A biaxial substance possesses two directions (_the optic axes_) along which a single beam is transmitted. If such a stone be examined along the line bisecting the acute angle between the optic axes (_the acute bisectrix_) an interference picture[4] will be seen which in particular positions of the stone with respect to the crossed nicols takes the forms illustrated on Plate III. As before, there is a series of rings which are coloured in white light; they, however, are no longer circles but consist of curves known as lemniscates, of which the figure of 8 is a special form. Instead of an unchangeable cross there are a pair of black “brushes” which in one position of the stone are hyperbolæ, and in that at right angles become a cross. On rotating the stone we find that the rings move with it and are unaltered in form, whereas the brushes revolve about two points, called the “eyes,” where the optic axes emerge. If the observation were made along the obtuse bisectrix the angle between the optic axes would probably be too large for the brushes to come into the field, and the rings might not be visible in white light, though they would appear in monochromatic light. In the case of a substance like sphene the figure is not so simple, because the positions of the optic axes vary greatly for the different colours and the result is exceedingly complex; in monochromatic light, however, the usual figure is visible. It would probably not be possible in the case of a faceted stone to find a pair of faces perpendicular to the required direction. Nevertheless, so long as a portion of the figures described is in the field of view, the character of the double refraction, whether uniaxial or biaxial, may readily be determined.