REVIEWS 163 



CRYSTALLOGRAPHY 



A Manual of Geometrical Crystallography. Treating solely of those portions 

 of the Subject useful in the Identification of Minerals. By G. Montague 

 Butler, E.M. [Pp. viii + 155, with 107 figures.] (New York: John 

 Wiley & Sons, 1918. Price 7s. net.) 

 ACCORDING to the preface this book is intended for those whose sole aim in 

 acquiring a knowledge of crystallography is to use it in the sight-recognition of 

 minerals, and consequently every part of the subject not pertaining directly thereto 

 is rigidly omitted. The detailed treatment of the crystal systems is prefaced by 

 an introductory chapter giving the fundamental definitions and followed by con- 

 cluding sections dealing with twinning, cleavage, habit, and so forth. The major 

 part of the book is occupied by a description of the forms occurring in the various 

 systems and the means by which they can be readily recognised. 



The treatment of the idea of symmetry is very unsatisfactory, as, except for an 

 erroneous definition of a symmetry axis on p. 4, the only symmetry element 

 considered throughout the book is the plane. This neglect of axial symmetry in 

 the discussion of the various crystal classes compels the author to introduce a 

 "law of crystal axes" to explain the presence of two parallel faces in monoclinic 

 and triclinic forms, and then to violate this law in his definition of hemimorphic 

 crystals. The omission, in the systematic portion of the book, of those crystal 

 classes in which no mineral is known to crystallise is to be commended, but the 

 utility of this part would have been increased by the mention of a few mineral 

 examples, particularly as many of the figures represent combinations characteristic 

 of particular minerals. The Weiss notation is used throughout in place of the 

 more usual Miller's symbols, though at the end of each system comparative tables 

 of symbols of several notations are given, but without any explanation of the 

 methods of derivation. In the section on twinning the statement that in certain 

 classes a twin plane may be parallel to a symmetry plane seems to be based on a 

 misconception of supplementary twinning. 



It is very doubtful if such a radical departure from the orthodox method of treat- 

 ment will result in any appreciable conservation of the student's time, particularly 

 where simplicity is attained at the expense of accuracy. The possibility of the 

 student making further excursions into the subject should not be forgotten, and 

 consequently care should be taken that there be as little to " unlearn " as possible. 



Many of the figures are set obliquely and a few misprints occur, the most 

 notable being on pp. 100 and 121. 



A. Scott. 



Lectures on the Principle of Symmetry and its Application in all Sciences. 



By F. M. Jaegar, Ph.D., Professor of Inorganic and Physical Chemistry 



in the University of Groningen, Holland. [Pp. xii + 333, with 170 figures.] 



(Amsterdam : Publishing Co. "Elsevier," 1917.) 



Although the principle of symmetry is of considerable importance in many 



branches of science, yet very few works, with the exception of some mathematical 



and crystallographic treatises, discuss it in a systematic way. Morphological 



symmetry is indeed mentioned in some general biological books, while molecular 



symmetry, or rather the so-called "asymmetry," is usually discussed in connection 



with organic chemistry ; but the treatment, particularly in the latter case, is 



often very inadequate, and certainly never systematic. This book, therefore, 



is assured a welcome, particularly as few authors are so well qualified as Professor 



Jaegar to deal with this subject. His chemical researches have been largely 



