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seen before the rotation of the figure commenced. If the pyramid had been square, the raised would have passed into the hollow pyramid by rotations of 45° each. If it had been rectangular, the change would have been effected by rotations of 90°. If the space between the two circular sections of the cone in Fig. 31 had been uniformly shaded, or if lines had been drawn from every degree of the one circle to every corresponding degree in the other, in place of from every 90th degree, as in the Figure, the raised cone would have gradually diminished in height, by the rotation of the figure, till it became flat, after a rotation of 90°; and by continuing the rotation it would have become hollow, and gradually reached its maximum depth after a revolution of 180°.

5. The Single-Prism Stereoscope.

Although the idea of uniting the binocular pictures by a single prism applied to one eye, and refracting one of the pictures so as to place it upon the other seen directly by the other eye, or by a prism applied to each eye, could hardly have escaped the notice of any person studying the subject, yet the experiment was, so far as I know, first made and published by myself. I found two prisms quite unnecessary, and therefore abandoned the use of them, for reasons which will be readily appreciated. This simple instrument is shewn in Fig. 37, where A, B are the dissimilar pictures, and P a prism with such a refracting angle as is sufficient to lay the image of A upon B, as seen by the right eye. If we place a second prism before the eye E, we require it only to have half the refracting angle of the prism p, because each prism now refracts the picture opposite to it only half way between A and B, where they are united. This, at first sight, appears to be an advantage, for as there must always be a certain degree

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of colour produced by a single prism, the use of two prisms, with half the refracting angle, might be supposed to reduce the colour one-half. But while the colour produced by each prism is thus reduced, the colour over the whole picture is the same. Each luminous edge with two prisms has both red and blue tints, whereas with one prism each luminous edge has only one colour, either red or blue. If the picture is very luminous these colours will be seen, but in many of the finest opaque pictures it is hardly visible. In order, however, to diminish it, the prism should be made of glass with the lowest dispersive power, or with rock crystal. A single plane surface, ground and polished by a lapidary, upon the edge of a piece of plate glass, a little larger than the pupil of the eye, will give a prism sufficient for every ordinary purpose. Any person may make one in a few minutes for himself, by placing a little bit of good window glass upon another piece inclined to it at the proper angle, and inserting in the angle a drop of fluid. Such a prism will scarcely produce any perceptible colour.

If a single-prism reflector is to be made perfect, we have only to make it achromatic, which could be done extempore, by correcting the colour of the fluid prism by another fluid prism of different refractive and dispersive power.

With a good achromatic prism the single-prism stereoscope is a very fine instrument; and no advantage of any value could be gained by using two achromatic prisms. In the article on New Stereoscopes, published in the Transactions of the Royal Society of Arts for 1849, and in the Philosophical Magazine for 1852, I have stated in a note that / believed that Mr. Wheatstone had used two achromatic prisms. This, however, was a mistake, as already explained,1 for such an instrument was never made, and has never been named in any work previous to 1849, when it was mentioned by myself in the note above referred to.

If we make a double prism, or join two, as shewn at r, p' in Fig. 38, and apply it to two dissimilar figures A, B, one of which is the reflected image of the other, so that with the left eye L and the prism p we place the refracted image of A upon B, as seen by the right eye E, we shall see a raised cone, and if with the prism p' we place the image of B upon A we shall see a hollow cone. If we place the left eye L at o, behind the common base of the

i See Chap. i. pp. 33-36.

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prism, we shall see with one-half of the pupil the hollow cone and with the other half the raised cone.

6. The Opera-Glass Stereoscope.

As the eyes themselves form a stereoscope to those who have the power of quickly converging their axes to points nearer than the object which they contemplate, it might have been expected that the first attempt to make a stereoscope for those who do not possess such a power, would have been to supply them with auxiliary eyeballs capable of combining binocular pictures of different sizes at different distances from the eye. This, however, has not been the case, and the stereoscope for this purpose, which we are about to describe, is one of the latest of its forms.

In Fig. 39, Un is a small inverting telescope, consisting of two convex lenses M, N, placed at the sum of their focal distances, and Op another of the same kind. When the two eyes, r, l, look through the two telescopes directly at the dissimilar pictures A, B, they will see them with perfect

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distinctness; but, by the slightest inclination of the axes of the telescopes, the two images can be combined, and the stereoscopic effect immediately produced. With the dissimilar pictures in the diagram a hollow cone is produced;

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but if we look at B with the telescope M'n', as in Fig. 40, and at A' with O'p', a raised cone will be seen. With the usual binocular slides containing portraits or landscapes, the

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