280 Notices respecting New Books. 



of the faces lying in the same zone in a novel and clearer light. 

 Thus, suppose we have a series of such faces ABCDEEGrHI, 

 no two of which are parallel ; we select the two most prominent 

 faces, A and B, as coordinate faces and the next in importance, C, 

 as the unit face. The remaining faces, then, fall into groups 

 [DE], [FGrHI], and so on, as shown in the following Table. The 

 members of each group will be similar in their characters : size, 

 frequency of appearance, &c. 



Primary faces : A B 



N = oo Normal row 0. 



1 complication: A C B 



N t = 1 oo Normal row I. 



2 complication : D D C E B 



N 2 = } ■ M oo Normal row 2. 



3 complication : AEDGCHEIB 



N 3 = 0^§lf23oo Normal row 3. 



The numbers under each face are the ratio of the corresponding 

 indices, supposing that A and B are the pinakoids (01) and (1 0). 

 Each row is developed from the preceding in precisely the same 

 way. 



It was natural to one of Professor Gold Schmidt's philosophical 

 temperament not to confine his attention to the morphological 

 characters of crystals, but to investigate the possibility of a wider 

 application of this same law. His investigations resulted in the 

 work under discussion, Ueber Harmonie und Complication. 



The brief introduction deals with the arrangement of the faces 

 on a crystal, from which, as we have pointed out, the author 

 originally deduced his law of complication. Then follows pro- 

 bably the most important and — running as it does to 66 pages — 

 certainly the longest part of the book, on the Sensations of Tones. 

 The science of sound in its physical, its aesthetic, and its physio- 

 logical aspect has received so much attention and study as to 

 provide obviously a ready means of testing the principle of compli- 

 cation developed by the author. We may here remark that the 

 later treatise, Uber harmonische Analyse von Musikstiicken, is an 

 extension of this part with a somewhat different treatment, as 

 will be explained below, and is intended more particularly for 

 musicians. 



The notes comprising the diatonic scale of C major and their 

 relative vibrations (z) are 



d e f g a 



9. 5. 4 3. 5_ 



8 4 3 2 3 



tonic second third fourth fifth sixth seventh octave 



9. 5. 4 3. 5_ JJL o 



1 843 2 3 8 z 



