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a candle at A—are invisible to an eye at A; but when the other eye at B 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,1 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 qua; To, erigsa. (fa stereo) 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 the vertices of the optical pyramids (namely, Haf, Gbe, Fig. 1) are not always equal, for beside the direct view in which the pyramids ought to be equal, into whatever direction both eyes are turned, they receive pictures of the object under inequal angles, the greatest of which is that which is terminated at the nearer eye, and the lesser that which regards the remoter eye. This, I think, is perfectly evident; but I consider it as worthy of admiration, how it happens that bodies seen by both eyes are not all confused and shapeless, though we view them by the optical axes fixed on the bodies themselves. For greater bodies, seen under greater angles, appear lesser bodies under lesser angles. If, therefore, one and the same body which is in reality greater with one eye, is seen less on account of the inequality of the angles in which the pyramids are terminated, (namely, Haf, Gbe,1) the body itself must assuredly be seen greater or less at the same time, and to the same person that views it; and, therefore, since the images in each eye are dissimilar (minime sihi congruun£) the representation of the object must appear confused and disturbed (canfusa ac periurbata) to the primary sense."
1 Opticorum Libri Sex Philosophit juxla ae Mathematics utiles. Folio. Antverpin, 1613.
s In Fig. 1. Ahf is the optical pyramid seen by the eye A, and Ege tbe optical pyramid seen by the eye b.
"This view of the subject," he continues, "is certainly consistent with reason, but, what is truly wonderful is, that it is not correct, for bodies are seen clearly and distinctly with both eyes when the optic axes are converged upon them. The reason of this, I think, is, that the bodies do not appear to be single, because the apparent images, which are formed from each of them in separate eyes, exactly coalesce, (sihi rrvutuo exacte congruunt,} but because the common sense imparts its aid equally to each eye, exerting its own power equally in the same manner as the eyes are converged by means of their optical axes. Whatever body, therefore, each eye sees with the eyes conjoined, the common sense makes a single notion, not composed of the two which belong to each eye, but belonging and accommodated to the imaginative faculty to which it (the common sense) assigns it. Though, therefore, the angles of the optical pyramids which proceed from the same object to the two eyes, viewing it obliquely, are inequal, and though the object appears greater to one eye and less to the other, yet the same difference does not pass into the primary sense if the vision is made only by the axes, as we have said, but if the axes are converged on this side or on the other side of the body, the image of the same body will be seen double, as we shall shew in Book iv., on the fallacies of vision, and the one image will appear greater and the other less on account of the inequality of the angles under which they are seen."1
1 These angles are equal in this diagram and in the vision of a sphere, but they are inequal in other bodies.
Such is Aguilonius's theory of binocular vision, and of the union of the two dissimilar pictures in each eye by which a solid body is seen. It is obviously more correct than that of Dr. Whewell and Mr. Wheatstone. Aguilonius affirms it to be contrary to reason that two dissimilar pictures can be united into a clear and distinct picture, as they are actually found to be, and he is therefore driven to call in the aid of what does not exist, a common sense, which rectifies the picture. Dr. Whewell and Mr. Wheatstone have cut the Gordian knot by maintaining what is impossible, that in binocular and stereoscopic vision a long line is made to coincide with a short one, and a large surface with a small one; and in place of conceiving this to be done by a common sense overruling optical laws, as Aguilonius supposes, they give to the tender and pulpy retina, the recipient of ocular pictures, the strange power of contracting or expanding itself in order to equalize inequal lines and inequal surfaces!
1 Aguilonius, Opticorum, lib. U. book mviii. pp. 140,141.
In his fourth and very interesting book, on the fallacies of distance, magnitude, position, and figure, Aguilonius resumes the subject of the vision of solid bodies. He repeats the theorems of Euclid and Gassendi on the vision of the sphere, shewing how much of it is seen by each eye, and by both, whatever be the size of the sphere, and the distance of the observer. At the end of the theorems, in which he demonstrates that when the diameter of the sphere is equal to the distance between the eyes we see exactly a hemisphere, he gives the annexed drawing of the mode in which the sphere is seen by each eye, and by both. I)
In this diagram E is the right eye and D the left, Chpi the section of that part of the sphere Be which is seen by the right eye E, Bhga the section of the part which is seen by the left eye D, and Blc the half of the great circle which is