If we now wish, by directing the axes of the eyes beyond MN to b, to ascertain the value of Ce', which will give different depths d of the hollow solids corresponding to different values of Cb, we

E

dE

shall have Ab : =d: Cc and Ce' = ; which, making AC8

2

2AB

inches as before, will give the following results:

The values of h and d, when the excentricities Cc, Ce', as we may call them, are known, will be found by the formulæ

h=

CcE 2AB

and d=

C&E 2Ab

As Cc is always equal to Cd' in each pair of figures or dissimilar pictures, the depth of the hollow solid will always appear much greater than the height of the raised solid one. When Cc and Cd are both 0.75 h: d=3:12, and when they are both 0·4166, h: d=2: 4, and when they are both 0.139 h:d=0·8:1·0.

III. Account of a Binocular Camera, and of a Method of obtaining Drawings of Full Length and Colossal Statues, and of Living Bodies, which can be exhibited as Solids by the Stereoscope. By Sir DAVID BREWSTER, K.H., D.C.L., F.R.S., and V.P.R.S. Edin.*

IN

N explaining the construction and use of the lenticular and other stereoscopes, I have referred only to the duplication and union of the dissimilar drawings on a plane of geometrical and symmetrical solids. The most interesting application, however, of these instruments is to the dissimilar representations of statues and living bodies of all sizes and forms, and also to natural scenery, and the objects which enter into its composition. Professor

* From Trans. of Royal Scottish Society of Arts, 1849. See also Report of British Association at Birmingham, 1849, Trans. of Sect., p. 5.

Wheatstone had previously applied his stereoscope to the union of dissimilar drawings of small statues, taken by the Daguerreotype and Talbotype processes; and in an essay on Photography, lately published*, I have mentioned its application to statues of all sizes, and even to living figures, by means of a binocular camera. The object of the present paper is to describe the binocular camera, and to explain the principles and methods by which this application of the stereoscope is to be carried into effect.

The vision of bodies of three dimensions, or of groups of such bodies combined, has never been sufficiently studied either by artists or philosophers. Leonardo da Vinci, who united in a remarkable degree a knowledge of art and science, has, in a passage of his Trattato della Pittura, quoted by Dr. Smith of Cambridget, made a brief reference to it insofar as binocular vision is concerned; but till the publication of Professor Wheatstone's interesting memoir "On some remarkable and hitherto unobserved Phænomena of Binocular Vision ‡," the subject had excited no attention.

In order to understand the subject, we shall first consider the vision with one eye of objects of three dimensions, when of different magnitudes and placed at different distances. When we thus view a building or a full-length or colossal statue at a short distance, a picture of all its visible parts is formed on the retina. If we view it at a greater distance, certain parts cease to be seen, and other parts come into view; and this change on the picture will go on, but will become less and less perceptible as we retire from the original. If we now look at the building or statue from a distance through a telescope, so as to present it to us with the same distinctness, and of the same apparent magnitude as we saw it at our first position, the two pictures will be essentially different; all the parts which ceased to be visible as we retired will still be invisible, and all the parts which were not seen at our first position, but became visible by retiring, will be seen in the telescopic picture. Hence the parts seen by the near eye, and not by the distant telescope, will be those towards the middle of the building or statue, whose surfaces converge, as it were, towards the eye; while those seen by the telescope, and not by the eye, will be the external parts of the object whose surfaces converge less, or approach to parallelism. It will depend on the nature of the building or the statue which of these pictures gives us the most favourable representation of it.

* North British Review, vol. vii. p. 502, August 1847.
+ Complete System of Optics, vol. ii. Remarks, p. 41. § 244.

Phil. Trans., 1838, p. 371; see also Edinburgh Transactions, vol. xv. pp. 349 and 663.

If we now suppose the building or statue to be reduced in the most perfect manner,-to half its size, for example, then it is obvious that these two perfectly similar solids will afford a different picture, whether viewed by the eye or by the telescope. In the reduced copy, the inner surfaces visible in the original will disappear, and the outer surfaces become visible; and, as formerly, it will depend on the nature of the building or the statue whether the reduced or the original copy gives the best picture.

If we repeat the preceding experiments with two eyes in place of one, the building or statue will have a different appearance. Surfaces and parts, formerly invisible, will become visible, and the body will be better seen because we see more of it; but then the parts thus brought into view being seen, generally speaking, with one eye, will have only one-half the illumination of the rest of the picture. But, though we see more of the body in binocular vision, it is only parts of vertical surfaces perpendicular to the line joining the eyes that are thus brought into view, the parts of similar horizontal surfaces remaining invisible as with one eye. It would require a pair of eyes placed vertically, that is, with the line joining them in a vertical direction, to enable us to see the horizontal as well as the vertical surfaces; and it would require a pair of eyes inclined at all possible angles, that is, a ring of eyes 24 inches in diameter, to enable us to have a perfectly symmetrical view of the statue.

These observations will enable us to answer the question, whether or not a reduced copy of a statue, of precisely the same form in all its parts, will give us, either by monocular or binocular vision, a better view of it as a work of art. As it is the outer parts or surfaces of a large statue that are invisible, its great outline and largest parts must be best seen in the reduced copy; and consequently its relief, or third dimension in space, must be much greater in the reduced copy. This will be better understood if we suppose a sphere to be substituted for the statue. If the sphere exceeds in diameter the distance between the pupils of the right and left eye, or 21 inches, we shall not see a complete hemisphere unless from an infinite distance. If the sphere is larger, we shall see only a segment, whose relief, in place of being equal to the radius of the sphere, is equal only to the versed sine of half the visible segment. Hence it is obvious that a reduced copy of a statue is not only better seen from more of its parts being visible, but is also seen in stronger relief.

With these observations, we shall be able to determine the best method of obtaining dissimilar plane drawings of full-length and colossal statues, &c., in order to reproduce them in three dimensions by means of the stereoscope. Were a painter called upon to take drawings of a statue, as seen by each eye, he would

fix, at the height of his eyes, a metallic plate with two small holes in it, whose distance is equal to that of his eyes, and he would then draw the statue as seen through the holes by each eye. These pictures, however, whatever be his skill, would not be such as to reproduce the statue by their union. An accuracy, almost mathematical, is necessary for this purpose; and this can only be obtained from pictures executed by the processes of the Daguerreotype and Talbotype. In order to do this with the requisite nicety, we must construct a binocular camera, which will take the pictures simultaneously and of the same size; that is, a camera with two lenses of the same aperture and focal length, placed at the same distance as the two eyes. As it is impossible to grind and polish two lenses, whether single or achromatic, of exactly the same focal lengths, even if we had the very same glass for each, I propose to bisect the lenses, and construct the instrument with semilenses, which will give us pictures of precisely the same size and definition. These lenses should be placed with their diameters of bisection parallel to one another, and at the distance of 21 inches, which is the average distance of the eyes in man; and, when fixed in a box of sufficient size, will form a binocular camera, which will give us, at the same instant, with the same lights and shadows, and of the same size, such dissimilar pictures of statues, buildings, landscapes, and living objects, as will reproduce them in relief in the stereoscope.

It is obvious, however, from observations previously made, that even this camera will only be applicable to statues of small dimensions, which have a high enough relief, from the eyes seeing, as it were, well around them, to give sufficiently dissimilar pictures for the stereoscope. As we cannot increase the distance between our eyes, and thus obtain a higher degree of relief for bodies of large dimensions, how are we to proceed in order to obtain drawings of such bodies of the requisite relief? Let us suppose the statue to be colossal, and ten feet wide, and that dissimilar drawings of it about three inches high are required for the stereoscope. These drawings are forty times narrower than the statue, and must be taken at such a distance that, with a binocular camera having its semilenses 21 inches distant, the relief would be almost evanescent. We must, therefore, suppose the statue to be reduced n times, and place the semilenses of the binocular camera at the distance n x 21 inches. If n=10, the statue will be reduced to, or to 1 foot, and nx 2, or the distance of the semilenses will be 25 inches. If the semilenses are placed at this distance, and dissimilar pictures of the colossal statue taken, they will reproduce by their union a statue one foot high, which will have exactly the same appear

ance and relief as if we had viewed the colossal statue with eyes 25 inches distant. But the reproduced statue will have also the same appearance and relief as a statue a foot high, reduced from the colossal one with mathematical precision; and therefore it will be a better and a more relieved representation of the work of art than if we had viewed the colossal original with our own eyes, either under a greater, an equal, or a less angle of apparent magnitude.

We have supposed that a statue a foot broad will be seen in proper relief by binocular vision; but it remains to be decided whether or not it would be more advantageously seen, if reduced with mathematical precision to a breadth of 2 inches, the width of the eyes, which gives the vision of a hemisphere 2 inches in diameter, with the most perfect relief. If we adopt this principle, and call B the breadth of the statue of which we require

B

dissimilar pictures, we must make n= and n × 21=B, that is, 212 the distance of the semilenses in the binocular camera, or of the semilenses in two cameras, if two are necessary, must be made equal to the breadth of the statue.

In the same manner we may obtain dissimilar pictures of living bodies, buildings, natural scenery, machines, and objects of all kinds, of three dimensions, and reproduce them by the stereoscope, so as to give the most accurate idea of them to those who could not understand them in drawings of the greatest

accuracy.

The art which we have now described cannot fail to be regarded as of inestimable value to the sculptor, the painter, and the mechanist, whatever be the nature of his production in three dimensions. Lay figures will no longer mock the eye of the painter. He may delineate at leisure on his canvas, the forms of life and beauty, stereotyped by the solar ray and reconverted into the substantial objects from which they were obtained, brilliant with the same lights and chastened with the same shadows as the originals. The sculptor will work with similar advantages. Superficial forms will stand before him in three dimensions, and while he summons into view the living realities from which they were taken, he may avail himself of the labours of all his predecessors, of Pericles as well as of Canova; and he may virtually carry in his portfolio the mighty lions and bulls of Nineveh,-the gigantic sphinxes of Egypt,-the Apollos and Venuses of Grecian art, and all the statuary and sculpture which adorn the galleries and museums of civilized nations.