258 Prof. J. P. Cooke on the Vermiculites. 



fraction yielding a biaxial ring system, with uniform distribution 

 of colours, and very variable optical angle. I have measured 

 angles from about 30° to about 13°. The angle often varies 

 widely in different parts of the same plate. Thus I have mea- 

 sured on different laminse, from a single plate not exceeding 3 

 inches in diameter, the three angles 30°, 24°, and 13°; and, 

 again, I have noticed a similar variation on one and the same 

 lamina. Indeed the phenomena which I observed were almost 

 identical with those I had previously observed on plates of ripi- 

 dolite from Texas, Pennsylvania (loc. cit.). On moving the lamina 

 just referred to parallel to itself, in front of the polarizing micro- 

 scope, the optical angle varied as I passed from one side of the 

 field to the other. Beginning with a value of about 30°, the 

 angle decreased to about 13°. Moving the plate still further, I 

 found a region of indistinctness ; and then the axes opened again, 

 the new plane making an angle of 120° with the old. I had evi- 

 dently here a macling precisely similar to that I had previously 

 described in the Texas ripidolite, and shown in fig. 8, where the 

 lines of shading represent the position of the plane of the optical 

 axes. This represents what we may call an ideal made; for I 

 have seldom been able to trace more than three individuals on 

 the same plate, and, as a rule, these are very unequally developed. 

 On many of the specimens of the North-Carolina vermiculite, 

 the macling is externally marked by the eminent cleavage or 

 jointing parallel to the shorter diagonal of the rhomb section ; 

 and in several of the specimens I have examined it was quite 

 symmetrical. A study of these specimens led me to an expla- 

 nation of the cause of the remarkable variation of the optical 

 angle, which I believe not only applies to the vermiculites and 

 ripidolites, but also, in many cases at least, to the micas. It 

 would be expected that the several members of such macles as 

 fig. 8 represents would penetrate each other; and I therefore 

 made a series of experiments to ascertain what would be the 

 effect of the interfoliation of laminse in which the planes of the 

 two sets of optical axes had the same relative position as in the 

 several members of the made. To that end I divided a plate, 

 which presented the largest optical angle I had observed, into 

 as thin laminse as possible, and then superimposed them in the 

 relative position I have mentioned, so that the planes of the op- 

 tical axes should be inclined at an angle of 60°. The result was 

 (when the thickness of the plates in each position was nearly 

 equal) that a symmetrical ring system was obtained in which the 

 optical angle was about 13° — the smallest I had measured; and 

 by varying the relative thickness, intermediate degrees of optical 

 divergence were produced. By now introducing laminae into 

 the compound crystal in the position of the third member of the 



