flame should not be perfectly yellow, or rather of a nankeen colour, owing to an excess of alcohol, a small proportion of salt thrown into the cup \(D\) will have the same effect as a farther dilution of the alcohol.

Sometimes a little blue light will be found mixed with the yellow, but this may be easily absorbed by a piece of yellow glass placed on any part of the microscope through which the rays pass. Although this light is feeble compared with that of white flames, yet, by using larger lenses for condensing it, it is quite easy to obtain a pencil sufficiently powerful for all microscopic observations.

A stronger flame may be produced by using a gas lamp, or, what is still better, a portable gas one containing compressed gas. This gas, when rushing out in a full stream, explodes when burned with atmospheric air, emitting much heat and a faint bluish and reddish light. As the force of the issuing gas is sufficient to blow out the flame, a contrivance for sustaining it becomes necessary. The method which we contrived for this purpose is shown in the annexed figure, where \(N\) is the main body of the lamp, \(MN\) the principal burner, and \(A\) the screw which opens the main cock. A small gas tube \(abc\), communicating with the main

---

**CHAPTER VII.**

**ON THE MONOCHROMATIC ILLUMINATION OF MICROSCOPIC OBJECTS.**

If a simple and easily applied system of monochromatic illumination, that is, of illuminating objects with homogeneous light—which a prism, and consequently a lens, is not capable of dispersing or refracting in different directions—could be contrived, we should never again hear of compound achromatic microscopes. We believe it will be admitted that in Sir John Herschel's doublet of no aberration the spherical aberration is more completely corrected than in any double, or even triple, achromatic object-glass. Hence it follows, that in homogeneous light such a doublet would be a better microscope than the compound lens. But in the best system of achromatic compensation that can be executed the secondary spectrum still remains without a remedy; and hence the doublet of no aberration, in which there can be no secondary colour in homogeneous light, must be a superior instrument to the compound achromatic lens. Now, in telescopes it is impossible, except in

---

1 Mr Ross, we understand, has contrived a Lieberkühn for his highest powers to illuminate uncovered opaque objects. 2 Microscopical Journal, vol. iv., p. 58.

---

A solar telescope should never be an achromatic one, but should consist of a compound lens of no aberration, all the colours of the spectrum but one being absorbed by the darkening glass. One of these telescopes, in which the object-glass is corrected for spherical aberration upon Sir John Herschel's principle, was constructed for Sir David Brewster by Dollond, at the expense of the Royal Society of London, and has been used in his observations on the lines of the spectrum.

Edinburgh Transactions, vol. ix., p. 435.

When this was written, such lamps were used in Edinburgh, and supplied by a company which did not succeed. burner, terminates above the burner, and has a short tube de movable up and down within it, but so as to be gas light. This tube de, closed at d, communicates with the hollow ring fg, in which four apertures are perforated so as to throw their jets of gas to the apex of a cone whose base is fg. When the gas is made to issue from the burner M, it rushes also into the tube abcf, and issues in four small flames at the apertures in the ring f; and the height of these flames is regulated by the stop-cock at b. The explosive mixture of air and gas which rushes up through the ring is sustained in combustion by these small flames, through which it passes. A broad collar, made of coarse cotton-wick, and thoroughly soaked in a saturated solution of common salt, is fixed on a ring h; and when the bluish flame of the explosive mixture rises above h, it will be converted by the salted collar into a strong mass of homogeneous yellow light. A hollow cylinder of sponge, with numerous projecting tufts, may be substituted for the cotton collar, or a collar of asbestos cloth might be used, and supplied from a capillary fountain containing a saturated solution of salt.

When the few blue rays which sometimes mingle themselves with this yellow light are absorbed, every part of the light will be found to have a definite refrangibility, greater than any other artificial light that can be produced. The minutest objects and the smallest type will appear perfectly distinct in this light when seen or read through the largest possible angle of the greatest dispersive prism,—an irrefragable proof of the perfect homogeneity of the light.

2. The second method of producing homogeneous light, and by far the simplest and most easily applicable to microscopes, is that of absorption; and the best rays to leave unabsorbed or insulated are the red. It requires some experience and scientific knowledge of the action of different absorbing media to select those which will leave the narrowest and brightest band of the red space in the spectrum. We have now under our microscope (a grooved sphere of garnet executed by Mr Blackie) two scales of a moth lying in sulphuric acid and covering each other. With solar light the spaces between the lines glitter with all the hues of the rainbow; but when a thickish plate of red mica is combined with another plate of red glass, and placed beneath the object, all these colours instantly disappear, and a perfection of vision is obtained, which can be disturbed only by the very small portion of spherical aberration which must exist in the sphere, and which an increased depth of the groove would render almost insensible. Blue glasses, and green and yellow as well as coloured fluids, may be successfully used in narrowing the range of refrangibility of the red space.

3. The third method, or that of prismatic refraction, is perhaps the surest and the best method of obtaining homogeneous light with the smallest extent of refrangibility. A certain effect may be produced by small prisms; but in order to have a perfect apparatus, the microscope should form part of the apparatus for examining the lines of the solar spectrum; that is, it should screw into the eye-piece of the telescope, in front of the object-glass of which is placed a fine large prism, for forming the spectrum within the telescope. By this method, which we have put to the test of experiment, microscopical observations can be carried on with an accuracy and satisfaction which nothing can exceed. We enjoy the luxury of perfectly monochromatic vision greater than which the most perfect achromatic compensation cannot give; and while we have the spherical aberration corrected, we have no secondary colours, and none of the imperfections of vision which must arise in transmitting light through six or eight lenses of plate and flint glass.

Although we hope the scientific reader will admit that the preceding views are demonstrably correct, yet Dr Goring has pronounced a most unfavourable opinion of the system of monochromatic illumination. We endeavoured to convert him from this heresy, and hoped that we had succeeded; but in the Micrographia, since published, he devoted a whole chapter to the reproduction and support of his former views. We shall therefore again examine his objections in their order, as they obstruct the progress of improvement among those who justly admire Dr Goring's ingenuity and knowledge in everything which relates to the microscope.

1. Dr Goring's first objection to monochromatic illumination is, that it is too weak, and must be about one-seventh of the whole beam of light. This we are not disposed to dispute; but Dr Goring is too well acquainted with the resources of optical science, to forget that this monochromatic seventh of a beam of light may be made seven times more intense than the whole beam. The objection, however, does not apply to the solar spectrum, for one-seventh of the sun's light is too intense for any eye to bear.

2. The second objection of our author is, that the colours of the spectrum, when separated by the prism, are actually separated into different colours when they are refracted in oblique pencils by a microscope. If this observation is correct, then we must denounce the prism that produced such a spectrum as utterly useless. Dr Goring, however, conceives his observation and his prism to be good, and endeavours to explain the result by referring to Sir David Brewster's analysis of the spectrum, in which it is shown that white light exists at every point of it; but this white light, which has been rendered visible by absorption, cannot be decomposed by refraction of any kind, as it consists of red, yellow, and blue rays, of the same refrangibility. Such white light is the light that is wanted for the microscope; and there can be little doubt that absorptive media will yet be discovered to effect its insulation in sufficient quantity for practical purposes.

3. Another objection to monochromatic light is, that it will not show the real colours of microscopic bodies. This is true; but the object of the microscope is not to find out colours but structures. A common glass lens, with common light, will let the observer know all that he wants of the colours of objects; and when he has learned this, he will then gladly avail himself of coloured light for more important purposes. We can truly say, that though we have wrought with the microscope for fifty years, we do not at present recollect a single case where we required to know anything of the precise colours of minute bodies. Notwithstanding this discussion, Dr Goring concludes his chapter with the following observation, in which we entirely concur:—"A monochromatic light, therefore, being once obtained in a sufficient state of intensity for practical purposes, bids fair to conduct us to the highest perfection of which aplanatic object-glasses and magnifiers are susceptible." It may be proper to add, that the best system of compound achromatic object-glasses now in use would be freed of all their secondary colours by using monochromatic light; and they may be also greatly improved by employing suitable coloured media to absorb what are called the outstanding rays in an achromatic combination. Although Dr Goring has objected to the use of monochro-

---

1 Edinburgh Journal of Science, New Series, No. 1, p. 108. 2 Ibid., p. 143. 3 Ibid., p. 153. M I C R O S C O P E.

matic light, he has himself given some remarkable illustrations of its value, as removing entirely the effects of chromatic aberration.¹

CHAPTER VIII.

ON THE PREPARATION OF THE OBJECT AND THE EYE FOR MICROSCOPICAL OBSERVATIONS.

In using lenses of short focus, either singly or in doublets and triplets, the object is so near the lens, and its thickness, even when very small, forms such a considerable part of its distance from the nearest refracting surface, that any bend or want of flatness in the object completely interferes with the distinct vision of its parts. When the object will bear pressure, the best way is to lay above it a thin transparent film, with perfectly parallel and polished surfaces, such as a splinter of New Holland topaz, a thin plate of sulphate of lime, or a film of mica.² If these plates are a little less thick than the distance between the lens and the object, a little bees' wax should be interposed between the brass setting of the lens and the plate, so that the lens in the act of adjustment would press the wax against the plate, and the plate against the object, till distinct vision is obtained. The object should be placed upon a deeply-curved concave surface.

The proper flattening of the object, when it is tender, may be effected by pressing a thick balsam above it, and allowing the lens to dip into the balsam. If the surface of the lens is flat, its magnifying power will suffer no diminution.

When grooved spheres are used, such as the garnet one above mentioned, the object requires to be very near its surface. It should therefore be placed in a concave lens of glass, of a little greater radius than the sphere, and pressed into the concave form by interposing a narrow strip of a thin film of mica, and, if necessary, pieces of wax or India-rubber, as before; the pieces filling up the space between the lens and the mica, so as not to interfere with the part of the object under examination.

If a diminution of the magnifying power can be permitted, a fluid may be placed between the concave object-plates and the grooved sphere, and the chromatic aberration greatly reduced. By the interposition of a fluid, a grooved diamond sphere may be used; for though its focus for parallel rays falls within the sphere when the refractions are made from air and into air, yet, when the first refraction is made from a suitable fluid, the focus will fall without the sphere.

When the object is put into the best possible condition for observation, and the illuminator applied in the best possible manner, the observer will have every advantage in his researches; but still the structure which he seeks to develop may escape his eager research. Under these circumstances, he must perform his part of the observation in the best possible manner.

Unless particular arrangements are made by the observer for his own comfort, there is no bodily fatigue to be compared with that of the use of the microscope. The eye, the mind, and the whole frame, are on the stretch. The observer must therefore first try if his own eye is in a right state for observation. The fluid which lubricates the cornea, which must be considered as a lens and as part of the microscope, is sometimes in such a viscid state, that when the eyelids roll over the cornea by that beautiful provision of nature by which it is kept smooth and clean, the lubricating fluid, which is pushed into a ridge between the eyelids, does not quickly recover a convex surface. This state of the cornea is incompatible with delicate microscopic observations, and its existence may be ascertained by viewing the expanded image of a luminous point held close to the eye, and, after shutting the eyelids and again opening them slowly, observing if the luminous disc recovers its uniform luminosity quickly or slowly. If the luminous line produced by the fluid accumulated between the eyelids continues to be visible, and the general surface mottled and spotted, the lubricating secretion should be excited by exposing the eye to the vapour of hartshorn, raised by pouring a few drops on the surface of boiling water. The secretion will now flow copiously, the cornea will be swept clean by the purer and less viscid fluid, and the vision of the observer greatly improved. But this movable fluid surface of the cornea generates another imperfection of vision, which has already been referred to. This fluid, when undisturbed by the eyelids, descends by the influence of gravity in vertical lines, and the minute ridges thus formed obliterate and render indistinct all horizontal lines seen by the eye, but have a tendency rather to improve the vision of vertical lines. In proof of this, we may state the unquestionable fact, that if we take a striped pattern of any fabric, and bend part of it into a horizontal direction, while the rest remains vertical, or vice versa, the vertical part will always appear the most distinct. Hence, in viewing lined objects, when the position of the observer's head is either vertical or oblique, the lines of the lined object should be always placed parallel to the direction of the descending fluid. If the axis of the lenses is vertical, and the eye looks downwards, the lubricating fluid will collect irregularly at the apex of the cornea, and injure vision. If the axis of the lenses is horizontal, and the observer's head in its natural position, the fluid will descend in vertical lines; but if the observer lies on his back and looks into the microscope upwards, a position, we admit, not favourable for research, the fluid will flow equally in all directions from the apex to the margin of the cornea, and leave a clear centre well fitted for distinct vision. We may here notice the beautiful contrivance, not mentioned by natural theologians, that the effect of the vertical descent of the lubricating fluid is counteracted by the eyelids opening horizontally, and consequently effacing the tendency of the fluid to form vertical currents. Had the eyelids opened vertically, the vertical ridges would have been increased, and vision greatly impaired.

When everything has been done to fit the cornea (the only part of the eye over which we have any direct command) for accurate vision, the general state of the health, or any casual irregularity of diet, or the accumulation of those minute transparent vessels which produce mucosae rotantes,¹ will be sometimes found to affect the state of the organ, and unfit it for nice observation. To remedy this defect of vision, we must refer the patient to the prescriptions of his physician.

When these precautions have been taken, the observer must protect his eye from all extraneous light; and the most effectual way of doing this is to use the snow spectacles of the Greenlanders, which are cut out of wood, so as to exclude all light whatever, except what enters through a circular aperture the size of the pupil, and directly in front of it.² A cast should be taken in plaster of Paris,

¹ See Edinburgh Transactions, 1843, vol. xv., p. 377. ² In the snow spectacles a long narrow slit is used, to enable the wearer to look on each side of him. An interesting account of the great value of these spectacles, by the celebrated Professor Illumenbach, will be found in the Edinburgh Phil. Journal, vol. viii., p. 261.

¹ See Pritchard's Microscopic Illustrations, pp. 271, 272, 3d edit., 1845. ² Plates of very thin glass are now made for the express purpose of inclosing objects for the microscope. from the part of the face to which they are to be applied, to enable the artist to cut them of a proper shape; and when finished they should be lined with black velvet.

The last requisite for accurate microscopical observation is steadiness in the microscope, and a steady and comfortable position for the observer. The first is easily attained; the second may be accomplished by the observer resting his doubled arms upon a stool or frame nearly the height of the eye-glass of the microscope, but unconnected with it, while his chin rests either upon his arms or upon his breast.

When all these means and precautions fail in unraveling a mysterious structure, we have often derived advantage, in the case of lined objects, by looking through cylindrical lenses or good prisms; the length of the cylinder, or the refracting edges of the prism, being at right angles to the lines. Narrow slits may also be used with advantage next the eye; but in all these cases, while we improve and give a finer definition to the lines and the spaces between them, we deteriorate vision for other parts of the structure.

CHAPTER IX.

APPLICATION OF PHOTOGRAPHY TO THE MICROSCOPE.

Photography may be applied to the microscope in two ways.—1st. In furnishing us with magnificent photographs of microscopic objects; and, 2d. In converting, for special purposes, large objects into small ones which are visible only in the microscope.

1. Mr Richard Hodgson seems to have been the first person who obtained microscopic photographs upon daguerreotype plates by the sun's direct rays. In Oct. 1852 Mr Joseph Delves, of Tunbridge Wells, exhibited to the Microscopical Society beautiful magnified photographs both on paper and glass, namely, the spiracle and trachea of the silk-worm, magnified 60 diameters, and the proboscis of the fly magnified 180 diameters. In November Mr George Shadbolt exhibited a photograph of a fly's proboscis, taken by a very small camphene lamp.

The method of taking these pictures is very simple. The eye-piece of the microscope being removed, the end of the tube from which it was taken is fixed into a dark box (or a photographic camera), at the opposite end of which is a groove for carrying the ground-glass plate. When the object is well illuminated either by solar or artificial light, a distinct picture of the object is thrown upon the ground-glass plate, and the sensitive plate is placed so as to be in the chemical focus of the object-glass, which, in low powers, is at some distance beyond the luminous focus.

Mr Shadbolt obtains the chemical focus by altering the luminous focus by the fine adjustment; an alteration of two turns of the milled head, or \( \frac{1}{3} \) th of an inch, being sufficient for an inch-and-half object-glass; an alteration of half a turn for a \( \frac{3}{4} \) inch object-glass, or \( \frac{1}{3} \) th of an inch; and an alteration of about 2 divisions, or the \( \frac{1}{3} \) th part of an inch, for a \( \frac{1}{4} \) th of an inch object-glass. The time of exposure varies from 1 to 10 minutes.

Mr F. H. Wenham has greatly improved the process of microscopic photography by using the ordinary microscope as a solar one, and using a dark room in place of a camera, by a new mode of combining the chemical and visual foci, and by obscuring for a time the parts of the object which are either easily solarized and lost, or out of focus. He prefers sunlight to artificial light, though he justly considers it of great importance to have what he calls a photographic fusee that will burn with the necessary actinic power for sufficient time to take nocturnal or underground photographs. He has produced photographic pictures by burning phosphorus, by balls of fine zinc turnings, by a succession of electric sparks, and by the oxyhydrogen or lime light.

Mr Wenham has succeeded in obtaining by the photographic microscope the markings on the most difficult tests. One of these, of the P. angulatum, magnified about 15,000 diameters, shows the configuration of the markings, perfectly black and distinct, in a far greater degree than we can ever hope to see them through the compound microscope; and Mr Wenham is of opinion "that if ever the structure of those difficult tests is to be proved, it will be by the aid of photography."

Photographs of a still more minute character were presented to the Academy of Sciences on the 10th August by M. Bertsch. They were five in number.

The first was one of the Diatomaceae, from guano, obtained by a magnifying power of 500 diameters. The focal length of the object-glass was the 50th of an inch (a demi-millimetre). It was achromatized for the superior rays of the spectrum, and its chemical focal length was 24 centimetres. The focus for the inferior rays was the \( \frac{1}{10} \) th of a millimetre from the luminous focus.

The second specimen was two Naviculae, of that species of which it is difficult to see the structure and the strie with the best microscopes. One is magnified 800 and the other 500 diameters. They were illuminated with light so oblique that the field of view was almost dark.

The third represented, with a power of 500, the globules of the human blood. The annular space and the depression were distinctly shown on a larger field than is given by the best microscope, and the light traversed them without changing its direction.

The fourth specimen consisted of two pictures of the crystals of salicine seen in polarized light; the one illuminated by the ordinary, and the other by the extraordinary ray.

M. Hartnach constructed for M. Bertsch a complete instrument for taking this class of photographs, with a magnifying power of from 50 to 1000 diameters for transparent objects, and from 50 to 150 for opaque objects.

2. Photography has been successfully applied in reducing, for special purposes, large objects into such small dimensions that they are invisible to the naked eye, and can be seen only with a good microscope.

It has long been a trial of skill to include the Lord's Prayer in the smallest circle by the unaided hand of the writer. More recently results of the most remarkable kind have been obtained by machinery. Sir John Barton drew Barton; with a diamond point, upon steel, lines at the distance of the 10,000th of an inch. M. Nobert exhibited at the Crystal Palace in 1851 ten groups of lines upon glass in which the number of lines in an English inch varied from 11,263 to 49,910; and M. de la Rue examined another specimen of ten groups in which they varied from 11,261 to 58,306!

In order to see the lines in the widest of these groups, a power of 100 is sufficient, but one of 2000 is required to separate those in the closer groups. They thus become

---

1 This suggestion has been specially attended to in the latest form of Mr Rose's microscope. He has obtained the most perfect steadiness by giving solidity to those parts which are most liable to tremble; and he attaches so much importance to this part of the instrument, that he tests it by the "inverted pendulum." The object of this apparatus is to exhibit vibrations which could not otherwise be perceived. He varies the size of the parts of the stand till he obtains such an equality of vibration between the stage and the body of the microscope as will prevent any visible tremor in the object under examination.

2 They were produced in from 5 to 10 seconds in sun-light. With low powers "a moment's exposure" is sufficient.

3 See Transactions of the Microscopical Society, vol. i., p. 57; and Microscopical Journal, vol. i., p. 165.

VOL. XIV. Microscopic effects still more wonderful have been produced by M. Froment of Paris, one of the most distinguished artists of modern times. A piece of writing, for example, about 3½ inches in diameter, was compressed into the space of 1/6th of an inch. The mode of doing this has not yet been published; but Dr Lardner informs us "that it consists of a mechanism by which the point of the graver or style (a diamond point generally) is guided by a system of levers, which are capable of imparting to it three motions in right lines, which are reciprocally perpendicular; two of them being parallel, and the third at right angles to the surface on which the characters or design are written or engraved. The combination of the motions in the direction of the axes, parallel to the surface on which the characters are engraved or written, determines the form of the characters; and the motion in the direction of the axes, at right angles to that surface, determines the depths of the incision, if it be engraving, or the thickness of the stroke, if it be writing."

Wonderful as are the specimens published by M. Froment, they have been greatly surpassed by those produced by our countryman Mr Peters, who has invented and described the machine by which they are produced. Mr Peters has inscribed the Lord's Prayer in 6 lines in a rectangular space one of whose sides is the 1/24th part of an inch, and the other the 1/25th part of an inch; that is, the area of the rectangle is 1/24 x 1/25, or the 1/600th part of a square inch. The height of each letter is the 1/125th part of a linear inch, and therefore the space occupied by any letter, such as u or n, which are as wide as they are high, is no more than the hundred millionth of a square inch.

Among the wonders of microscopic photography not the least interesting and useful are the fine microscopic portraits taken by Mr Dancer of Manchester, and copies of monumental inscriptions so minute, that the figures in the one, and the letters in the other, are invisible to the eye. A family group of seven complete portraits occupies a space the size of the head of a pin; so that ten thousand single portraits could be included in a square inch. They are executed upon films of collodion as transparent as glass; so that a family group could be placed in the centre of a brooch, a locket, or a ring, and magnified by the central jewel cut into a lens sufficient to exhibit the group distinctly when looked into or held up to the light.

Microscopic copies of despatches and valuable papers and plans might be transmitted by post, and secrets might be placed in spaces not larger than a full stop or a small blot of ink.

We have already had occasion to mention in the article Micrometer the application of photography in making micrometers and micrometrical scales of all kinds; and it is obvious that groups of test-lines like those of Nobert could be produced upon transparent collodion with an accuracy and distinctness greater than could be done upon glass. The original groups, drawn on a large scale either by the hand or a ruling-machine, could thus be copied and reduced ad infinitum.

CHAPTER X.

ON TEST OR PROOF OBJECTS FOR TRYING THE PERFORMANCE OF MICROSCOPES.

This class of objects, and their application to the microscope, we owe to Dr Goring; and to their introduction we must ascribe much of the rapid improvement which this instrument has undergone. The finest test-objects are the scales of butterflies and moths, which were suggested to Dr Goring by the following passage in Leuwenhoek:

"If we examine the wings of this creature (the silk-worm object, moth, Phalena mori) by the microscope, we shall find them covered with an incredible number of feathers (scales), of such various forms, that if a hundred or more of them were to be seen lying together, each would appear of a different shape. To show more clearly this wonderful object, I caused eight feathers to be delineated, for I do not remember that I ever saw them of so curious a make in any flying insect.

Although the microscope by which these feathers were drawn represented objects very distinctly, the limner could not through it see the ribs or streaks in each feather until I pointed them out to him. Therefore I put into his hands a microscope which magnified objects almost as much as that by which the silk-worm's thread was drawn, desiring him to give the figure of that feather which through it he could see the most distinct."

From this passage Dr Goring naturally inferred, that Dr Goring there were some peculiar properties in the lines on the feathers and scales of insects, which rendered them more difficult to be discovered than other microscopic objects; and hence he discovered their properties as test or proof objects for trying the penetrating powers of microscopes.

Dr Goring regards the penetrating power of a microscope as dependent on its angle of aperture, and its defining power as in the inverse ratio of the quantity of chromatic and spherical aberration. When the angle of aperture was less than a certain quantity, he found that the lined structure of the scales could not be rendered visible, however perfect the instrument was.

These new and apparently important results were confirmed by Mr Pritchard; and since that time opticians, both chandlery in this and in foreign countries, have contended with each other in producing object-glasses with the largest angles of aperture. Mr Ross, as we have seen, has produced object-glasses 1/8th of an inch focus, with an angle of aperture of 170°; and in a communication to Mr Quckett from Mr Ross himself, he gives a history of the steps by which he advanced to this remarkable angle:

| Focal length | Angle of aperture | |--------------|------------------| | 1832 Mr Ross | 1 inch | | 1833 Do | 1/2 | | 1834 Do | 1/4 | | 1835 Do | 1/8 | | 1842 Do | 1/16 | | 1844 Professor Amiel | 1/32 |

In closing his communication to Mr Quckett, Mr Ross remarks that 135° is the largest angular pencil that can be passed through a microscopic object-glass, and yet he had increased it in 1855 to 170°. Some writers speak of angular apertures of 175°, and even 180°!

---

1 Select Works, p. 63. 2 Some writers have very unwisely substituted the term resolving in place of penetrating, and have applied the latter to a property of the microscope which all low powers possess; that is, seeing into an object, or seeing parts out of focus. The term resolving, applied to the telescope, is the power of separating minute luminous points. 3 Practical Treatise on the Microscope, 1848, p. 490. It is well known to every observer with the microscope that object-glasses of large angular aperture exhibit objects which are not seen with those of a smaller aperture and the same focal length; but it is equally well known that they often show objects less distinctly than those of a smaller aperture. This being the fact, we ask, What great advantage is derived from merely seeing that there are lines in an object, unless the object-glass shows us what is the nature and structure of these lines?

As instruments for studying structures and making useful discoveries with the microscope, let us compare the object-glass of large aperture with one of small aperture:

1. It is obvious that, owing to the larger size of the lenses in the large-aperture lenses, the rays must pass through a much greater thickness of glass of doubtful homogeneity.

2. With large apertures, the spherical aberrations and the chromatic aberration, primary, and secondary especially, must be less perfectly corrected.

3. The surface of glass with the most perfect polish must have pores produced by the attrition of the polishing material; and light falling upon the sides of these pores with extreme obliquity must be refracted less perfectly than when incident at a greater angle.

4. The structures actually seen, however distinctly, and even if the lenses are absolutely perfect, are false structures, the falsehood of the picture being proportional to the angle of aperture.

This result, which the optician and the optical student will receive not only with scepticism, but we fear with disdain, as the photographers have done an analogous truth, may be illustrated in the following manner:

It has been demonstrated\(^1\) that all objects in relief are misrepresented by large lenses when their pictures are taken in the camera obscura. The human face divine is caricatured. Parts invisible are displayed, and parts visible are deformed. When Polyphemus admired Galatea she was not the beauty who fascinated Acis; and we think a national reward should be offered to the daring Ulysses who should extinguish the orb of every photographic Polyphemus in the land. But if the photographic lens thus deforms youth and beauty and age, and even trespasses upon inanimate nature, what may we not expect from the cyclopean eye of a twelfth-of-an-inch object-glass viewing microscopic objects in relief, several thousand times less in diameter, and so near it that it would see nearly the whole of its surface were it a sphere?

For the purpose of illustration, we may suppose the microscopic object to be the head, in relief, of the Venus de Medici, on a much smaller scale than the beautiful microscopic portraits of Mr Dancer of Manchester, and that the microscopical observer is requested to make a drawing of it. We cannot venture to say what would be its expression, but we are sure that it could have no resemblance to the original, both ears being fully brought out, and almost the whole round of the head. In like manner, every ridge in a microscopic object will show to the observer both its perpendicular sides as well as the side opposite the eye, and the resulting picture will be an incoincident combination of a thousand different pictures, as seen from every point of the object-glass. The reason is therefore obvious why a large aperture shows lines that are invisible with a small aperture. The relief of a bust, or of a reliquo, either basso or alto, is best seen when we look at it in profile. Its height is then actually seen, whereas it is merely inferred when we look it full in the face. When the raised lines of a test-object are illuminated only obliquely, they are seen obliquely, and consequently much better than with a small aperture, which may not show them at all; not because the object-glass is inferior in penetrating power, but because the thing looked at in the one case is not the thing looked at in the other, and is actually a smaller object.

Hence the perfection of a microscope consists in its having the smallest angular aperture consistent with distinct vision. Errors of such a microscope will not show certain objects of great minuteness, but it will give a perfect representation of what it does show. The large angular aperture will show the same objects, and others far more minute, but whatever it does show will be a mockery of the truth.

Admitting the truth of these observations, it follows that an observer who examines a microscopic structure in relief, and executes a correct drawing of it with an object-glass of large aperture and an eye-piece of small magnifying power, will obtain a very different and a much more correct drawing if, with the same magnifying power, he uses an object-glass of a less focal length of small aperture, and an eye-piece of a high magnifying power.

In the use of high magnifying powers obtained by object-glasses of short focal length we encounter another evil, well known to every microscopical observer. We can see only at one instant the parts of the object which are in the same focal plane, and by a fresh adjustment we see in succession the parts in other planes nearer to or farther from the object-glass.

We are thus led to a new form of the microscope, in New form which object-glasses of large angular aperture should not be of the employed. In place of observing the object with such microscope object-glasses, observe an image of the object formed with another achromatic object-glass with a proper angular aperture. This image may be the exact size of the object as produced by placing the object at a distance equal to twice its focal length, or it may be made greater by diminishing that distance, or less by increasing it. In all these cases the distance of the object from the first lens is so great that opaque objects may be illuminated by a Lieberkühn, or any method that may be preferred, and large objects may be submitted to examination to which the microscope in its present form cannot be applied. When the angular aperture is large, and the magnifying power great, the object approaches so near to the lens that the microscope becomes quite unfit for important physiological researches. It is unfit also for all researches in which experiments require to be made upon the objects under examination, for the examination of objects inclosed in minerals or other transparent bodies, and for objects in which there is any distance between their near and remote parts.

The following is the list of test-objects given by Mr Mr Pritchard, and arranged in relation to penetrating and defining power,—a distinction which the preceding observations justify us in preserving; the word penetrating meaning nothing more than the effect produced by angular aperture:

I.—Penetrating Power.

Sect. I. Easy. 1. Petrobus maritimus, scales of. 2. Lepisma saccharina, scales of.

Sect. II. Standard. 1. Morpha Menelaus, feathers of. 2. Alacta pentadactyla, feathers of the. 3. Alacta hexadactyla, feathers from the body of it. 4. Lycaenae Argus, feathers of the. 5. Tinea vestianella, or clothes-moth, feathers from under ends of the wing.

Sect. III. Difficult. 1. Pieris or Pontia brassicae, or cabbage-butterfly, feathers from the. 2. Podura plumbea, scales from the.

II.—Defining Power.

1. Hair of the common mouse. 2. Hair of the bat genus. 3. Leaf of the moss Hypnum, species unknown. 4. Spotted scales of the Lycaenae Argus.

---

\(^1\) Brewster's Optics, chap. vii., p. 65, edit. of 1853. Since the publication of Mr Pritchard's *Micrographia*, the microscope has undergone great improvements, and the structure of test-objects has been more successfully examined. Mr Quckett, in his treatise of 1848, has given the following list of test-objects as furnished by Mr Topping:

| Hairs | Scales | |-------|--------| | Bat. Larva of Dermestes. | Tinea vestinella. | | Mole. | Lepisma saccharina. | | Mouse. | Podura plumbea. | | Rabbit. | Aquatica. | | Squirrel. | Hipparchia janira. | | | Plumed gnat. |

| Scales | Insects | |--------|---------| | Azure blue, P. argiolus. | Navicula hippocampus. | | P. Argus. | Spenceri. | | Pontia brasica. | angulata (Humber.) | | Vanessa io. | (America.) | | Morpho Menelaus. | Tripoli from Kitchelberg. | | Alcita pentadactyla. | | | Catocala nupta. | Muscular fibre. |

From each class of these test-objects Mr Quckett has selected a certain number, and given in four plates highly-magnified representations of them, which exhibit great skill in the engraver, and still more in the artist, Mr Leonard. The magnifying power employed was sometimes 2000 diameters.

Very fine drawings of test-objects have been recently made by Dr Griffiths, one of the able authors of the *Micrographic Dictionary*. Those drawings, which we have been kindly permitted to copy, occupy the first eighteen figures of Plate XX. We have added to these figures a few from Mr Quckett's practical *Treatise on the Microscope*; the best work on the subject which has appeared in our language.

The following is a particular description of Plate XX:

1. The hairs of the larva of *Dermestes lardarius*, placed in Canada balsam. 2. Hairs of the common bat (*Vespertilio pipistrellus*), in balsam. 3. Hair of mouse (*Mus domesticus*), in balsam. 4. Flies of coniferous wood, common deal (*Abies cedrea*), viewed dry. 5. Mucus (or salivary corpuscles), seen with different powers. 6. Scales of *Lepisma saccharina*, dry. 7. Scale from the wing of *Morpho Menelaus*, dry. 8. Scale from under side of wing of common clothes-moth (*Tinea vestinella*), dry. 9. Scales of *Hipparchia janira*: a, dry, and by oblique light; b, in balsam, by direct light; c, dry, after Schacht. 10. *Didymoscelis ferruginea*, under different powers: b, with imperfect adjustment; c, with perfect adjustment; d, separate fibres. 11. *Didymoscelis Berrieri*, empty cells. 12. Scales of *Podura plumbea* under different powers: a, 220 diameters. 13. Pygidium of flea. 14. Frustule of *Grammatophora marina*: a, front view; b, side view. 15. Frustule of *Grammatophora subtilissima*: a, front view; b, side view. 16. *Gyrosigma angularis*: dry valve showing the dots. 17. *Gyrosigma attenueum*: dry valve showing the lines. 18. *Gyrosigma elongatum*: dry valve showing the lines.

The following ten figures are from Mr Quckett's plates:

19. Hair of a species of bat from India. 20. a. Large scale from *Podura plumbea*; b, the same magnified 1500 diameters. 21. *Navicula Spenceri* as drawn by Mr Warren de la Rue, magnified 1500 diameters. Mr Spencer saw lines only with the power of 800; M. de la Rue saw the dots as holes or depressions.

22. *Navicula angularis*: a, magnified 1200 diameters; b, magnified 2000 diameters. 23. Ultimate fibrilla of muscular fibre. Their true structure is shown in b, d, f. 24. Scale from the wing of the male *Pontia brasica*, dry. 25. Portion of wing of *Pontia brasica*, showing the imbrication of the scales. 26. Portion of valve of *Gyrosigma striatum*, magnified 1800 and 4700 diameters.

The following observations, showing the relation between the magnifying powers and angles of apertures of English microscopes, and the objects most useful for testing object-glasses, have been given by Dr Griffith and Professor Henry. The magnifying power is given in diameters:

1. Object glass 1½ or 2 inches.—Magnifying power, 20; aperture, 12° to 20°. Test-objects: The pygidium of the flea, Plate XX., fig. 13, a—the outline and the hairs should be distinct; the hair of the mouse, fig. 3. 2. 1-inch or ¾-inch Object-glass.—Magnifying power, 60; aperture, 22° to 27°. Tests: Hair of Dermestes, fig. 1; of bat, fig. 2; the pygidium of the flea, the outline of the areola being distinguishable under the high eye-piece with power 120 to 200, but not the rays. 3. ¾-inch or ¼-inch Object-glass.—Magnifying power, 100 to 120; aperture, 25°. Tests: Hairs, figs. 1, 2, 3; disks on deal, fig. 4; the coarser scales of *Lepisma*, fig. 6, a; the pygidium of the flea, fig. 13, a, b; the entire structure being visible with the high eye-piece; a dark scale of *Podura*, fig. 12, a. 4. ¼-inch Object-glass.—Magnifying power, 220; aperture, 75° to 140°. Tests: The hair of Dermestes; disks of deal; salivary corpuscles, fig. 5, the moving molecules being clearly distinguishable; the smaller scales of *Lepisma*, fig. 6, a, b; the scales of *Podura*; filaments of *Didymoscelis*, fig. 10, a; the pygidium of the flea, and the scales of *Pontia brasica*, fig. 26. 5. ¼-inch Object-glass.—Magnifying power, 420 to 450; aperture, 110° to 150°. Tests: The paler scales of *Podura*; the pygidium of the flea; the scales of *Pontia brasica*; the filaments of *Didymoscelis*, showing the component fibres; the salivary corpuscles. 6. ¼-inch or ⅛-inch Object-glass.—Magnifying power, 600 to 650; angular aperture, 80° to 120°. Tests: The paler scales of *Podura*; the filaments of *Didymoscelis*, mounted in balsam; and the ultimate fibrilla of muscular fibre, fig. 27.

Different writers have proposed different objects for testing microscopes. The test employed by Professor Amici is the exhibition of the lines on the *Navicula gracilis*, which the writer of this saw beautifully displayed by the professor himself. It is a good test for angular apertures.

Mohl uses the scales of *Hipparchia janira* for testing penetrating power; and pollen grains, the scaly elytra of the diamond beetle, or bat's hair, for testing definition.

The most perfect of all tests are the test-lines of M. Nobert's Nobert of Barth in Prussia. These tests consist of ten test-lines, separate bands of parallel lines, traced upon glass with the point of a diamond, the lines being drawn closer and closer to each other, from No. I., where they are widest, to No. X., where they are closest, varying, as shown in the following table, from the 11,000th to the 50,000th of an inch:

| Thousandths of an English inch | Thousandths of an English inch | |-------------------------------|-------------------------------| | No. I. 11,255 | No. VI. 24,309 | | II. 13,142 | VII. 28,433 | | III. 15,352 | VIII. 33,153 | | IV. 17,873 | IX. 38,613 | | V. 20,853 | X. 49,910 |

All these bands are engraved on the same plates of glass; and when seen by the naked eye they appear like the small

---

1 New Winchester Street, Pentonville. Mr Norman, Fountain Place, City Road, also supplies excellent sets of test objects. 2 This work forms vol. vi. of Mr Baillière's *Library of Illustrated Standard Scientific Works*, a collection of treaties of very rare merit.

---

1 *Micrographic Dictionary*, art. Test Objects, p. 635, 637. 2 See Poggendorf's *Annalen der Physik*, 1846. black line \( mn \) in the annexed fig., ABCD being the size of the plates of glass on which they are engraved.

The subdivision of an inch has been more recently carried farther by M. Nobert. In a plate of fifteen bands the lines amount to fifty-six thousand in an inch. The following table, calculated by Mr Warren de la Rue, shows not only the number of the lines, but their distance also, in parts of an English inch:

| No. | Distance | Number of Lines | |-----|----------|----------------| | I | 0.00008380 | 11261 | | II | 0.00007548 | 13248 | | III | 0.00006482 | 15437 | | IV | 0.00005506 | 18162 | | V | 0.00004884 | 20475 | | VI | 0.00004202 | 23463 | | VII | 0.00003552 | 28153 | | VIII| 0.00003108 | 32175 | | IX | 0.00002664 | 37537 | | X | 0.00002142 | 40930 | | XI | 0.00001720 | 45045 | | XII | 0.00001313 | 47325 | | XIII| 0.00001098 | 50065 | | XIV | 0.00000891 | 52882 | | XV | 0.00000776 | 56308 |

The resolution of these lines is regarded as the best test for angular aperture and oblique light. Dr Griffith states that even the group of the 60,000 (56,306 in the above table) can be resolved by the 4th of an inch object-glass, and he considered the resolution of it "much easier than that of the markings upon the valves of many of the Diatomaceae." A considerable difference of opinion exists respecting the magnifying power necessary to resolve different groups of these lines.

CHAPTER XII.

ON MICROSCOPIC OBJECTS.

In the preceding chapter we have already described some objects of the most interesting objects for microscopical observation. Every department of nature is full of objects, from the examination of which the most important discoveries may be expected; but though the zealous observer can never be at any loss for subjects of research, it is desirable to know what has been done by our predecessors, and what trains of inquiry are most likely to prove of general interest. There are subjects of microscopic inquiry which are closely connected with the most interesting parts of physiology; and even geology itself, conversant with the grandest subjects of research, has recently been illustrated by the aid of the microscope.

Dr Ehrenberg of Berlin, to whom we are indebted for so many important discoveries respecting the organization of infusorial animalcules, has made the most remarkable discovery of infusorial organic remains. These remains are the siliceous shells of animalcules belonging to the division Bacillaria, and form strata of tripoli, or polischief (polishing-slate), at Franzenbad in Bohemia. M. Ehrenberg has more recently discovered them in the semi-opal found along with the polishing-slate in the tertiary strata of Bilin, in the chalk flints, and even in the semi-opal or noble opal of the porphyritic rocks. The size of a single individual of these animals is about \( \frac{1}{10} \) of a line, or \( \frac{1}{1000} \) of an inch. In the polishing-slate from Bilin, in which there appear to be no vacuities, a cubic line contains, in round numbers, 23,000,000 of these animals, and a cubic inch contains 41,000,000,000 of them!

The weight of a cubic inch of the polishing-slate is 270 grains. There are therefore 187,000,000 of these animals in a single grain, or the siliceous coat of one of these animals weighs the 187,000,000th part of a grain!

In the annexed figure we have given representations of these singular microscopic objects, as seen by Ehrenberg. The siliceous shells found in the Franzenbad polischief are much more distinct than those found in the Bilin strata.

Another example of the value of microscopical observations may be drawn from the discovery of the teeth of the crystalline fibres which compose the crystalline lenses of almost all line lenses animals. The crystalline lens is composed of innumerable fibres of nearly the same length, each of which tapers from its middle to its two extremities, where it comes to the sharpest point. The sides of each of these fibres are furnished with teeth like those of a watch-wheel, and the teeth of the one lock into those of the adjacent ones, as shown in the annexed figure. When the power is small, or the microscope not good, or the lamina too thick, and not nicely detached, each row of interlocking teeth appears as a dark line, sometimes as sharp as a black line drawn upon paper with a pen. Sometimes the lines appear rough and ragged; and as the fibres become less and less in approaching the poles, the black lines are as difficult to resolve into teeth as the lines on test-objects already described. The following measures, taken by Sir David Brewster, will show what a wonderful structure in the eye has been thus disclosed to us by the microscope. The calculations refer to the lens of a cod, 4-10ths of an inch in diameter:

- Number of fibres in each lamina or spherical coat: 2,500 - Teeth in each fibre: 12,500 - Teeth in each spherical coat: 31,250,000 - Fibres in the whole lens: 5,000,000 - Teeth in the lens: 62,500,000,000

or the lens of a cod contains five millions of fibres and sixty-two thousand five hundred millions of teeth; and if we reckon the curved end of the tooth as one surface, each tooth will have six surfaces, which come into contact with the corresponding surfaces of the adjacent tooth, so that the number of touching surfaces will be three hundred and seventy-five thousand millions; and yet this little sphere of tender jelly is as transparent as a drop of the purest water, and allows a beam of light to pass across these almost innumerable joints without obstructing or reflecting a single ray!

There is another class of objects of extreme interest,

---

1 See Lardner on the Microscope, p. 67 and 72; and the reports by the juries of the Great Exhibition, p. 298. 2 Organization Systematik der Infusions Thierehen, 3 vols. folio, Berlin, 1830-1831, and Micropogon das Erden und Fleiss Schaffende Wirkung des unsichtbar kleinen selbständigen Lebens auf der Erde, von Christian Gottfried Ehrenberg, 1 vol. folio., with 40 folio plates. 3 Poggendorff's Annalen der Physik, 1836, No. V., p. 225.

---

1 Poggendorff's Annalen der Physik, No. VI., 464. 2 This includes the concave surface between two adjacent teeth. 3 Philosophical Transactions, 1833, p. 329. which Mr Pritchard and other writers have omitted to notice, and the development of which calls forth all the resources of optical knowledge and optical experience with the microscope. These objects are the microscopic cavities in minerals, containing two fluids unknown to the chemist; groups of crystals of different forms, and floating balls, and exhibiting actual chemical operations going on in these minute laboratories when exposed to changes of temperature. These various phenomena have been described and represented in drawings, in two papers by Sir David Brewster published in the Transactions of the Royal Society of Edinburgh. In some of the precious stones, particularly in diamond, garnet, &c., these cavities are perfect spheres; but owing to the great refractive power of the gem, they appear completely black and opaque, though the microscope describes a small spot of light in their centre, which is the pencil of light which they refract. These spherical cavities, and this central spot, are the finest objects for examining the aberration of lenses and specula, and are infinitely preferable to the reflected patches of light from small spheres of quicksilver. Dr Goring has observed spherical cavities or air-bubbles in fluids, and, with his usual ingenuity, recognised their utility for indicating the effects of aberration. Those which we have used in the gems are, however, permanent instruments of much greater utility, not only from our being able to use the same bright spot with all instruments and on all occasions, but from the dark ring round the bright spot being incomparably greater in the gems than in fluids. Representations of some of the cavities containing the two new fluids, which will not mix, though in the same cavity, are given in fig. 103. The little white circle is the bubble either of gas or of vacuity. The fluid round it, shown by dots, is a highly evaporable fluid, and the fluid in the angles and ends of the long cavities, shown by the shading, is a thick and unevaporable fluid, which indurates when exposed to the air. These cavities lie in strata, and millions of them, which no microscope can resolve, occupy a very small area.

Our limits will not permit us to pursue this subject further, and we shall conclude the article with a very brief selection of microscopic objects from Mr Pritchard's admirable little pamphlet, entitled A List of Two Thousand Microscopic Objects.

1. Insects (eggs, wings, tongues, antennae, and scales of). Eyes of Agrilus, 12,000 eyes; Bombyx mer, 6236 eyes; Phalerae, 11,300; Scarabaeus, 3189; Hawk-moth, 20,000; Libellula, 12,544; Melanatha, 8820; Mordella, 25,083; Papilio, 17,000.

2. Hairs of Animals.—Hair of an infant, Ornithorynchus, mouse, bat, bee, Acilius canaliculatus, Meleca punctatus, Siberian fox, spider, wing of Tipalis, stag-beetle, white cat, dormouse, dromedary, caterpillar, badger, ant-eater, civet cat.

3. Scales or Insects.—Podura plumbea, Pontia brassica, Pieris brassicae, Papilio Apollo, Atlas moth, diamond-beetle, Esphora limacinae, house-moth, Lepidoptera saccharina, 10-plumed moth, 20-plumed moth, Morpho Menelaus, Papilio Apollo, Papilio Paris, Urania leilus, privet-moth.

4. Circulation in Plants of Cyclost.—Nitella hyalina, Nitella translucens, Chara vulgaris, Caulinia frigida, Hydrocharis or frog-bit in the stipule of the leaves and the ends of the roots, Tradescantia virginica or spiderwort in the filaments around the stamens, Senecio vulgaris or groundsel in the hairs surrounding the stalks and flowers.

5. Circulation in Animals.—In the arachnoids or spider tribe at the joints of the legs, Perla viridis and Semblis bilineata in the antennae and wings where they have just emerged from the chrysalis, larvae of the Ephemeridae, larva of Hydropilus, small Dytiscus, Agrion pontica, Libellula, round Lygaeus, fresh-water shrimp, water-beetle (Osmoderma), Ligia, water-flea (Daphnia pulex).

6. Circulation in Zoophytes.—Mr Lester has discovered a circulation resembling that in plants in some of the polyphorous zoophytes, as the Tabularia indivisa, Sertularia, Campanularia, Plumularia, &c.

7. Crystals.—For an account of various interesting microscopic phenomena observed by H. F. Talbot, Esq., of Lacock Abbey, we must refer the reader to a series of papers in the recent numbers of the London and Edinburgh Philosophical Magazine, and to others which will be found in the Philosophical Transactions.

The oxalate of potash, and potash dissolved in water, and rapidly crystallized, is a fine object. In polarized light a very splendid effect is the Faro apophyllite, when the prisms are complete, as represented by Sir David Brewster in a coloured drawing in the Edinburgh Transactions, vol. ix., p. 317, plate xxi., fig. 1. But the most beautiful of all objects, as seen by polarized light, are the circular crystals, first described by Mr Talbot, as produced by a peculiar process. In a recent paper "On Circular Crystals," by Sir David Brewster, no fewer than about eight circular crystals have been described, with twenty-five coloured drawings of the most interesting. Several of these are to be found in the slides sold by the preparers of microscopic objects.

8. Animalcules:— Monas Testacea, 18,000th of an inch. Monas commune, 4000th of an inch. Monas volvox, 3,456th to 1728th of an inch. Volvox globator, found in stagnant water, 30th of an inch. Vibrio bipunctatus, 200th of an inch. Vibrio spirillus, like a screw, 2000th to 1000th of an inch. Vibrio glutinis. Kolpoda cucullus, 28th of an inch. Cercaria podura. Cercaria viridis. Cercaria hirta. Leucophrys fluida, 400th of an inch. Trichoda vulgaris, 1200th to 240th of an inch. Trichoda locomunda. Vorticella polymorpha. Vorticella convallaria. Vorticella senta, 100th of an inch. Vorticella rotatoria.

The reader will find beautiful drawings and full descriptions of these and many other animalcules in Mr Pritchard's works interesting work entitled The Natural History of Animalcules, London 1834; in the Microscopical Illustrations of Mr Pritchard and Dr Goring; and in the Microscopic Cabinet by the same authors he will find much information respecting microscopic objects.

In the more recent work of Ehrenberg, Quckett, and Lardner, already cited; in Pritchard's large work recently published, entitled A History of Infusorial Animalcules, Living and Fossil, illustrated with 24 plates; and in Dr Griffith and Professor Henry's Micrographic Dictionary, the reader will find everything that he desires. This last work is illustrated with no fewer than 41 engravings and coloured plates, and with 816 wood-cuts admirably executed; and owing to these illustrations and its alphabetical arrangement, the general reader will find in it a store of easily-accessible and popular information, apart from its science, which cannot fail to amuse and instruct him.

(D.B.)