edges a b and c d, be represented by fig. 193, and the dotted line e f will represent the line of junction of the upper and lower parts 1, 2, 1 and 1, 2, 1 of fig. 192, and consequently also the plane of section a b c d, of fig. 190, which being parallel with the secondary edge c f of that figure, is therefore parallel with the planes of the primitive form, as a reference to figures 18 to 27, Pl. 16, will evince. In place of the edge a b, fig. 192, which is the edge of the secondary pyramid, the primitive plane P is seen on fig. 218, Pl. 25, which plane gives on its opposed plane P of the same figure (not visible on the figure, but which, as it were, replaces the edge c d of fig. 192) by the reflecting goniometer an exact incidence of 180°. It follows of course that the edges a b and c d, fig. 193, are parallel with each other; and also that the intermediate line of section e f must be parallel with each, and therefore with the edge of the secondary pyramid e f, fig. 190.
For the discovery of the construction of that macle of the oxyd of tin, which, when viewed in the direction in which it generally occurs, and in which it is delineated by fig. 188, Pl. 24, appears to take the form of a dodecahedron with triangular faces, I was principally indebted to the direction of the striæ on its planes. Having noticed them to be mostly visible as described on that figure, a suspicion arose that this macle was composed of equal parts of the prism formed by the planes of the first modification, and I found by the common goniometer that the incidence of any plane of the upper, on its connected plane on the lower pyramid, exactly corresponded with that of 1 on 1, fig. 27, being 90°. The idea of its being composed of similar and equal portions of several crystals, was further corroborated by observing, in almost every instance, their natural joints along the edges from one apex to the other. This apparently dodecahedral macle, fig. 188, Pl. 24, at first