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tions by means of lines, he will finally give his assent to them when he has made the following experiment :Standing near a column, and shutting each of the eyes in succession ;-when the right eye is shut, some of those parts of the column which were previously seen by the right eye on the right side of the column, will not now be seen by the left eye; and when the left eye is shut, some of those parts which were formerly seen by the left eye on the left side of the column, will not now be seen by the right eye. But when we, at the same time, open both eyes, both these will be seen, for a greater part is concealed when we look with either of the two eyes, than when we look with both at the same time."1
In such distinct and unambiguous terms, intelligible to the meanest capacity, does this illustrious writer announce the fundamental law of binocular vision-the grand principle of the Stereoscope, namely, that the picture of the solid column which we see with both eyes is composed of two dissimilar pictures, as seen by each eye separately. As the vision of the solid column, therefore, was obtained by the union of these dissimilar pictures, an instrument only was wanted to take such pictures, and another to combine them. The Binocular Photographic Camera was the one instrument, and the Stereoscope the other.
The subject of binocular vision was studied by various optical writers who have flourished since the time of Galen. Baptista Porta, one of the most eminent of them, repeats, in his work On Refraction, the propositions of Euclid on the vision of a sphere with one and both eyes, and he cites from Galen the very passage which we have given 1 De Usu Partium Corporis Humani, edit. Lugduni, 1550, p. 593.
above on the dissimilarity of the three pictures seen by each eye and by both. Believing that we see only with one eye at a time, he denies the accuracy of Euclid's theorems, and while he admits the correctness of the observations of Galen, he endeavours to explain them upon other principles.
In illustrating the views of Galen on the dissimilarity of the three pictures which are requisite in binocular vision, he employs a much more distinct diagram than that which is given by the Greek physician. "Let A," he says, "be the
pupil of the right eye, B that of the left, and DC the body to be seen. When we look at the object with both eyes we see DC, while with the left eye we see EF, and with the right eye GH. But if it is seen with one eye, it will be seen otherwise, for when the left eye B is shut, the body CD, on the left side, will be seen in HG; but when the right eye is shut, the body CD will be seen in FE, whereas, when both eyes are opened at the same time, it will be seen in CD." These results are then explained by copying the passage
from Galen, in which he supposes the observer to repeat these experiments when he is looking at a solid column.
In looking at this diagram, we recognise at once not only the principle, but the construction of the stereoscope. The double stereoscopic picture or slide is represented by HE; the right-hand picture, or the one seen by the right eye, by HF; the left-hand picture, or the one seen by the left eye, by GE; and the picture of the solid column in full relief by DC, as produced midway between the other two dissimilar pictures, HF and GE, by their union, precisely as in the stereoscope.1
Galen, therefore, and the Neapolitan philosopher, who has employed a more distinct diagram, certainly knew and adopted the fundamental principle of the stereoscope; and nothing more was required, for producing pictures in full relief, than a simple instrument for uniting HF and GE, the right and left hand dissimilar pictures of the column.
In the treatise on painting which he left behind him in MS.,2 Leonardo da Vinci has made a distinct reference to the dissimilarity of the pictures seen by each eye as the reason why "a painting, though conducted with the greatest art, and finished to the last perfection, both with regard to its contours, its lights, its shadows, and its colours, can never shew a relievo equal to that of the natural objects, unless these be viewed at a distance and with a single eye," "3 which he thus demonstrates. "If an object c be viewed by a single eye at A, all objects in the space behind it—included, as it were, in a shadow ECF, cast by
1 Joan. Baptista Porta Neap., De Refractione Optices parte, lib. v. p. 132, and lib. vi. pp. 143-5. Neap. 1593.
2 Trattata della Pictura, Scultura, ed Architettura. Milan, 1584.
3 Dr. Smith's Compleat System of Opticks, vol. ii., Remarks, pp. 41 and 244.
a candle at Aare invisible to an eye at A; but when the other eye at в is opened, part of these objects become visible to it; those only being hid from both eyes that
are included, as it were, in the double shadow CD, cast by two lights at A and B and terminated in D; the angular space EDG, beyond D, being always visible to both eyes. And the hidden space CD is so much the shorter as the object c is smaller and nearer to the eyes. Thus he observes that the object c, seen with both eyes, becomes, as it were, transparent, according to the usual definition of a transparent thing, namely, that which hides nothing beyond it. But this cannot happen when an object, whose breadth is bigger than that of the pupil, is viewed by a single eye. The truth of this observation is, therefore, evident, because a painted figure intercepts all the space behind its apparent place, so as to preclude the eyes from the sight of every part of the imaginary ground behind it. Hence," continues Dr. Smith, "we have one help to distinguish the place of a near object more accurately with both eyes than with one, inasmuch as we see it more detached from other objects
beyond it, and more of its own surface, especially if it be roundish."
We have quoted this passage, not from its proving that Leonardo da Vinci was acquainted with the fact that each eye, A, B, sees dissimilar pictures of the sphere c, but because it has been referred to by Mr. Wheatstone as the only remark on the subject of binocular vision which he could find "after looking over the works of many authors who might be expected to have made them." We think it quite clear, however, that the Italian artist knew as well as his commentator Dr. Smith, that each eye, a and B, sees dissimilar parts of the sphere c. It was not his purpose to treat of the binocular pictures of c, but his figure proves their dissimilarity.
The subject of binocular vision was successfully studied by Francis Aguillon or Aguilonius, a learned Jesuit, who published his Optics in 1613. In the first book of his work, where he is treating of the vision of solids of all forms, (de genere illorum quæ rà origɛa (ta sterea) nuncupantur,) he has some difficulty in explaining, and fails to do it, why the two dissimilar pictures of a solid, seen by each eye, do not, when united, give a confused and imperfect view of it. This discussion is appended to the demonstration of the theorem, "that when an object is seen with two eyes, two optical pyramids are formed whose common base is the object itself, and whose vertices are in the eyes, "2 and is as follows:
"When one object is seen with two eyes, the angles at
1 Opticorum Libri Sex Philosophis juxta ac Mathematicis utiles. Folio. Antverpiæ, 1613.
2 In FIG. 1, AHF is the optical pyramid seen by the eye A, and BGE the optical pyramid seen by the eye B.