CHAPTER VII.DESCRIPTION OF DIFFERENT STEREOSCOPES.

Although the lenticular stereoscope has every advantage that such an instrument can possess, whether it is wanted for experiments on binocular vision—for assisting the artist by the reproduction of objects in relief, or for the purposes of amusement and instruction, yet there are other forms of it which have particular properties, and which may be constructed without the aid of the optician, and of materials within the reach of the humblest inquirers. The first of these is—

In this form of the instrument, shewn inFig. 28, the pictures are seen by reflexion from two specula or prisms placed at an angle of 90°, as in Mr. Wheatstone’s instrument. In other respects the two instruments are essentially different.

In Mr. Wheatstone’s stereoscope he employs two mirrors, eachfour inchessquare—that is, he employsthirty-twosquare inches of reflecting surface, and is therefore under the necessity of employing glass mirrors, and making a clumsy, unmanageable, and unscientific instrument, with all the imperfections which we have pointed out in a preceding chapter. It is not easy to understand whymirrors of such a size should have been adopted. The reason of their being made of common looking-glass is, that metallic or prismatic reflectors of such a size would have been extremely expensive.

Fig. 28.

It is obvious, however, from the slightest consideration, that reflectors of such a size are wholly unnecessary, and thatone squareinch of reflecting surface, in place ofthirty-two, is quite sufficient for uniting the binocular pictures. We can, therefore, at a price as low as that of the 4-inch glass reflectors, use mirrors of speculum metal, steel, or even silver, or rectangular glass prisms, in which the images are obtained by total reflexion. In this way the stereoscope becomes a real optical instrument, in which the reflexion is made from surfaces single and perfectly flat, as in the second reflexion of the Newtonian telescope and the microscope of Amici, in which pieces of looking-glass were never used. By thus diminishing the reflectors, we obtain a portable tubular instrument occupying nearly as little room as the lenticular stereoscope, as will be seen fromFig. 28, whereABCDis a tube whose diameter is equal to the largest size of one of the binocular pictures which we propose to use, the left-eye picture being placed atCD, and the right-eye one atAB. If they are transparent, they will be illuminated through paper or ground-glass, and if opaque, through openings in the tube. The image ofAB, reflected to the left eyeLfrom the small mirrormn, and that ofCDto the right eyeRfrom the mirrorop, will be united exactly as in Mr. Wheatstone’s instrument already described. The distance of the two ends,n,p, of the mirrors should be a little greater than the smallest distance between the two eyes. If we wish to magnify the picture, we may use two lenses, or substitute for the reflectors a totally reflecting glass prism, in which one or two of its surfaces are made convex.[40]

This very simple instrument, which, however, answers only for symmetrical figures, such as those shewn atAandB, which must be either two right-eye or two left-eye pictures, is shewn inFig. 29. A single reflector,MN, which may be either a piece of glass, or a piece of mirror-glass, or a small metallicspeculum, or a rectangular prism, is placed atMN. If we look into it with the left eyeL, we see, by reflexion from its surface atC, a reverted image, or a right-eye picture of the left-eye pictureB, which, when seen in the directionLCA, and combined with the figureA, seen directly with the right eyeR, produces araisedcone; but if we turn the reflectorLround, so that the right eye may look into it, and combine a reverted image ofA, with the figureBseen directly with the left eyeL, we shall see ahollowcone. AsBC+CLis greater thanRA, the reflected image will be slightly less in size than the image seen directly, but the difference is not such as to produce any perceptible effect upon the appearance of the hollow or the raised cone. By bringing the picture viewed by reflexion a little nearer the reflectorMN, the two pictures may be made to have the same apparent magnitude.

Fig. 29.

If we substitute for the single reflectorMN, two reflectors such as are shewn atM,N,Fig. 30, or a prismP, which gives two internal reflexions, we shall have a general stereoscope, which answers for landscapes and portraits.

Fig. 30.

The reflectorsM,NorPmay be fitted up in a conical tube, which has an elliptical section to accommodate two figures at its farther end, the major axis of the ellipse being parallel to the line joining the two eyes.

This instrument differs from the preceding in having a single reflector,MN, M′N′, for each eye, as shewn inFig. 31, and the effect of this is to exhibit,at the same time, the raised and the hollow cone. The image ofB, seen by reflexion fromMNat the pointC, is combined with the picture ofA, seen directly by therighteyeR, and forms ahollowcone; while the image ofA, seen by reflexion fromM′N′at the pointC′, is combined with the picture ofB, seen directly by the left eyeL, and forms araisedcone.

Fig. 31.Fig. 32.

Fig. 31.

Fig. 32.

Another form of the double reflecting stereoscope is shewn inFig. 32, which differs from that shewn inFig. 31in the position of the two reflectors and of the figures to be united. The reflecting faces of the mirrors are turned outwards, their distance being less than the distance between the eyes, and the effect of this is to exhibit at the same time theraisedand thehollowcone, the hollow cone being now on the right-hand side.

If in place of two right or two left eye pictures, as shewn in Figs.29,31, and32, we use one right eye and one left eye picture, and combine the reflected image of the one with the reflected image of the other, we shall have araisedcone with the stereoscope, shewn inFig. 31, and ahollowcone with the one inFig. 32.

The double reflecting stereoscope, in both its forms, is a general instrument for portraits and landscapes, and thus possesses properties peculiar to itself.

The reflectors may be glass or metallic specula, or total reflexion prisms.

This form of the stereoscope is a very interesting one, and possesses valuable properties. It requires only a small prism andonediagram, or picture of the solid, as seen by one eye; the other diagram, or picture which is to be combined with it, being created by total reflexion from the base of the prism. This instrument is shewn inFig. 33, whereDis the picture of a cone as seen by the left eyeL, andABCa prism, whose baseBCis so large, that when the eye is placed close to it, it may see, by reflexion, the whole of the diagramD. The anglesABC, ACBmust be equal, but may be of any magnitude. Great accuracy in the equality of the angles is not necessary; and a prism constructed,by a lapidary, out of a fragment of thick plate-glass, the faceBCbeing one of the surfaces of the plate, will answer the purpose. When the prism is placed ata,Fig. 34, at one end of a conical tubeLD, and the diagramDat the other end, in a cap, which can be turned round so as to have the linemn,Fig. 33, which passes through the centre of the base and summit of the cone parallel to the line joining the two eyes, the instrument is ready for use. The observer places his left eye atL, and views with it the pictureD, as seen by total reflexion from the baseBCof the prism,Figs. 33and35, while with his right eyeR,Fig. 33, he views the real picture directly. The first of these pictures being the reverse of the secondD, like allpictures formed by one reflexion, we thus combine two dissimilar pictures into araisedcone, as in the figure, or into ahollowone, if the picture atDis turned round 180°. If we place the images of two diagrams, one like one of those atA,Fig. 31, and the other like the one atB, vertically above one another, we shall then see, at the same time, theraisedand thehollowcone, as produced in the lenticular stereoscope by the three diagrams, two like those inFig. 31, and a third like the one atA. When the prism is good, the dissimilar image, produced by the two refractions atBandC, and the one reflexion atE, is, of course, more accurate than if it had been drawn by the most skilful artist; and therefore this form of the stereoscope has in this respect an advantage over every other in which two dissimilar figures, executed by art, are necessary. In consequence of the length of the reflected pencilDB+BE+EC+CLbeing a little greater than the direct pencil of raysDR, the two images combined have not exactly the same apparent magnitude; but the difference is not perceptible to the eye, and a remedy could easily be provided were it required.

Fig. 33.Fig. 34.

Fig. 33.

Fig. 34.

If the conical tubeLDis held in the left hand, the left eye must be used, and if in the right hand the right eye must be used, so that the hand may not obstruct the direct vision of the drawing by the eye which does not look through the prism. The coneLDmust be turned round slightly in the hand till the linemnjoining the centre and apex of the figure is parallel to the line joining the two eyes. The same line must be parallel to the plane of reflexion from the prism; but this parallelism is secured by fixing the prism and the drawing.

It is scarcely necessary to state that this stereoscope is applicable only to those diagrams and forms where the one image is the reflected picture of the other.

Fig. 35.

If we wish to make a microscopic stereoscope of this form, or to magnify the drawings, we have only to cement plano-convex lenses, of the requisite focal length, upon the facesAB, ACof the prism, or, what is simpler still, to use a section of a deeply convex lensABC,Fig. 35, and apply the other half of the lens to the right eye, the faceBChaving been previously ground flat and polished for the prismatic lens. By using a lens of larger focus for the right eye, we may correct, if required, the imperfection arising from the difference of paths in the reflected and direct pencils. This difference, though trivial, might be corrected, if thought necessary, by applying to the right eye the central portion of the same lens whose margin is used for the prism.

Fig. 36.

If we take the drawing of a six-sided pyramid as seen by the right eye, as shewn inFig. 36, and place it in the total-reflexion stereoscope atD,Fig. 33, so that the lineMNcoincides withmn, and is parallel to the line joining the eyes of theobserver, we shall perceive a perfect raised pyramid of a given height, the reflected image ofCD,Fig. 36, being combined withAF, seen directly. If we now turn the figure round 30°,CDwill come into the positionAB, and unite withAB, and we shall still perceive a raised pyramid, with less height and less symmetry. If we turn it round 30° more,CDwill be combined withBC, and we shall still perceive a raised pyramid with still less height and still less symmetry. When the figure is turned round other 30°, or 90° degrees from its first position,CDwill coincide withCDseen directly, and the combined figures will be perfectly flat. If we continue the rotation through other 30°,CDwill coincide withDE, and a slightly hollow, but not very symmetrical figure, will be seen. A rotation of other 30° will bringCDinto coalesence withEF, and we shall see a still more hollow and more symmetrical pyramid. A further rotation of other 30°, making 180° from the commencement, will bringCDinto union withAF; and we shall have a perfectly symmetrical hollow pyramid of still greaterdepth, and the exact counterpart of the raised pyramid which was seen before the rotation of the figure commenced. If the pyramid had been square, theraisedwould have passed into thehollowpyramid by rotations of 45° each. If it had been rectangular, the change would have been effected by rotations of 90°. If the space between the two circular sections of the cone inFig. 31had been uniformly shaded, or if lines had been drawn from every degree of the one circle to every corresponding degree in the other, in place of from every 90th degree, as in the Figure, the raised cone would have gradually diminished in height, by the rotation of the figure, till it became flat, after a rotation of 90°; and by continuing the rotation it would have become hollow, and gradually reached its maximum depth after a revolution of 180°.

Although the idea of uniting the binocular pictures by a single prism applied to one eye, and refracting one of the pictures so as to place it upon the other seen directly by the other eye, or by a prism applied to each eye, could hardly have escaped the notice of any person studying the subject, yet the experiment was, so far as I know, first made and published by myself. I found two prisms quite unnecessary, and therefore abandoned the use of them, for reasons which will be readily appreciated. This simple instrument is shewn inFig. 37, whereA, Bare the dissimilar pictures, andPa prism with such a refracting angle as is sufficient to lay the image ofAuponB, as seen by the right eye. If we place asecondprism before the eyeR, we require it only to have half the refracting angle of the prismP, because each prism nowrefracts the picture opposite to it only half way betweenAandB, where they are united. This, at first sight, appears to be an advantage, for as there must always be a certain degree of colour produced by a single prism, the use of two prisms, with half the refracting angle, might be supposed to reduce the colour one-half. But while the colour produced by each prism is thus reduced, the colour over the whole picture is the same. Each luminous edge with two prisms has both red and blue tints, whereas with one prism each luminous edge has only one colour, either red or blue. If the picture is very luminous these colours will be seen, but in many of the finest opaque pictures it is hardly visible. In order, however, to diminish it, the prism should be made of glass with the lowest dispersive power, or with rock crystal. A single plane surface, ground and polished by a lapidary, upon the edge of a piece of plate-glass, a little larger thanthe pupil of the eye, will give a prism sufficient for every ordinary purpose. Any person may make one in a few minutes for himself, by placing a little bit of good window glass upon another piece inclined to it at the proper angle, and inserting in the angle a drop of fluid. Such a prism will scarcely produce any perceptible colour.

Fig. 37.

If a single-prism reflector is to be made perfect, we have only to make it achromatic, which could be doneextempore, by correcting the colour of the fluid prism by another fluid prism of different refractive and dispersive power.

With a good achromatic prism the single-prism stereoscope is a very fine instrument; and no advantage of any value could be gained by usingtwo achromatic prisms. In the article on New Stereoscopes, published in the Transactions of the Royal Society of Arts for 1849, and in the Philosophical Magazine for 1852, I have stated in a note thatI believedthat Mr. Wheatstone had usedtwo achromatic prisms. This, however, was a mistake, as already explained,[41]for such an instrument was never made, and has never been named in any work previous to 1849, when it was mentioned by myself in the note above referred to.

If we make a double prism, or join two, as shewn atP,P′inFig. 38, and apply it to two dissimilar figuresA,B, one of which is the reflected image of the other, so that with the left eyeLand the prismPwe place the refracted image ofAuponB, as seen by the right eyeR, we shall see araisedcone, and if withthe prismP′we place the image ofBuponAwe shall see ahollowcone. If we place the left eyeLatO, behind the common base of the prism, we shall see with one-half of the pupil thehollowcone and with the other half theraisedcone.

Fig. 38.

As the eyes themselves form a stereoscope to those who have the power of quickly converging their axes to points nearer than the object which they contemplate, it might have been expected that the first attempt to make a stereoscope for those who do not possess such a power, would have been to supply them with auxiliary eyeballs capable of combining binocular pictures of different sizes at different distances from the eye. This, however, has not been the case, and the stereoscope for this purpose, which we are about to describe, is one of the latest of its forms.

Fig. 39.Fig. 40.

Fig. 39.

Fig. 40.

InFig. 39,MNis a small inverting telescope, consisting of two convex lensesM,N, placed at the sum of theirfocal distances, andOPanother of the same kind. When the two eyes,R,L, look through the two telescopes directly at the dissimilar picturesA,B, they will see them with perfect distinctness; but, by the slightest inclination of the axes of the telescopes, the two images can be combined, and the stereoscopic effect immediately produced. With the dissimilar pictures in the diagram ahollowcone is produced; but if we look atBwith the telescopeM′N′, as inFig. 40, and atA′withO′P′, araisedcone will be seen. With the usual binocular slides containing portraits or landscapes, thepictures are seen in relief by combining the right-eye one with the left-eye one.

The instrument now described is nothing more than a double opera-glass, which itself forms a good stereoscope. Owing, however, to the use of a concave eye-glass, the field of view is very small, and therefore a convex glass, which gives a larger field, is greatly to be preferred.

The little telescopes,MN, OP, may be made one and a half or even one inch long, and fitted up, either at a fixed or with a variable inclination, in a pyramidal box, like the lenticular stereoscope, and made equally portable. One of these instruments was made for me some years ago by Messrs. Horne and Thornthwaite, and I have described it in theNorth British Review[42]as having the properties of aBinocular Cameoscope, and of what has been absurdly called aPseudoscope, seeing that every inverting eye-piece and every stereoscope is entitled to the very same name.

The little telescope may be made of one piece of glass,convexat each end, orconcaveat the eye-end if a small field is not objectionable,—the length of the piece of glass, in thefirstcase, being equal to thesum, and, in thesecondcase, to thedifferenceof the focal lengths of the virtual lenses at each end.[43]

As it is impossible to obtain, by the ocular stereoscope, pictures in relief from the beautiful binocular slides which are made in every partof the world for the lenticular stereoscope, it is very desirable to have a portable stereoscope which can be carried safely in our purse, for the purpose of examining stereoscopically all such binocular pictures.

If placed together with their plane sides in contact, a plano-convex lens,AB, and a plano-concave one,CD, of the same glass and the same focal length, will resemble a thick watch-glass, and on looking through them, we shall see objects of their natural size and in their proper place; but if we slip the concave lens,CD, to a side, as shewn inFig. 41, we merely displace the image of the object which we view, and the displacement increases till the centre of the concave lens comes to the margin of the convex one. We thus obtain a variable prism, by means of which we can, with the left eye, displace one of the binocular pictures, and lay it upon the other, as seen by the right eye. We may use semi-lenses or quarters of lenses, and we may make them achromatic or nearly so if we desire it. Double convex and double concave lenses may also be used, and the motion of the concave one regulated by a screw. In one which I constantly use, the concave lens slides in a groove over a convex quarter-lens.

Fig. 41.

By employing two of these variable prisms, we have anUniversal Stereoscopefor uniting pictures of various sizes and at various distances from each other, and the prisms may be placed in a pyramidal box, like the lenticular stereoscope.

If we take a reading-glass whose diameter is not less than two inches and three quarters, and look through it with both eyes at a binocular picture in which the right-eye view is on the left hand, and the left-eye view on the right hand, as in the ocular stereoscope, we shall see each picture doubled, and the degree of separation is proportional to the distance of the picture from the eye. If the distance of the binocular pictures from each other is small, the two middle images of the four will be united when their distance from the lens is not very much greater than its focal length. With a reading-glass 4½ inches in diameter, with a focal length of two feet, binocular pictures, in which the distance of similar parts isnineinches, are united without any exertion of the eyes at the distance of eight feet. With the same reading-glass, binocular pictures, at the usual distance of 2½ inches, will be united at the distance of 2¼ or even 2½ feet. If we advance the reading-glass when the distance is 2 or 3 feet, the picture in relief will be magnified, but, though the observer may not notice it, the separated images are now kept united by a slight convergency of the optic axes. Although the pictures are placed so far beyond the anterior focus of the lens, they are exceedingly distinct. The distinctness of vision is sufficient, at least to long-sighted eyes, when the pictures are placed within 16 or 18 inches of the observer, that is, 6 or 8 inches nearer the eye than the anterior focus of the lens. In this case we can maintain the union of the pictures only when we begin to view them at a distance of 2½ or 3 feet, and then gradually advance the lenswithin 16 or 18 inches of the pictures. At considerable distances, the pictures are most magnified by advancing the lens while the head of the observer is stationary.

The object of this instrument is to unite the transient pictures of groups of persons or landscapes, as delineated in two dissimilar pictures, on the ground-glass of a binocular camera. If we attach to the back of the camera a lenticular stereoscope, so that the two pictures on the ground-glass occupy the same place as its usual binocular slides, we shall see the group of figures in relief under every change of attitude, position, and expression. The two pictures may be formed in the air, or, more curiously still, upon a wreath of smoke. As the figures are necessarily inverted in the camera, they will remain inverted by the lenticular and every other instrument but the opera-glass stereoscope, which inverts the object. By applying it therefore to the camera, we obtain an instrument by which the photographic artist can make experiments, and try the effect which will be produced by his pictures before he takes them. He can thus select the best forms of groups of persons and of landscapes, and thus produce works of great interest and value.

The chromatic stereoscope is a form of the instrument in which relief or apparent solidity is given to a single figure with different colours delineated upon a plane surface.

If we look with both eyes through a lensLL,Fig. 42, about 2½ inches in diameter or upwards, at any object having colours of different degrees of refrangibility, such as the coloured boundary lines on a map, a red rose among green leaves and on a blue background, or any scarlet object whatever upon a violet ground, or in general any two simple colours not of the same degree of refrangibility,the differently coloured parts of the object will appear at different distances from the observer.

Fig. 42.

Let us suppose the rays to beredandviolet, those which differ most in refrangibility. If the red rays radiate from the anterior focusR, or red rays of the lensLL, they will emerge parallel, and enter the eye atm; but the violet rays radiating from the same focus, being more refrangible, will emerge in a state of convergence, as shewn atmv,nv, the red rays beingmr,nr. The part of the object, therefore, from which the red rays come, will appear nearer to the observer than the parts from which the violet rays come, and if there are other colours or rays of intermediate refrangibilities, they will appear to come from intermediate distances.

If we place a smallredandvioletdisc, like the smallest wafer, beside one another, so that the line joining their centres is perpendicular to the line joining the eyes, and suppose that rays from both enter the eyes with their optical axes parallel, it is obvious that the distance between the violet images on each retina will belessthan the distance between theredimages, and consequently the eyes will require to converge their axes to anearerpoint in order to unite the red images, than in order to unite the violet images. The red images will therefore appear at this nearer point of convergence, just as, in the lenticular stereoscope, the more distant pair of points in the dissimilar images appear when united nearer to the eye. By the two eyes alone, therefore, we obtain a certain, though a small degree of relief from colours. With the lensLL, however, the effect is greatly increased, and we have thesumof thetwoeffects.

From these observations, it is manifest that the reverse effect must be produced by a concave lens, or by the common stereoscope, whentwocoloured objects are employed or united. Thebluepart of the object will be seennearerthe observer, and the red part of it moreremote. It is, however, a curious fact, and one which appeared difficult to explain, that in the stereoscope the colour-relief was not brought out as might have been expected. Sometimes the red was nearest the eye, and sometimes the blue, and sometimes the object appeared without any relief. The cause of this is, that the colour-relief given by the common stereoscope was the opposite of that given by the eye, and it was only thedifferenceof these effects that ought to have been observed; and though theinfluence of the eyes was an inferior one, it often acted alone, and sometimes ceased to act at all, in virtue of that property of vision by which we see only with one eye when we are looking with two.

In the chromatic stereoscope,Fig. 42, the intermediate partmnof the lens is of no use, so that out of the margin of a lens upwards of 2½ inches in diameter, we may cut a dozen of portions capable of making as many instruments. These portions, however, a little larger only than the pupil of the eye, must be placed in the same position as inFig. 42.

All the effects which we have described are greatly increased by using lenses of highly-dispersing flint glass, oil of cassia, and other fluids of a great dispersive power, and avoiding the use of compound colours in the objects placed in the stereoscope.

It is an obvious result of these observations, that in painting, and in coloured decorations of all kinds, the red or less refrangible colours should be given to the prominent parts of the object to be represented, and theblueor more refrangible colours to the background and the parts of the objects that are to retire from the eye.

The lenticular form of the stereoscope is admirably fitted for its application to small and microscopic objects. The first instruments of this kind were constructed by myself with quarter-inch lenses, and were 3 inches long and only 1 and 1½ deep.[44]They may be carried in the pocket, and exhibit all the properties of the instrument to the greatest advantage. The mode of constructing and using the instrumentis precisely the same as in the common stereoscope; but in taking the dissimilar pictures, we must use either a small binocular camera, which will give considerably magnified representations of the objects, or we must procure them from the compound microscope. The pictures may be obtained with a small single camera, by first taking one picture, and then shifting the object in the focus of the lens, through a space corresponding with the binocular angle. To find this space, which we may callx, makedthe distance of the object from the lens,nthe number of times it is to be magnified, or the distance of the image behind the lens, andDthe distance of the eyes; then we shall have

that is, the space is equal to the distance between the eyes divided by the magnifying power.

With the binocular microscope of Professor Riddell,[45]and the same instrument as improved by M. Nachet, binocular pictures are obtained directly by having them drawn, as Professor Riddell suggests, by the camera lucida, but it would be preferable to take them photographically.

Portraits for lockets or rings might be put into a very small stereoscope, by folding the one lens back upon the other.

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