correctly centred, and they march rapidly to the crossing point in the centre, where the dark hyperbolæ unite to produce the rectangular St Andrew’s cross, the rings, figure-eight curves, and other lemniscates passing through the most exquisite evolutions and colour changes all the time until they form the circular Newton’s rings, around the centre of the cross; after this the cross and circles again open out, but along the vertical diameter of the screen, into hyperbolæ and rings and loop-like lemniscates surrounding two axes once more. It is wise as soon as the separation in this plane is complete and the first or second separate rings have appeared round the axes, to arrest the heating by merely interposing intermittently a hand screen between the lantern and polariser, or by blowing a current of cool air past the crystal, which will cause the axes to recede again, and the phenomena to be reversed, the crossing point being repassed, and the axes brought into the original horizontal plane again. By manipulation of the screen, or air-current, the axes can thus be caused to approach or to recede from the centre at will, along either the horizontal or vertical diameter. Four characteristic stages of the experiment are shown in Figs. 52 to 55, Plate XII. Fig. 52 exhibits the appearance just after commencing the experiment, the optic axes being well in the field of view. Fig. 53 shows the axes horizontally approaching the centre. Fig. 54 shows the actual crossing, which occurs for different crystals at temperatures varying from 105°.5 to 111°.5 C.; and Fig. 55 represents the axes again separated, but vertically.