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dressed plank, the surface of the mineral has necessarily an inequal and undulating appearance.

In viewing good photographic or well-painted miniature portraits in an erect and inverted position, and with or without a lens, considerable changes take place in the apparent relief. Under ordinary vision there is a certain amount of relief depending upon the excellence of the picture. If we invert the picture, by turning it upside down, the relief is perceptibly increased. If we view it when erect, with a lens of about an inch in focal length, the relief is still greater; but if we view it when inverted with the same lens the relief is very considerably diminished.

A very remarkable illusion, affecting the apparent position of the drawings of geometrical solids, was first observed by the late Professor Neckar, of Geneva, who communicated it to me personally in 1832.1 "The rhomboid Ax," (Fig. 51,) he says, "is drawn so that the solid


angle A should be seen nearest to the spectator, and the solid angle x the farthest from him, and that the face Acbd should be the foremost, while the face Xdc is behind. But in looking repeatedly at the same figure, you will perceive that at times the apparent position of the rhomboid is so changed that the solid angle x will appear the nearest, and the solid angle A the farthest, and that the face Acdb will recede behind the face Xdc, which will come forward, —which effect gives to the whole solid a quite contrary apparent inclination." Professor Neckar observed this change " as well with one as with both eyes," and he considered it as owing "to an involuntary change in the adjustment of the eye for obtaining distinct vision. And that whenever the point of distinct vision on the retina was directed to the angle A for instance, this angle, seen more distinctly than the other, was naturally supposed to be nearer and foremost, while the other angles, seen indistinctly, were supposed to be farther away and behind. The reverse took place when the point of distinct vision was brought to bear upon the angle x. What I have said of the solid angles (a and x) is equally true of the edges, those edges upon which the axis of the eye, or the central hole of the retina, are directed, will always appear forward; so that now it seems to me certain that this little, at first so puzzling, phenomenon depends upon the law of distinct vision."

1 See Edinburgh Philosophical Journal, November 1832, vol. L p. 334

In consequence of completely misunderstanding Mr. Neckar's explanation of this illusion, Mr. Wheatstone has pronounced it to be erroneous, but there can be no doubt of its correctness; and there are various experiments by which the principle may be illustrated. By hiding with the finger one of the solid angles, or making it indistinct, by a piece of dimmed glass, or throwing a slight shadow over it, the other will appear foremost till the obscuring cause is removed. The experiment may be still more satisfactorily made by holding above the rhomboid a piece of finely-ground glass, the ground side being farthest from the eye, and bringing one edge of it gradually down till it touches the point A, the other edge being kept at a distance from the paper. In this way all the lines diverging from A will become dimmer as they recede from A, and consequently A will appear the most forward point. A similar result will be obtained by putting a black spot upon A, which will have the effect of drawing our attention to A rather than to x.

From these experiments and observations, it will be seen that the conversion of form, excepting in the normal case, depends upon various causes, which are influential only under particular conditions, such as the depth of the hollow or the height of the relief, the distance of the object, the sharpness of vision, the use of one or both eyes, the inversion of the shadow, the nature of the object, and the means used by the mind itself to produce the illusion. In the normal case, where the cavity or convexity is shadowless, and upon an extended surface, and where inverted vision is used, the conversion depends solely on the illusion, which it is impossible to resist, that the side of the cavity or elevation next the eye is actually farthest from it, an illusion not produced by inversion, but by a false judgment respecting the position of the surface in which the cavity is made, or upon which it rests.



There are many persons who experience great difficulty in uniting the two pictures in the stereoscope, and consequently in seeing the relief produced by their union. If the eyes are not equal in focal length, that is, in the distance at which they see objects most distinctly; or if, from some defect in structure, they are not equally good, they will still see the stereoscopic relief, though the picture will be less vivid and distinct than if the eyes were in every respect equal and good. There are many persons, however, whose eyes are equal and perfect, but who are not able to unite the pictures in the stereoscope. This is the more remarkable, as children of four or five years of age see the stereoscopic effect when the eye-tubes are accommodated to the distance between their eyes. The difficulty experienced in uniting the binocular pictures is sometimes only temporary. On first looking into the instrument, two pictures are seen in place of one; but by a little perseverance, and by drawing the eyes away from the eye-tubes, and still looking through them, the object is seen single and in perfect relief. After having ceased to use the instrument for some time, the difficulty of uniting the pictures recurs, but, generally speaking, it will gradually disappear.


In those cases where it cannot be overcome by repeated trials, it must arise either from the distance between the lenses being greater or less than the distance between the

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