MINERALOGY. 537 



isometric, pseudo-tetragonal, pseudo-hexagonal, &c., species. The most 

 common typical species under the systems of high grade of symmetry 

 have thus been thrown over into systems of lower symmetry 5 the list 

 includes such species as garnet, fluorite, analcite, apophyllite, rutile, 

 zircon, beryl, apatite, and so on. 



Opposed to the theory of Mallard is that advanced by Marbach and 

 Reuscb, and developed by Klocke, Klein, Ben Saude, and other min- 

 eralogists, which explains the "optical anomalies" by reference to the 

 state of molecular tension existing within the crystal and produced 

 during its growth. According to this view, the apparent geometrical 

 form of the crystal represents its true symmetry, and the optical proper- 

 ties observed which are at variance with it do not belong inherently 

 to the substance of the crystal, but have been produced by secondary 

 causes. Klocke has applied this theory to alum, Klein to boracite and 

 garnet, and Ben Saude to analcite and perofskite, but the full explana- 

 tion would require an amount of detailed description inconsistent with 

 the space allotted for this summary. 



As between the two theories, it may be said that while pseudo- 

 symmetry has a real existence — twins of orthorhombic species, arago- 

 nite, for example, often imitating hexagonal forms — still the weight of 

 argument seems to be in favor of referring the phenomena observed to 

 secondary causes, so that it is not yet necessary to call garnet a triclinic 

 species. On the other hand, although the extreme view of Mallard 

 may not be accepted, it is beyond question true that the result of the 

 accurate crystallographic and optical investigations of the past few 

 years has been to show that many crystals really belong to systems of a 

 lower grade of symmetry than that to which they have been previously 

 referred. It is impossible at present to say how far this may be carried. 

 The number of minerals to whose crystalline form and optical properties 

 especial attention has been directed in the past two years is so large 

 that they cannot be even enumerated here. 



One explanation for the great amount of study that has been devoted 

 to the questions above mentioned, and for the interest which they have 

 excited, is to be found in the fact that recent years have brought great 

 improvements in the instruments for the investigation of both the form 

 and optical properties of crystals. The microscope of Rosenbusch, since 

 1876 much used in the study of rock-sections, has been improved so as 

 to be suitable for the optical study of minute crystals. A microscope 

 especially adapted for this purpose has been devised by Bertrand in 

 Paris, and in his hands, as also those of Des Cloizeaux, it has given ac- 

 curate results in very many cases where the earlier instruments would 

 have yielded nothing. Improvements have also been made in the 

 polariscope and other similar instruments. New methods have been 

 introduced for the determination of the indices of refraction of crystal- 

 lized minerals; the most recent is that employed by Bauer, in which 

 he obtains the desired values by calculation from the measured distances 



