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When we look with both eyes open at a sphere, or any other solid object, we see it by uniting into one two pictures, one as seen by the right, and the other as seen by the left eye. If we hold up a thin book perpendicularly, and midway between both eyes, we see distinctly the back of it and both sides with the eyes open. When we shut the right eye we see with the left eye the back of the book and the left side of it, and when we shut the left eye we see with the right eye the back of it and the right side. The picture of the book, therefore, which we see with both eyes, consists of two dissimilar pictures united, namely, a picture of the back and the left side of the book as seen by the left eye, and a picture of the back and right side of the book as seen by the right eye.

In this experiment with the book, and in all cases where the object is near the eye, we not only see different pictures of the same object, but we see different things with each eye. Those who wear spectacles see only the left-hand spectacle-glass with the left eye, on the left side of the face, while with the right eye they see only the right-hand spectacle-glass on the right side of the face, both glasses of the spectacles being seen united midway between the eyes, or above the nose, when both eyes are open. It is, therefore, a fact well known to every person of common sagacity that the pictures of bodies seen by both eyes are formed by the union of two dissimilar pictures formed by each.

This palpable truth was known and published by ancient mathematicians. Euclid knew it more than two thousand years ago, as may bo seen in the 2Gth, 27th, and 28th theorems of his Treatise on Optics.1 In these theorems he shews that the part of a sphere seen by both eyes, and having its diameter equal to, or greater or less than the distance between the eyes, is equal to, and greater or less than a hemisphere; and having previously shewn in the 23d and 24th theorems how to find the part of any sphere that is seen by one eye at different distances, it follows, from constructing his figure, that each eye sees different portions of the sphere, and that it is seen by both eyes by the union of these two dissimilar pictures.

More than fifteen hundred years ago, the celebrated physician Galen treated the subject of binocular vision more fully than Euclid. In the twelfth chapter of the tenth book of his work, On the use of the different parts of the Human Body, he has described with great minuteness tho various phenomena which are seen when wc look at bodies with both eyes, and alternately with the right and the left. He shews, by diagrams, that dissimilar pictures of a body are seen in each of these three modes of viewing it; and, after finishing his demonstration, he adds,—

"But if any person does not understand these demonstrations 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 rigid 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."i

i Edit of Pena, pp. 17,18, Paris, 1577; or Optra, by Gregory, pp. 618, «20. Oion. 1703.

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 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.

i Dc Usu Partium Corporis Humani, edit. Lugduni, 1550, p. 593.

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


Fig. 1.

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. Baptistse Portee Neap., Be Refractione Optica parte, lib. v. p. 132, and lib. vi. pp. 143-5. Neap. 1593.

2 Traltata detla Piclura, Sculttira, ed Architetlura. Milan, 1584.

3 Dr. Smith's CompUat System qfOpticks, voL ii., Remarks, pp. 41 and 244.

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