Crystallization in the Mineral Kingdom, 1 31 



It may be asserted that not only clinochlore, but also the 

 other micas (the Aster ites, ' B. M/ p. 375) which have been 

 believed to possess one optical axis, but which have indeed two 

 weakly developed axes, and may therefore be said to have nearly 

 one axis, belong to the hexagonal system. And now my mea- 

 surements of the tourmalines, so long doubted, will be recognized 

 as correct. I may here remark that the angles I gave as belong- 

 ing to the red tourmaline from Siberia, may require some correc- 

 tion, owing to the crystals examined not being well fitted for 

 the purpose. But for the other tourmalines I had always good, 

 sometimes first-rate crystals to operate on ; moreover, occasionally 

 differences of more than 30 minutes appeared in the inclination 

 of the rhombohedral planes. Why have not these measurements 

 been repeated by others, that they might be confirmed or rejected? 

 Why has the incorrect assumption been retained, that the pri- 

 mary form of all tourmalines is a symmetrical rhombohedron ? 

 Measurements are possible with a hand goniometer to a quarter 

 of a degree when the crystals are good. Truly, next to want of 

 truth, indolence is the greatest foe to the advance of science. 



The essential crystallographical varieties extend still further. 

 Many years ago I observed that the four planes of a crystal 

 of anatase had at one pole a fourfold inclination towards the 

 tetragonal base ; a learned friend at that time induced me to 

 believe that I had supposed a plane to be the basal one, which 

 was in fact only very obtusely pyramidal. Unfortunately I gave 

 in — and ceased my measurements too soon, for I had found im- 

 portant differences. I have since lost the notes I took at that 

 time. The mighty architect of the universe can have forgotten 

 no law in the construction of the " crystal world " which would 

 tend to the completeness and harmony of the whole. 



I have often repeated these observations, and can now say 

 with certainty that we find in anatase a fourfold inclination of 

 the pyramidal planes to the base, which differ 34 minutes alto- 

 gether, and form a tetraplohedron. These observations, how- 

 ever, are not yet terminated, and must be often repeated to 

 ensure perfect accuracy. On this account anatase also must 

 have two optical axes. Unfortunately a crystal of anatase which 

 I sent to be cut and polished, in order to test this fact, broke 

 during the operation. Further, I believe I may say from care- 

 fully conducted investigation, that the tungstates of lime (Pyra- 

 midites hystaticus and Pyramidites macrotypicus, c Breithaupt's 

 Mineralogy/ pp. 266, 268) have also an asymmetrical arrange- 

 ment of their pyramidal planes, and will be found to have two 

 optical axes. The following hexagonal minerals, from the 

 analogy of careful observations, must be asymmetrical, and 

 those which are transparent have two optical axes. 



