illustrating the Relation of their Optic Axes. 25 



passing through it axially, is able to show its own spirals, 

 which of course are double. They are not seen at all in par- 

 allel light ; and, on the other hand, if we increase the rings 

 by convergence, the spirals become more definite. Here, 

 for instance, is a rather thin quartz (one of a pair generally 

 used to show Airy's spirals) : in this strongly-convergent 

 circularly polarized light, it shows spirals as well defined as did 

 our calcite. A crucial test of this view readily suggests itself. 

 If it be well founded, obviously we can combine the two pro- 

 perties of our quartz artificially, as it were, since many fluids 

 possess the same power of dividing into two opposite circular 

 waves, differently retarded, a plane-polarized ray. If there- 

 fore we take a column of such fluid of sufficient length, and 

 any ordinary uniaxial crystal, the one will represent the pecu- 

 liar axial properties, and the other the ordinary doubly- 

 refractive properties of the quartz ; and the two ought to give 

 similar double spirals. In fact an adequate column of fluid 

 ought to replace the quartz successfully in all the foregoino- 

 experiments. Our last step, therefore, is to prove that this is 

 the case. I have here a tube of oil of lemons 200 millimetres 

 (8 inches) in length, which we introduce into the parallel- 

 plane-polarized beam in place of the quartz, whose axial pro- 

 perties it now represents. In the crystal-stage we adjust the 

 calcite, which in all except being a negative crystal (and a 

 positive one would be just the same) represents the ordinary 

 doubly-refractive properties. And now introducing the 

 quarter-wave plate between crystal and analyzer, we have the 

 spirals as given by the quartz in all respects. The same 

 effects are produced by other crystals, any slight inferiority 

 being due to the slightly yellowish tint of the fluid, which so 

 far approximates to homogeneous light. Spirit of turpentine 

 is free from this defect ; but we could hardly project through a 

 tube of sufficient length. 



These phenomena hold good through all the ordinary analo- 

 gies with, or substitutes for, natural crystals. This round disk 

 of chilled glass, placed in parallel light, which behaves in all 

 other respects like a crystal in convergent light, also gives 

 double spirals like those of the calcite. I have here also an 

 artificial uniaxial crystal formed of crossed mica-films, after 

 Korremberg, and an artificial quartz of mica-films, after 

 Reusch, for both of which I am indebted to my kind friend 

 Mr. Fox, who made them with his own hands. The first 

 gives the calcite spirals with a quarter-wave plate and quartz ; 

 the Reusch preparation gives the quartz spirals with the 

 quarter-wave plate alone. 



These experiments of course add nothing to the theory of 



