sight, seems to have no analogy with the preceding macles, but that it results from the same law of section as those described by figs 186 and 187, may be readily shewn. Let the section a b c d, fig. 190, which is parallel with the edges e f and g h of that figure be represented by a section a b c d, fig. 194, parallel with the edges e f and g h of that figure; then let c b h d be a section in the opposite direction parallel with the edges f a and e g. By placing the prism so that the edge k b i of fig. 194 shall be represented by k b i, fig. 195, it will be seen that the lines of section a b c d and e b h d are the same on each figure, and that by these sections two equal portions b h d a and b c d e are obtained from the prism, the former of which is shewn by fig. 196; and it will also be seen that the planes 1, 1, of the latter figure, correspond with those of 1, 1, fig 188. It will be understood therefore that this macle consists of a number of equal portions of the prism, described by fig. 196, and that the planes of the first modification alone are visible.
But there is a circumstance relating to the formation of this macle that deserves attention. If it were, as it seems to be, a dodecahedron with triangular faces, the two pyramids, of which it would be composed, being divided horizontally, would each have for its base a regular hexahedral plane, divisible into six equilateral triangles, fig. 197, and the six angles of the plane would necessarily be 120° each. If a diagonal section of a crystal, fig. 194, be made along the edges of the pyramids e f a and c g h, and along those of the prism e c and a h, the plane given to each portion by that section would also be a hexahedral plane, fig. 198. But since it has been shewn that the two sections on fig. 194, (represented by the lines a i c and e i h, fig. 198) are parallel with the edges e f and g h, and f a and e g; and since the incidence