24 Mr. L. Wright on Sjriral Figures observable in Crystals, 



in both. Arragonite (fig. 11), with an angle of 18£ degrees, 

 shows a spiral of several turns round each axis ; but still they 

 finally enwrap each other : and now mica, with an angle in 

 this specimen of 60° or 70° (fig. 12) gives the same pheno- 

 mena. With the wider separation the spiral round each axis 

 has room to show separately more of the character of the 

 single axis of the sugar; but the two always preserve the same 

 relation, and only crystals which, owing to very powerful dis- 

 persion of their axes, fail to show perfect lemniscates in the 

 ordinary wav, fail for the same reason to show these figures 

 complete. Here, for instance, is a plate of borax, whose axial 

 dispersion is considerable and peculiar; but as this still leaves 

 the ordinary lemniscate curves tolerably unbroken, we can 

 trace the spirals without difficulty. 



That these figures are solely due to differential action upon 

 the interferences of the quartz rotational colours, we shall de- 

 monstrate absolutely in a few minutes ; meantime we can 

 almost prove it in two ways. First, though all the arrange- 

 ments remain complete, the spirals disappear or lose their cha- 

 racter in monochromatic light ; and, secondly, substituting a 

 quartz of opposite rotation, the direction of the spirals is, as 

 you see, reversed. 



And now we will project the beautiful experiment of Prof. 

 Mitscherlich, afterwards applying to it this additional method 

 of analysis. There are the two axes arranged vertically ; as 

 we apply heat they gradually unite. The crystal is now uni- 

 axial. And now the axes open out again, but horizontally. 

 It is a beautiful demonstration, which never loses its fascina- 

 tion for the student. We now add our arrangements for the 

 spirals. There they are, arranged perpendicularly on the 

 screen. They approach as the crystal is heated, till now we 

 have them as in the calcite. Now they open out again in a 

 horizontal direction, like those of a plate of nitre turned round 

 90° in its own plane. Observe that all through we have the 

 double spiral. We can only get a single one by taking a single 

 axis ; while the axis of a uniaxial always preserves what we 

 may call its " twin " character. Thus we have the ocular 

 illustration sought at the commencement, of the precise rela- 

 tion predicated by Fresnel's theory between the axes of uni- 

 axial and biaxial crystals, and that the former class do con- 

 tain, within their single axis, elements (capable of being made 

 optically visible) of both the axes in the latter class. 



We have here also objectively demonstrated the reason of 

 the double spiral, first observed by Mr. Airy, in quartz itself. 

 We see that the quartz, considered as an ordinary uniaxial 

 crystal, owing to its peculiar effects upon plane-polarized light 



