82 



SCIENCE. 



[N. S. Vol. II. No. 29. 



The object of tlie book, to give an ac- 

 count of the Lepidox)tera of Teneriflfe which 

 will enable students to identify their 

 specimens, is certainlj^ accomplished. An- 

 other edition should be enlarged to include 

 brief descriptions and, if possible, figures 

 of all the moths known to occur in Ten- 

 erifife. The systematic arrangement of the 

 moths in the text should also be revised to 

 correspond with that of the list. 



Samuel Henshaw. 



A Treatise on the Morphology of Crystals. By 

 ]Sr. Stoey-Maskelyxe, M. A., F. E-. S., 

 Professor of Mineralogy, Oxford. Octavo 

 xii. 4-521. New York, Macmillan & Co. 

 1895. S3.50. 



Although the constancy of angle between 

 like planes of crystals furnishes the basis for 

 a purely mathematical treatment, students 

 in mineralogy, chemistrj' and petrology, to 

 whom some knowledge of crystallogi-aphy 

 is essential, have rarely had the high math- 

 ematical training essential to the under- 

 standing of works like those of Liebisch, Mal- 

 lard or Klein, and they will appreciate this 

 treatise of the veteran Oxford professor, in 

 which the principles and problems of 

 crystallography are designedly treated in 

 the ' simplest form compatible with sti'ict 

 geometrical methods.' 



The work deals solely with the morphol- 

 ogy of crj'stals, and is to be followed bj^ a 

 volume treating, in a similar manner, the 

 phj'sical problems necessary to a thorough 

 knowledge of crystallography. After a 

 brief statement of the general properties of 

 crystals, especially the physical characters, 

 the author proceeds to the logical devel- 

 opment of his subject. The exjjressions 

 for the position of a plane and of an ori- 

 gin-edge or zone axis are first deduced and 

 the principles of stereographic projection 

 clearly and simplj' stated. The practical 

 application of the stereographic projection 

 is then made possible by the solving of cer- 



tain problems, such as: 'Given the projec- 

 tion of a great circle, to find that of its 

 pole ; ' 'To determine the magnitude of 

 an arc of a great circle from the projection 

 of that arc;' 'To draw the projection of 

 a great circle in which two points are given,' 

 etc. 



The properties of zones, the relation con- 

 necting tautozonal planes and the relations 

 between edges and normals are examined, 

 and the necessarj^ expressions deduced by 

 purely geometrical methods and also by the 

 methods of analytical geometry. Prelimi- 

 narjr to a discussion of symmetry, it is 

 clearly brought out that the only angles 

 possible between consecutive normals in 

 isogonal zones are 90°, 60°, 45° and 30°. 



Chapter IV. deduces expressions for 

 changing parametal planes and axes, and 

 proves that axes are not arbitrary diamet- 

 ral lines but are necessarily origin edges or 

 face normals. 



The possible varieties of sj'mmetry, holo 

 and mero, and composite and twin ci-ystals, 

 are elaborately treated. The author's word- 

 ing of the law of symmetry or second fun- 

 damental law of crj'stallography is new and 

 very thorough. "On a crystal the extant 

 or absent features of a form must be extant 

 or absent in the same way in respect to 

 equivalent systematic* planes." The six 

 systems are separatefy considered each un- 

 der the headings: holosymmetrical forms, 

 hemisymmetrical forms, combinations of 

 forms, and twinned forms. The balance of 

 the book is taken up with methods of meas- 

 urement, calculation and representation. 



The work is clearly printed and the dia- 

 grams are well conceived. The mathemat- 

 ical deductions can usually be followed by 

 any one with a working knowledge of ge- 

 ometry and analytical geometry. The 

 statements and definitions are verj"^ exact 

 but not alwaj's concise. For instance, the 

 definitions of a crj'Stalloid system of planes 



*PlaDes of symmeti'y. 



