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XXXV. Notices respecting New Books. 



Ueber Harmonie unci Complication. Von Dr. Victor Goldschmidt. 

 Pp. 136 +iv, with 28 figures in the text. Berlin: Julius 



## Springer. 1901. 



Tiber harmonische Analyse von Musikstucken. Von Victor Gold- 

 sohmidt. Ostwald's Annalen cler Naturphilosophie : Leipzig. 

 1904, vol. iii. pp. 449-508. 



UOE centuries has it been a favourite study of able thinkers to 

 investigate the fundamental principles upon which the various 

 branches of knowledge have been developed, and to trace a con- 

 cordant relationship in phenomena to all appearance entirely 

 dissimilar and disconnected. No doubt it will be ultimately dis- 

 covered that the varied and apparently divergent paths along 

 which science progresses meet eventually in the same, though may 

 be many-sided, goal — the constitution of matter. In these days 

 of extreme specialization, when each worker sees little more than a 

 small portion of some particular subject, it is of importance to 

 have our thoughts occasionally brought back to the possible re- 

 lations underlying the fundamental principles of different branches 

 of science. Professor Goldschmidt is well known as one of the 

 leading crystallographers of the day ; and his work has always been 

 distinguished by its versatile and philosophical character. In this 

 remarkable treatise Ueber Harmonie unci Complication he has, with 

 characteristic energy, undertaken a task requiring a breadth of know- 

 ledge such as is rarely possessed by any individual. Pew probably 

 feel at home in all of such a diversity of subjects as are discussed by 

 him ; and, indeed, to many such a conjunction may seem altogether 

 fantastic, to be dismissed with a jest. Nevertheless Professor 

 Goldschmidt submits to the reader a strong case ; and the evidence 

 produced is far sounder than the kind met with in most philo- 

 sophical writings dealing with uniformity in the universe. 



More than a century has elapsed since Haiiy established the 

 great crystalline law on which the whole science of crystallography 

 has been built. This law, usually known as the law of rational 

 indices, states that the positions of the natural faces bounding a 

 crystal are not haphazard, but obey a very simple relation. Haiiy 

 himself studied the more complicated question of the arrangement 

 of the ultimate units in a crystal ; and the law mentioned is an 

 immediate deduction from the principles laid down by him. Later 

 writers have, however, seldom gone behind the law, and they 

 mostly ignore the absolute positions of the faces. The habit, that 

 little understood character of crystals, w T hich varies so strangely in 

 crystals identical in other respects, is not considered or explained 

 by this law, beyond that all crystals have the symmetry of one of 

 thirty-two classes. Professor Goldschmidt, in the course of a 

 number of important papers which have appeared in the Zeitschrift 

 fur Krystallographie unci Mineralogie during recent years, pro- 

 poses an extended form of this law, which includes the principle 

 of symmetry and at the same time places the relative development 



