Having described in the former papers the appearances observable when pencils of light from small circular apertures are partially intercepted by certain opaque or transparent objects of definite shape and size ; and having shown that whether shadows or illuminated spaces are thus used, they serve to exemplify the magnifying power of short intervals existing between the organ of vision and the object to be examined, inasmuch as they occupy some position in space, and have a certain form, qualities which pertain to them in common with all substances appreciable by the sense of sight, we proceed to notice the phenomena which result when exceedingly narrow linear apertures are substituted for those of a circular form. In conducting these investigations it was not unreasonable to suppose, à priori, that if the size, the quality, and the position of the object to be examined, the direction and the intensity of the light which was used, the sensitiveness and immediate response of the pupil of the eye to the minutest variation in the quantity of light impinging on the retina, and the refracting qualities of the transparent portion of the visual organ, were each and all taken into account, so that a nice and delicate adjustment of the eye to the light, and of the light as well as of the size of the objects to the eye could be insured, appearances perhaps beautiful, doubtless uncommon, and certainly interesting to the physiologist might be fairly anticipated. Such anticipations, have been so far realized as to present a strong inducement to prosecute the subject with a legitimate prospect of still greater success.

It is obvious that the phenomena which have occupied our attention are chiefly due to the formation of shadows. For when a divergent pencil of light proceeding from a small circular perforation in a card falls upon the eye, and when a small object either transparent or opaque—a transparent cross on a black ground, or a black cross on a transparent ground, for instance, is allowed to intervene; it is evident that a shadow of the cross in the latter case, and an illuminated space equivalent to the shadow in size and shape, in the former, is portrayed on the retina of the eye.

The same kind of phenomena result even if no artificial body be interposed between the eye and the source of light, the pupillary aperture in this case constituting the transparent space, and the iris the blackened margin which gives it outline, so that those rays which are not intercepted by this curtain, pass onwards and ultimately form a picture of the pupil itself at the bottom of the eye.

When an opaque object is held either in a beam of light (bundle of parallel rays), or a pencil of light (rays proceeding from or towards some point), it intercepts a portion of the rays, and the space behind the object is in darkness. This dark space is called the shadow of the object Thus in figure 1, if the luminous body L emits a pencil of light which is stopped in its passage towards the screen by a round piece of blackened pasteboard, 0, the dark space between this and the screen, W, is the shadow.

A shadow may be received on a screen held near the object, when its outline will be similar to that of the body by which it is cast. Thus the shadow of the circle O (fig. 1,) is projected as a circle at S, on the white screen W.

The breadth of a shadow depends on the direction and disposal of the rays of light when they are stopped by the opposing body. These may be parallel, divergent, or convergent. In the remarks which immediately follow, I shall merely embody so much under each of these heads as relates to the subject of our present disquisition.

With respect to parallel rays it is to be observed, that the farther the luminous body is from an object, the less divergent are the rays which fall from it upon the object; or the more nearly do they approach to being parallel. “From a (fig. 2) there is much divergence, from b less, from c less still, and rays from a greater distance, as those represented by d and e, appear parallel. If the distance of the radiant point be very great, they really are so nearly parallel, that a very nice test is required to detect the deviation. Rays, for instance, coming to the earth from the sun, do not diverge the millionth of an inch in a thousand miles. Hence when we wish to make experiments with parallel rays, we take those of the sun.”* When such rays therefore are intercepted by an opaque body, the breadth of the shadow, for we are not now speaking of its length, is equal to that of the substance. The student in perspective, is aware of this fact, and the fine effect of a good landscape painting is to be referred in part to the strictness with which this relation is observed by the artist.

If the rays are divergent, as when the light-emitting body is very small, a mere point, the shadow is larger than the object. Thus if L (fig. 1) be the luminous body, and 0 the obstacle, the circular figure, S, on the screen, W, being a cross -section of a shadow which is continually increasing in breadth, is larger than the object O. “The shadow of a hand held between a candle and the wall is gigantic; and a small pasteboard figure of a man held in a divergent pencil of light, and near its source, throws a shadow as big as a real man. The latter fact has been amusingly illustrated by the art of making phantasmagoric shadows.” Divergent pencils are easily procured from a pin-hole, a taper, a street lamp, a carriage lamp, &c.

* See Arnott’s ‘Elements of Physics.’

When a convergent pencil of rays is obstructed by an opaque body, the shadow is smaller than the object, and if not received on a screen, would taper to a mere point. This is true of the shadows of all the planets, and of the earth, because they are less than the sun. It is exemplified when the moon falls into the earth’s shadow, and becomes eclipsed, or still better in a solar eclipse, when the moon being at her average distance from the earth, the shadow but just reaches the earth’s surface. Thus if S (fig. 1) represent the sun, and 0 the moon, that portion of the earth situated at L is in its shadow.

The shape of a shadow is regulated by the distance between the object and the screen on which the shadow is received. If this be great, the shadow bears no very definite relation in form to that of the object. On the contrary, it is a mere irregular darkened space, the boundaries of which are ill defined and the shape distorted. Thus a leaf at the distance of a yard or two from a wall, will, in the sunshine, give a shadow of indefinite outline, having a round instead of an angular edge: a leaf at a greater distance will produce a mere dimness, with an outline scarcely distinguishable. Instances of a like kind are afforded when the sun’s rays are obstructed by the topmost branches of a tree, or the summit of a tower, or by the intervention of passing clouds, which in their passage through the atmosphere contribute so much to the beauty and variety of the natural landscape, and are amongst those fleeting appearances which elude the vigilance of the pencil.

When the screen is at a great distance from the obstacle, as well as from the source of light, the shadow so far from taking the shape of the obstacle, will resemble that of the luminous body. Thus the shadow of an irregular body placed in the sun’s light is circular.

If on the other hand the object is brought to within a short distance of the screen, its shadow is so clearly defined as to be directly recognized as an exact facsimile, in shape, of the body itself. A leaf nearly close to the wall casts a shadow of a leaf.

“These observations regarding shadows are applicable to the illuminated space formed on a screen by making the sun’s light pass through an aperture.” This will be obvious, on reflecting, that if a shadow or darkened space be well defined, the adjacent, illuminated space must be equally so, and vice versa. For these are contrasted conditions, each of which causes the other to become visible. Neither light alone, nor darkness alone, but only contiguity of both will enable us to appreciate form. Hence light and shade are not only pleasant to the eye, but both are absolutely necessary for the distinguishing of one object from another. For this reason, probably, the visual organ is ever intuitively on the search for contrasts either of light, shade, or colour.

“When the screen is near the aperture, the illuminated portion is similar to the opening; but when the screen is sufficiently distant, it is similar to the luminous body. The interstices between the leaves of trees are so many small irregular apertures ; hence the cause of the numerous small bright circles seen in a sunny day in the shadow of a tree, or still more distinctly in that of a grove.”*

These simple laws which govern the projection of shadows, and which have been seen to adapt themselves to individual cases, may be easily verified. It is by their judicious combination, however, that we discover the best method of throwing large and well-defined images of small, near objects upon the bottom of the eye, which indeed constitutes the main design of our inquiry. Thus of the three modes of illuminating the object which have been enumerated, that is -obviously the best suited to our purpose which casts the broadest shadow. A divergent pencil of light is therefore chosen. In the next place he position of the screen demands attention, for on this, as we have seen, depends the definition as well as the enlargement of the image. Now in the investigation of small, near bodies, the screen cannot possibly be brought too close to the eye; indeed it is better to dispense with all artificial substitutes, and to use that kind of screen only which nature has provided. That is to say, the retina of the eye itself. This has accordingly been adopted.

Again, recollecting the impossibility of distinguishing outline at all, except by contrast,—a mass of shade bounded by light, or light by shade,—definite contiguous portions of the retina are simultaneously affected with such impressions by using a darkened tube to exclude the light, having small inlets of determined size to regulate its admission at one end, and openings to secure its transmission and exit at the other. In this way, light and dark spaces are brought into direct contiguity with a well-defined line of demarcation between them. Thus small objects are appreciable.

But, moreover, a shadow, like its substance, appears larger as it approaches the eye ; and the amount of enlargement is regulated by the same law. Hence the one is equivalent in this respect to the other: and as a shadow can be projected directly in front of the eye, and received as an image, it is thereby much magnified; nevertheless at such short distances, both shadow and substance, by any other process, would prove invisible.

Here, then, we have within our reach the combination of elements which appear necessary for examining small objects, at very short distances from the eye ; namely:—A darkened retina, a diminutive object less than the pupillary aperture, held close in front of the eye, awl a small divergent pencil of light. From which it results, that the object when held in this pencil, intercepts a portion of the light, and so casts a shadow greater than itself, which shadow is rendered visible by contrast, still further magnified by proximity, and eventually forms a visible image at the bottom of the eye.

This principle of opposition or dissimilitude of shade, as well as of colouring, called contrast, a term in very general use in painting, is of universal application, because it contributes not to the beauty only, but to the visibility of all objects. Whether these opposite and contiguous colours or shades are seen at the same time, and that this gives rise to the effect of which we are all sensible, as is generally supposed, or whether it results from attentively looking at the one and then at the other in-rapid succession, as was insisted upon by Sir Charles Bell, it is not our province now to inquire, although there are reasons for believing that both of these theories are correct, and that the former holds good for minute objects near to the eye, while the latter applies to larger ones at greater or common intervals. Dismissing hypothesis, however, we know that with respect to bodies viewed at ordinary distances, if a white figure be delineated on a white ground, or a black figure on a black ground, neither is visible; in the first there is no shade, and in the second no light, consequently there is no contrast But the slightest variation of shade in the figures in relation to their respective grounds, is sufficient to render each of them definite. Hence the effect of a well-executed engraving, in which, although no colour is introduced, but merely white and black to imitate’ light and shade, the appearance is natural and satisfactory.

Two simple experiments will serve to show the importance of attending to contrast with respect to the examination of very near objects. By the first it is seen that although a well-defined image is known to be certainly received on the retina, it is invisible when the retina and it happen to be equally illuminated. For this purpose, let perforations with a needle, the tenth of an inch apart, and arranged in the form of a circle of about a quarter of an inch in diameter, be made in a piece of blackened cardboard (fig. 3). When brought close to the eye, these apertures appear as a ring of luminous circles (fig. 4), the remaining part of the retina being in darkness. If now a round piece be cut out from the centre of the first card, a portion as large, for instance, as that which is traced in outline, but not actually excised in figure 3, so as to admit light through the very middle of the perforated circle ; it will be found that while the discs are known to be still received on the retina of the eye as circles, inasmuch as the perforations remain intact, and their position unaltered, they are not perceived as such, because the surface at the bottom of the eye on which the inner half of each falls is illuminated. Hence they appear as semicircles (see fig. 5).

From which it is manifest, that however well defined an object may be, and however assured we may feel that its image is actually portrayed on the bottom of the eye, it is not recognised unless the contiguous surfaces are oppositely affected with respect to light and shade.

The second experiment is the converse of the last, and goes to prove that an image is visible only when the retina of the eye and the object are unequally illuminated. Let that portion of a common sewing-needle which contains the eye be mounted on a slip of glass as if for the microscope; and let the paper with which it is covered, have a very small circular aperture through which to examine it, thus (fig. 6) :

On holding the object close to the naked eye, it is found to be altogether invisible. Nothing is seen but vacant space. It is matter of certainty, however, that the front rays are intercepted, and that a shadow of the needle is therefore really formed, but before reaching its destination, lateral rays stream into the eye in all directions, which neutralise the shadow, and so nothing is seen (fig. 7).

But when these lateral superfluous rays are excluded by using a divergent pencil of light only, as in the diascope, the shadow becomes visible; and not only is the exposed portion of the body of the needle seen, but its eye is well defined, and both appear considerably magnified (fig, 8).

Hence we may safely assume that all small bodies, whether transparent or opaque, are undistinguishable when held close to the naked eye, in broad day-light, or diffused light of any kind, but that if it were possible to distinguish them while in this position, they would appear magnified; and moreover, that this may actually be effected in many instances by the artificial contrivances to which we have been endeavouring to direct attention.

If a single object be retained in a given position before a screen, it will intercept the rays emitted from any number of separate luminous bodies, or sources of light, situated in front of it, and so cast as many shadows. In this way the shadows are multiplied. Thus if a finger be held within an inch or two of the wall, and a number of tapers at as many yards, the pencils of light from the lapers crossing the finger in different directions, and being intercepted by it, an equal number of shadows are cast on the wall at intervals, related to the position of the taper. And if an opening of given shape were substituted for the opaque object, as many illuminated spaces would be projected on the wall instead of the shadows.

This is effected on a small scale in the diascope, where small perforations which admit the light are substituted for the tapers, transparent designs on glass for the object, and the retina of the eye for the screen on the wall.

Beautiful combinations on a large scale might be projected on an extended surface by the multiplication of shadows, but it is not our purpose to examine bodies at ordinary distances.

Hitherto but few experiments have been instituted for the purpose of showing what kinds of images are produced without a lens by bodies held close in front of the eye. It is not likely, therefore, that all the necessary conditions shall be devised until more care and attention shall have been bestowed on this interesting branch of optics. Those which have been mentioned in the former papers, and are resumed in this, may possibly prove sufficient to provoke inquiry, inasmuch as they are based on legitimate conclusions from the known laws of optics, and are confirmed by experiments.

Small circular, as well as elongated openings for the transmission of light were used by Grimaldi, Newton, Fresnel, and Frauenbofer for investigating the phenomena, which light produces, when passing near the edges of bodies, a branch of optics which is called the inflexion, or the diffraction of light.

A divergent beam of light was obtained by causing the sun’s rays to pass through one of these apertures, and it was ascertained that the shadows of all bodies whatever, held in this light, were not only surrounded, but encroached on by fringes of colours.

The experiments themselves were instituted for the purpose of ascertaining the magnitude, form, colour, and number of such fringes, when examined either by common or by homogeneous light.

The aperture, moreover, was held six feet or upwards from the eye, and the fringes were seen either by throwing them on a smooth white surface, where they could be examined with the naked eye, or by looking at them with a magnifying glass, in which case their peculiarities could be more carefully investigated.

According to Sir David Brewster, this curious property of light was ably and successfully investigated by Fresnel, but the finest experiments on this subject are those of Frauenbofer.*

The experiments illustrative of these curious phenomena in which the light becomes bent into hyperbolic curves when passing near the edges of bodies, present nothing in common with those which form the subject of the present paper, in which the short space which is caused to intervene between the eye and the light precludes the possibility of detecting the coloured fringes, supposing indeed that these were the objects of which we were in search. The only point of resemblance between them consists in the minuteness of the apertures through which the light is admitted, and this serves to show that by the same simple means different ends may be accomplished. The mere peeping through a pin-hole without some definite purpose,—some object to be examined,—some particular theory to be investigated, were indeed a childish occupation. ft is more than probable that some of the followers of Newton were not much better engaged when we find the celebrated Goethe afterwards using the words, si per foramen exiquum, somewhat tauntingly in referent e to the fact of their so frequently introducing this term into their writings.

The curious figures now about to be described, and which are produced by the transmission of light through minute narrow apertures, although related to those which have been shown to result from mere perforation, contrast with them, nevertheless, in several important particulars, of which not the least striking, is the production of quadrangular planes which are formed when the light is partially intercepted during its passage towards the eye, and which when muliplied by increasing the number of lines which produce them, appear to fall together at their edges, and so to resemble hollow semitransparent figures of considerable beauty.

It may not be withheld, however, that this part of our subject is, so far as 1 have yet proceeded, circumscribed within narrow limits, being restricted chiefly to the formation of images on the retina of the eye, of those solids known as parallelopipeds, with composite forms, resulting from the multiplication of the simple ones. The peculiar feature in the experiments, consisting not so much in the novelty of the forms themselves, as in their mode of production.

We proceed to consider the phenomena which light presents when introduced through a narrow aperture held at a short interval of an inch or two from the eye.

When an exceedingly small transparent space or aperture* made on glass, or in tin-foil, is held at the end of a darkened tube about two inches long, and examined by placing the eye at the opposite end, and looking either at a white cloud or a window blind on a sunny day, or at a lamp with a ground glass shade, it appears altered in size, shape, and transparency.

In order to illustrate this, and to give an idea of the image thus formed on the retina of the eye, let AA (fig. 9) be one of these apertures fixed in the end of a darkened tube T, and let AC, AD be rays of light admitted through it. This light will diverge in lines AC and AD, and form an image CD at the bottom of the eye.

If the same aperture be removed a few inches farther from the eye, it presents nothing remarkable, and in no wise differs in appearance from what we know to be its real form, namely, a transparent line of exceedingly small dimensions. But if it be again made to approach the eye, it will appear, first, to be much magnified ; secondly, to have lost its rectangular outline, and to become rounded at either extremity; and thirdly, to be traversed by dark bands which take a direction parallel to its long axis, as shown in figure 9.

These glass covers are sold by the ounce, and are out into squares or circles of various sizes for the convenience of mounting. The Indian ink might be painted on the glass by hand; but, after having made several gross of such black discs, the author of these papers strongly recommends a little instrument which, although constructed for a totally different purpose, answers most admirably for this. It is the invention of Mr. Shadbolt, and is described and figured in the second edition of Quekett’s ‘Treatise on the Microscope,’ p. 289. This instrument is nothing more nor less than a miniature horizontal turning lathe, which is worked by the finger, and by which, with the assistance of a camel’s-hair pencil, the ink may be laid on in circles with the greatest nicety and expedition. When dry the narrow line is erased with a finely pointed and slightly moistened one-nibbed quill; or, what is better, a style of brass drawn along a flat ruler. When tin-foil is used instead of glass, it may be held on a piece of smooth flat lead ; an aperture of the required size can then be cut completely through with the point of a penknife.

The magnitude of the image is of course due to the proximity of the object to the visual organ, the rounded appearance of its ends to the circular form of the pupillary aperture, while the dark bands are produced by interference. These phenomena claim a more attentive examination.

That the apparent magnitude of the luminous space is so increased that the latter loses its linear form, and becomes a plane, is only another example indeed of the general law in optics, that all bodies, without exception, appear to grow larger as they approach the eye, and to diminish as they recede from it. But here an objection may be naturally raised by one who has not familiarised himself with such inquiries, or with the refracting powers of the eye. He finds from direct observation, opportunities for which occur daily, that remote objects do appear diminished in accordance with the law to which we have referred, and with respect to objects at such distances, he is inclined therefore to acquiesce in its correctness. But on holding a small body, a needle we will suppose, close to the eye, he is disappointed on discovering not only that it is not magnified, but that it is altogether invisible. Such an experiment has doubtless been performed by many, and from its failure it has been concluded, and not without an appearance of reason, that the body was held too near to the eye to be visible, which however is not the case, as we have endeavoured to show in a former experiment. But this very failure indicates the necessity of means to an end. For if having satisfied ourselves theoretically that the eye is endowed with certain capabilities, which we have reason to believe there is a possibility of developing; and if, on the application of certain known laws in optics, some definite figure which it was anticipated should certainly result, does not make its appearance, we are driven to the conclusion, that the failure is attributable to the experiment itself. A fresh trial, however, is perhaps crowned with success, and it is thus that we become possessed of new optical instruments, the value of which is directly proportionate to the importance of the laws they are designed to illustrate. For what are all optical instruments, but material combinations which serve to elucidate fundamental principles in optics by direct experiment ?

When one of these apertures, only the 1-200th of an inch broad, is brought close to the eye, its apparent size is about two inches. This is easily proved by observing that the breadth of its image covers that of a line two inches long, held up for the purpose of comparing the two at an interval of ten inches, the distance at which we are accustomed to view ordinary objects in order to gain an idea of their supposed extension in space, and so to guess at their real magnitude. If this distance of ten inches were always preserved, and if surfaces whose real dimensions are required were always compared with a scale held at such a distance, the eye might become instructed to appreciate relations of magnitude with far greater accuracy than it has hitherto attained.

The comparison of the image of a very small object in close proximity to the eye, with that of any larger object at the usual distance for distinct vision, thus affords a correct method of measuring the apparent increased magnitude of all small bodies ; and it cannot be too strongly impressed on the mind, that on looking through any aperture, whether small or great, it always appears as large as all we see through it. This has been happily expressed by an eminent writer. “If you shut one eye and hold immediately before the other a small circle of plain glass, of not more than half an inch in diameter, you may see through that circle the most extensive prospects, lawns and woods, and arms of the sea, and distant mountains. You are apt to imagine that the visible picture you thus see is immensely great and extensive ; but it can be no greater than the visible circle through which you see it. If, while you are looking through the circle, you could conceive a fairy hand and a fairy pencil to come between your eye and the glass, that pencil might delineate upon that little glass the outlines of all those extensive lawns and woods, and arms of the sea, and distant mountains, in the dimensions in which they are seen by the eye.”

Since this was penned, the fairy hand and the fairy pencil have both been actually discovered in the beautiful art of photography.

2. The extremities of the aperture appear rounded or semicircular.—We have seen how a circular perforation considered as a radiant point admits a divergent pencil of rays, the circular base of which forms a large round disc or image at the bottom of the eye (fig. 10). Now as a line mathematically considered is made up of a number of points, so a transparent line may be assumed to consist of a number of radiant points, each of which lying side by side in a linear direction will produce exactly such a series of overlapping circles at the bottom of the eye (fig. 11). Hence a small, narrow, transparent slit for the transmission of light when brought very near to the organ of vision, forms an image not of a line but of a plane rounded at either extremity.

3. The area of the aperture appears to be traversed by longitudinal dark bands.—“If we hold the band between the eye and a bright cloud, or the ground-glass of alighted lamp, and open the fingers so as to admit the smallest portion of light, we shall perceive similar dark bands intersecting the luminous space at regular intervals.” * The explanation of this phenomenon is founded on the interference of light, which, according to the undulatory theory, takes place when the undulations meet in opposite phases : these being superposed produce darkness.

We have now to examine the appearance of bodies held close to the eye, and in the light admitted through small linear apertures such as we have been describing.

Bearing in mind that the image of a linear aperture is not a line hut a plane, and that this can be revolved by inserting it in the distal end of the diascope, it will be seen that if the object chosen for examination be a similar linear aperture held close to the eye we obtain a second plane, the first of which can be revolved in front of the second, and so the two can be made to intersect at any angle.

In order to illustrate this, let the planes P and p) (fig. 12), about two inches apart, be inserted at the ends of a darkened tube, and let a small linear aperture, a and d, be made in each of them. Now by revolving the plane p, the one aperture will intersect the other. When common diffused light is admitted through the further aperture d, the greater part is intercepted in its passage towards the eye at E by the plane P, but that which is transmitted will partake of the form of the luminous space produced by the intersection of the two. Thus when the apertures cross at a right angle, as shown-in the figure, the image which meets the eye is a square, while it is rhombic at all other angles.

This may be further illustrated by cutting two oblong pieces, exactly similar in shape and size, from the lid and the bottom of a common pill-box. When the former is revolved upon the latter, the quadrangular planes to which we have referred are easily imitated (fig. 13).

Hence by holding two very narrow, linear apertures before the eye, and examining them by diffused light, all idea of mere linear extension is lost, and we obtain images of the square and all possible varieties of the rhomb.

It is worthy of notice that such planes do not differ in form from the modifications which a square undergoes in obedience to the laws of isometric perspective ; and it is obvious that if we are enabled to form any kind of rhombic plane at pleasure, by the mere revolution of one narrow transparent line upon another, we can by simply multiplying these lines multiply also the planes, which when united at their edges will present every appearance of a geometric solid.

And as a single line held close to the eye appears by intersection as a single isolated rhomb, so two or more such lines will form as many images, the relative position of which, as well as their number, can be regulated by that of the apertures which produce them.

If, for example, three fine transparent lines are projected in the form of an equilateral triangle, sufficiently small to be enclosed within the boundaries of a circle not bigger than the pupil of the eye (fig. 16), and if such an object be held close to the eye, and examined by the light admitted through the single aperture at the distal end, its image will be that of the triangular prism (see fig. 21, Pl. IV.).

On revolving the distal end of the instrument, which contains the single aperture, the prism will appear in a variety of aspects, four of which are shown in the figs. 21, 22, 23, 24, Pl. IV., in which the image is depicted as seen at each quarter of the circle.

In order to insure the proper effect, it is essential that each object (that which is held at the near or ocular extremity of the instrument) shall be mere transparent outline (figs. 14 to 20), in contradistinction to many of those which were examined by the light from the circular perforations, and which consisted of considerable surfaces of illuminated space.

A few of the outlines, which I have found to bring out the -most satisfactory results, are given in the annexed figures (figs. 14 to 20).

Fig. 14. The straight line.

15. Two straight lines meeting at 60”.

16. Three straight lines meeting at 60° (the equilateral triangle).

17. Four straight lines meeting at 90° (the square).

18. Four straight lines meeting at 60° and 120° (the rhomb).

19. Six straight lines meeting at 120° (the regular hexagon).

20. The circle.

The first of these objects is converted into the rhomb or the square, the second into two rhombs which are united at their edges, the third forms the triangular prism, the fourth presents an image of the cube, the fifth of the rhombohedron, the sixth of the regular hexagonal prism, while the seventh forms a very beautiful image of the cylindrical tube. All these figures appear hollow, and their terminal planes are filled in by the imagination.

Hitherto we have assumed the existence of a single linear aperture at the distal extremity of the instrument, and hence the production of a single image; but we can by increasing the number of the apertures multiply the images, just as when an object is held in the pencils of light proceeding from many simple perforations, and from the same cause.

The relative position and distance of the apertures will also regulate the disposition of the images ; thus if they are arranged at regular intervals the images will be so also, and if in rays proceeding from a common centre the images will radiate in like manner. Several composite forms of considerable beauty are thus produced.

If, for example, a small hexagon drawn in transparent outline (fig. 19), be viewed in the light admitted through several alternating and equidistant linear apertures, thus (fig. 21), there will be seen the images of as many regular hexagonal prisms having the same relative position ; and the resulting compound form will present a beautiful honeycomb appearance, as in the following figure (fig. 22).

If a transparent circle in outline (fig. 20) is substituted for the hexagon, the resulting form presents an analogous arrangement of cylindrical tubes, as in fig. 23.

Were I not afraid of tiring the patience of my readers, I might here proceed to describe and delineate a considerable variety of beautiful figures, which are produced when the apertures at the most distant extremity of the instrument are tinted with different colours. The introduction of tints in this way merely modifies and does not alter the results, anti sufficient has been said in the former papers to show that the beauty of each image is much enhanced by the process. But I am not unmindful that, however interesting the results of these simple experiments with mere transmitted light may be to myself, it would be encroaching on the pages of the ‘Microscopical Journal’ to enter more into detail on this part of my subject. Neither does it appear desirable to attempt to give an air of importance to a set of phenomena which, saving that they constitute legitimate illustrations of the subject in hand, have at present scarcely more than their novelty and beauty to recommend them.

*

See Chambers’ ‘Optics,’ p. 14.

*

See Sir David Brewster’s ‘Optics,’ Cabinet Cyclopædia ; also Herschel’s ‘Treatise on Light,’ $ 735; also Edinburgh Cyclopædia, art. ‘Optics,’ vol. xv., p. 556 ; also ‘Elements of Natural Philosophy,’ by Bird and Brooke.

*

Lines for this purpose may be drawn on glass, or cut through tin-foil. When the former process is adopted, a small round disc of Indian ink is laid on a circular piece of very thin glass, such as is used for the cover of microscopic objects, and which may be procures of any microscope maker.

The glass or tin-foil should now be mounted on a piece of cardboard of the required dimensions to fit the diascope, and having a hole about one quarter of an inch in diameter punched from its centre. For this purpose the thin tracing paper used by architects is the best, as it answers the double purpose of keeping the glass in its place, and preventing too much light passing through the apertures.

The dimensions of these apertures should be about the 1-15th of an inch by the 1-15th of an inch, or nine times as long as broad (9 : 1 ) These dimensions can be easily ascertained by a micrometer with the aid of a microscope.

*

See Woodward, on ‘Polarized Light.’