the axes of the lamella. The particular construction of this natural polarizing apparatus described by Erman, which from the thinness of the lamella exhibits the systems of rings of an unusual size, and considerably removed toward their optical axes on account of the obliquity of the surface of emergence, is obtained optically by comparing these systems of rings seen without previous polarization, in size and position, with those which evolve light previously polarized rectilinearly and afterwards analysed also around the optical axes of the including individuals, of which the one serves for the polarizing, the other for the analysing arrangement. That this last is the case, is moreover apparent from the following observation, that when a tourmaline is revolved before the crystal viewed in ordinary light, one of the systems of rings disappears alternately without changing its form. As however the phænomenon remains the same when the crystal is revolved, the same holds good for the polarizing prism, with which also the alterations of intensity of the rings agree when the crystal is viewed with the naked eye in rectilinearly polarized light. A decisive proof, however, that the individual behind polarizes rectilinearly, lies, as it seems to me, in the following fact, that the rings seen with the naked eye do not take the form which corresponds with the light when this is circularly incident.
The third case, in which the axis of the lamina growing into the other is inclined at an angle toward the axis of the including crystal, is also of importance for uniaxal crystals. The modification of the system of rings round the axis of the including crystal thus produced must coincide with that in two exactly central plates when a crystallized lamina of definite thickness is inserted between them. As that lamina may here be replaced by another similarly acting crystal, this case may be treated in the same way without difficulty. Among seven plates of Iceland spar exhibiting a deviation from the usual system of rings, I found two which produced a very regular figure, namely, a black cross with curves alternately osculating, which appeared to me to be circles and lemniscates; the interior curve was completely entwined into a figure of 8. If the plate is turned in its own plane, the interior part of the system of rings consists of four triangular vacant spaces. I obtained precisely the same phaenomena by inserting a lamina of mica of definite thickness between two plates exactly centred and producing the regular system of rings, and by turning that lamina in its own plane.
7. Experiments on Circular Polarization by other Modifications.
Fluor spar is the only crystallized substance of the regular system which I have examined with respect to the effect of an unequal distribution of temperature within the body. The fragment I used in this instance was quite colourless and transparent, 1½ inch long, and was lent to me for these experiments by Professor Weiss. At a heat in which the difference of path had become 5⁄4 undulation in the glass cube, it exhi-
