In examining these categories with reference to our three leading divisions, according to which we consider the phenomena of colours in a physiological, physical, or chemical view, we find that the catoptrical colours are closely connected with the physiological; the paroptical are already somewhat more distinct and independent; the dioptrical exhibit themselves as entirely and strictly physical, and as having a decidedly objective character; the epoptical, although still only apparent, may be considered as the transition to the chemical colours. 142. If we were desirous of prosecuting our investigation strictly in the order of nature, we ought to proceed according to the classification which has just been made; but in didactic treatises it is not of so much consequence to connect as to duly distinguish the various divisions of a subject, in order that at last, when every single class and case has been presented to the mind, the whole may be embraced in one comprehensive view. We therefore turn our attention forthwith to the dioptrical class, in order at once to give the reader the full impression of the physical colours, and to exhibit their characteristics the more strikingly. IX. DIOPTRICAL COLOURS. 143. Colours are called dioptrical when a colourless medium is necessary to produce them; the medium must be such that light and darkness can act through it either on the eye or on opposite surfaces. It is thus required that the medium should be transparent, or at least capable, to a certain degree, of transmitting light. 144. According to these conditions we divide the dioptrical phenomena into two classes, placing in the first those which are produced by means of imperfectly transparent, yet light-transmitting mediums; and in the second such as are exhibited when the medium is in the highest degree transparent. X. DIOPTRICAL COLOURS OF THE FIRST CLASS. 145. Space, if we assume it to be empty, would have the quality of absolute transparency to our vision. If this space is filled so that the eye cannot perceive that it is so, there exists a more or less material transparent medium, which may be of the nature of air and gas, may be fluid or even solid. 146. The pure and light-transmitting semi-transparent medium is only an accumulated form of the transparent medium. It may therefore be presented to us in three modes. 147. The extreme degree of this accumulation is white; the simplest, brightest, first, opaque occupation of space. 148. Transparency itself, empirically considered, is already the first degree of the opposite state. The intermediate degrees from this point to opaque white are infinite. 149. At whatever point short of opacity we arrest the thickening medium, it exhibits simple and remarkable phenomena when placed in relation with light and darkness. 150.