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380 OPTICAL PROJECTION but this soon passes off, and the heat is applied till the desired effect is produced. One crystal will last for many demonstrations. Circularly polarised crystal figures are produced by placing a quarter-wave plate in the ordinary stage. The black brushes then disappear, nebulous lines taking their places; while the rings are dislocated half a wave in each alternate quadrant. The rings may instead be analysed circularly, by fitting a quarter-wave plate on either side of the focussing-lens, K (fig. 190), with the same results. If the rings be both polarised and analysed circularly, the brushes disappear entirely, and as the analyser is rotated, the quadrants (or halves in bi-axial rings) slide by each other, producing in the two principal positions unbroken rings with no brushes or interruption whatever. If at this point the quarter-wave be rotated with the analyser, the unbroken character of the rings is retained throughout all the rotation ; showing the perfectly circular character of the polarisation. Spiral Figures were discovered by myself, 1 in a search after phenomena which should more distinctly show the rela- tion of bi-axial to uni-axial crystals, and of the two axes of a bi- axial to the prismatic axis—or, in short, that the axis of a uni- axial was simply a case of the coincidence of two axes. For obvious reasons this was most likely to be brought about by the two circular waves concerned in rotary polarisation ; and it seemed worth while to seek for such demonstration, since when polarised and analysed circularly, one single axis of a bi-axial gives as unbroken a circle as a uni-axial. I sought for phenomena which might show that each axis of a bi-axial was only one sex, as it were, of a combination, both of which were found in a uni-axial. This is shown by placing in the ordinary stage of the polariscope a quartz plate 7^ mm. thick, and introducing between the crystal and the analyser a 1 See Proceedings of the Physical Society for November 12,1881, or Phil, Mag. January 1882,