that a b i k g and a b l m f are similar planes, each consisting of one isoscele and two halves, of similar triangles. It follows therefore that this macle is composed of three sections of the primitive prism, fig. 196, alternating with six halves, two and two, of the same figure.
It should be noticed that the angle l m c, fig. 200, to which there are five others similar, is about 120° by the common goniometer; but as the edges of the macle are very uneven, it cannot be relied on for admeasurement. The angle l m f like which there are also five others, nearly agrees, but is not accurate for the same reason with that of a e c, fig. 193, which is the result of a close combination of two similar isosceles triangles.
It will be understood that fig. 208, Pl. 25, and the seven succeeding figures, comprehending the series of that which is commonly termed the dodecahedral macle, (each being numbered with the figures of the several modifications of which it shews the planes) are not intended to represent dodecahedrons, as the macles themselves consist only of what is visible in the respective drawings, or at most of only one-third more, that is, of three or at most of only four sections of the prism, fig. 196, Pl. 24. Yet the apices of several of them are perfect, as for instance, the plane on the summit of fig. 210, which is perfectly defined, and which therefore indicates the regular combination of six sections of that figure, unitedly exhibiting a decrease on the apex by the plane of the fourth modification. As a corroborative proof, however, that these macles, under the most favourable circumstances for perfect crystallization could never become perfect dodecahedrons, it may be observed that several in the series which exhibit those planes of the fourth modifications which give to fig. 210 the form of a short prism, give uniformly an incidence of 4 on 4 by the reflecting goniometer of 112°. 10′.; whereas if they were