We have not space to exhibit fully the author’s ideas on these topics, but we can state what are regarded by M. Arréat as the two principle propositions which give to them their life and unity. One of these propositions is, that the first function of our dioptric apparatus consists in furnishing to our central visual organ, which M. Hirth terms the _internal eye_, material which the latter has to interpret. The other is that it is necessary to get rid of mathematical concepts, which are much too rigid to be applied to the delicate problems of vision, and to fall back on visual sensation such as it is. These propositions imply, moreover, the admission of an electro chemical process, “without which the properties of the eye and the marvels of vision remain inexplicable.” This last conclusion has a bearing on the nature of memory, or the recollection of the impressions received by the nerves and brain after the original excitation has disappeared. Thus, M. Hirth suggests that when we know the physiological procedure in the impregnation of cerebral molecules, or in their electric charging, memory will be found to be only the prolongation of the duration of consecutive images. The inquiries of M. Hirth throw great light on the difference between monocular and binocular vision, for information as to which and other details of his optical theory we must refer our readers to M. Arréat’s Introduction. This concludes with a consideration of the perception of light-movement, the reproduction of which is said to require a special exercise of attention, direct or indirect. Here we have the third degree of attention, according to the views of M. Hirth, who regards it as artistic apperception, having its end in itself and capable of being reproduced through co-ordination of the movements perceived.