322 Notices respecting New Books. 



that beats arise ; and consonant intervals are those in which no 

 beats are formed, or, at least, such as produce no unpleasant dis- 

 turbance. 



Most musical tones being rich in upper partials, the consonant 

 intervals are limited by the beats arising when one or both tones 

 are imperfect; and in those instruments which are deficient in 

 upper partials, such as tuning-forks and stopped organ-pipes, the 

 required limitation is to some extent supplied by the combinational 

 tones. 



Again, the superiority of the major chord over the minor is 

 mainly due to the combinational tones of the first order being 

 audible in the latter. 



Eameau and D'Alembert were the first to recognize the import- 

 ance of partial tones in limiting the consonant intervals, about the 

 middle of last century ; and Tartini showed the importance of 

 combinational tones ; but their conclusions, though important ad- 

 vances, were imperfect and partial. 



The last division of the book consists of an historical survey of 

 the progress of music, mainly with a view to the application of the 

 physical principles established in the first two parts. The tonal 

 relationship which was the characteristic of European music, and 

 developed into the dependence of all the chords of a piece on the 

 fundamental chord, is to be regarded as a principle of style, in the 

 same way that the Gothic style of architecture is due to sesthetical 

 feelings, and not to physical principles. The structure of the dif- 

 ferent parts of the musical edifice, however, is governed by phy- 

 sical laws quite as much as is the construction of great buildings. 



It is impossible to enter fully into this part of the work, or to 

 to do more than merely allude to the leading discoveries of its 

 distinguished author ; so we shall content ourselves with saying 

 that this treatise will henceforth be a necessary part of the study 

 of any English student wishing to master the theory of music. 



The mathematics of the work are conveniently placed at the end 

 of the book, along with a valuable collection of notes by the trans- 

 lator, among which we may specially mention those on Prof. 

 Helmholtz's vowel-theory. 



Climate and Time in their Geological Relations : a Tlieory of Secular 



Changes of the Earth's Climate. By James Croll, of H. M. 



Geological Survey of Scotland. London : Daldy, Isbister, and 



Co. 1875. 



Neither Mr. Croll nor his work requires any introduction to the 

 readers of the Philosophical Magazine, and it is almost a super- 

 fluous task on our part to recommend the present book to favour- 

 able notice. For a long series of years Mr. Croll has been an 

 honoured contributor to these pages ; and a great proportion of the 

 contents of " Climate and Time " will be found scattered over the 

 volumes of the last ten or twelve years. Besides doing simple 

 justice to himself, Mr. Croll has rendered great service to the 

 advancement of science by the collection, systematic arrangement, 



