1873-] Notices of Books. 397 



brought into being, the Natural Sciences are concerned with 

 dead, indifferent matter, obviously indispensable for the sake of 

 its practical utility, but apparently without any immediate bearing 

 on the cultivation of the intellect." The author is afterwards 

 led to compare the Natural Sciences with the other branches of 

 learning as a means of culture. He distinguishes between the^ 

 " Experimental " Sciences and the " Natural " Sciences ; and 

 asserts the advantage of the former because ''they can change 

 at pleasure the conditions under which a given result takes place, 

 and can thus confine themselves to a small number of charac- 

 teristic instances in order to discover the law." He regards the 

 discovery of the law of gravitation as " the most imposing 

 achievement that the logical powers of the human mind have 

 hitherto performed." The entire discourse indicates great 

 powers of generalisation. Such attempts to define and determine 

 the precise extent of syncretism which shall exist between diverse 

 sciences can only be made by master minds, which shall be ex- 

 cellently exact, and at the same time comprehensive, and such a 

 mind we have in Prof. Helmholtz. 



The second lecture treats of the scientific researches of Goethe. 

 It was said of Sir Humphry Davy that if he had not been a 

 great natural philosopher he would have been a great poet. In 

 the case of Goethe, the poet eclipsed the natural philosopher ; 

 while the " Egmont" and " Wilhelm Meister," " Hermann and 

 Dorethea " and " Faust" are always remembered in connection 

 with his name, few recognise the fact that he wrote a " Beitrage 

 zur Optik " two years before "Wilhelm Meister." He also wrote 

 on botany and osteology. He introduced into science two im- 

 portant and fruitful ideas : — "The first was the conception that 

 the differences in the anatomy of different animals are to be 

 looked upon as variations from a common phase or type, induced 

 by differences of habit, locality, and food." The second was "the 

 existence of an analogy between the different parts of one and 

 the same organic being." Goethe's theory of colour is open to 

 much criticism, and violent controversies have raged about it. 



The third lecture treats of a subject to which Prof. Helmholtz 

 has devoted considerable attention, and which has received at 

 his hands a notable development. It treats " of the Physiolo- 

 gical Causes of Harmony in Music," and was delivered in Bonn 

 during the winter of 1857. Since that time the celebrated 

 " Tonempfindungen " has appeared, and we are glad to learn 

 that this work is now being translated by Mr. Alexander Ellis, 

 and that it will soon be published by Messrs. Longmans. In 

 the lecture on Harmony, the author investigates the " foundation 

 of concord." He gives us eminently scientific definitions of 

 musical tone, pitch, sound, and quality of tone. The formation, 

 progress, and interference of waves is admirably treated, and 

 the woodcuts relating to this subject are worthy of close study 

 (notably Fig. 2, p. 72). In concluding, the author remarks, "For 



VOL. III. (N.S.) 3 F 



