illustrating the Relation of their Optic Axes. 23 



tive action of the axes of the other crystals upon the two axial 

 waves of the quartz and their interferences. A single axis of 

 iron sulphate, and this crystal, cut across a single axis of a 

 topaz, gives similar single spirals. 



The single axis being thus tested, we place in the stage a 

 biaxial cut across both axes — in this case nitre (fig. 9). The 

 supposed relation still holds good : each axis now has its own 

 distinct spiral, and the two mutually enwrap one another as in 

 the calcite. 



The same is true of crystals whose axes include much wider 

 angles; but to show their spirals we must alter our arrange- 

 ments. Extra convergent lenses are added in a moment ; but 

 if we placed a quartz plate in the strongly convergent light 

 we have to employ to bring both axes of such crystals upon 

 the screen togther, the rings and spirals proper to the quartz 

 itself, which have not appeared in the very moderate conver- 

 gence so far used, would now appear so stroDgly as to over- 

 power and distort those due to the crystals under examination. 

 We also want to ascertain beyond doubt that the effects are 

 not due to any convergence of the rays traversing the quartz, 

 but solely to selective action upon the right-handed and left- 

 handed waves traversing it axially. We therefore reverse the 

 combination, placing a large plate of quartz about 1\ millim. 

 thick next to the polarizing Nicol, in the parallel rays, and 

 removing the quarter-wave plate to a position between the 

 crystal to be examined and the analyzer. Of course, as it is 

 now the analyzer which is related in position to the quarter- 

 wave plate, the spirals only appear in complementary posi- 

 tions; while, on the other hand, when the analyzer is in those 

 positions the polarizer may be completely rotated. Of course, 

 also, we might have adopted this arrangement all along ; but 

 I have given the experiments as they were made, in order to 

 show how each successive question was determined. 



A multiplicity of ciystals would be useless: three of various 

 angles will show the uniformity and gradation of the pheno- 

 mena. Our former crystal of topaz cut across one axis, being 

 thin enough also for the more convergent arrangement, will 

 show that the single spiral appears precisely as before, the 

 convolutions being simply closer in this strongly convergent 

 light. Isext we will take again the small angle of another 

 nitre crystal, cut thin enough to show conspicuous figures in 

 the convergent apparatus (fig. 10). Observe that we can 

 now barely distinguish its two spirals, by their oval contour, 

 from those just now presented by the calcite: they are a little 

 drawn out, as it were, precisely as we should expect ; and that 

 is all ; otherwise the visible elements are manifestly the same 



