Among the binocular diagrams, consisting of white lines upon a black ground, which have been executed in Paris, there is one representing the apparatus in which a ray of light, polarized by reflexion from a glass plate, passes through a crystallized film perpendicular to the plane of the paper, and is subsequently analysed by reflexion from another plate at right angle to the following plate. This diagram, when placed in relief by the stereoscope, gives as correct an idea of the process as the apparatus itself. As an auxiliary in the investigation of questions of difficulty and importance, both in physics and metaphysics, the stereoscope is peculiarly valuable. It enables us to place in its true light the celebrated theory of vision on which Bishop Berkeley reared the ideal philosophy, of which he was the founder, and it gives us powerful aid in explaining many physical phenomena which have long baffled the ingenuity of philosophers. It would be out of place to give any account of these in a work like this, but there is one so remarkable, and at the same time so instructive, as to merit special notice. In order to exhibit, by means of _three_ diagrams, a solid in relief and hollow at the same time, which had not been previously done, I executed three drawings of the frustum of a cone, resembling those in Fig. 31, so that the _left_-hand one and the middle one gave the _hollow_ cone, while the _middle_ one and the _right_-hand one gave the _raised_ cone. Having their summits truncated, as in the figure, the cones exhibit, in the one case, a circle at the bottom of the hollow cone, and in the other, a circle on the summit of the raised cone. When these three diagrams[68] are placed in an open lenticular stereoscope, or are united by the convergency of the optical axes, so that we can not only see the _hollow_ and the _raised_ cones, but the flat drawing on each side of them, we are enabled to give an ocular and experimental proof of the cause of the large size of the horizontal moon, of her small size when in the meridian or at a great altitude, and of her intermediate apparent magnitude at intermediate altitudes,—phenomena which had long perplexed astronomers, and which Dr. Berkeley, rejecting previous and well-founded explanations, ascribed to the different degrees of brightness of the moon in these different positions. [68] A binocular slide, copied from the one originally designed by myself, forms No. 27 of the Series of white-lined diagrams upon a black ground executed in Paris. The drawings, however, are too large for the common stereoscope.