In repeating, at a subsequent period, the very beautiful experiments of M. Biot, on the action of homogeneous fluids upon polarized light, and in extending them to other fluids which he had not tried, I found it most convenient to place them in a triangular trough, formed by two plates of glass cemented together by two of their sides, so as to form an acute angle. The ends being closed up with pieces of plate glass cemented to the other plates, the trough was fixed horizontally, for the reception of the fluids. The eye being necessarily placed without the trough, and at one end, some of the cement, which had been pressed through between the plates at the object end of the trough, appeared to be arranged in a manner far more regular and symmetrical than I had before observed when the objects, in my early experiments, were situated at a distance from the reflectors. From the approximation to perfect symmetry which the figure now displayed, compared with the great deviation from symmetry which I had formerly observed, it was obvious that the progression from the one effect to the other must take place during the passage of the object from the one position to the other; and it became highly probable, that a position would be found where the symmetry was mathematically perfect. By investigating this subject optically, I discovered the leading principles of the Kaleidoscope, in so far as the inclination of the reflectors, the position of the object, and the position of the eye, were concerned. I found, that in order to produce perfectly beautiful and symmetrical forms, three conditions were necessary. 1. That the reflectors should be placed at an angle, which was an _even_ or an _odd_ aliquot part of a circle, when the object was regular, and similarly situated with respect to both the mirrors; or the _even_ aliquot part of a circle when the object was irregular, and had any position whatever. 2. That out of an infinite number of positions for the object, both within and without the reflectors, there was _only one_ where perfect symmetry could be obtained, namely, when the object was placed in contact with the ends of the reflectors. This was precisely the position of the cement in the preceding experiment with the triangular trough. 3. That out of an infinite number of positions for the eye, there was _only one_ where the symmetry was perfect, namely, as near as possible to the angular point, so that the circular field could be distinctly seen; and that this point was the _only one_ out of an infinite number at which the uniformity of the light of the circular field was a maximum, and from which the direct and the reflected images had the same form and the same magnitude, in consequence of being placed at the same distance from the eye. This, also, was the position in which the eye was necessarily placed when looking through the fluid with which the glass trough was partially filled.