PROFESSOR AT HEIDELBERG 215 



especially physiological part, treats of the excitation of the nerve 

 itself, in correspondence with different sensations; and the 

 third, and more essentially psychological, section endeavours 

 to lay down the laws by which the ideas of definite external 

 objects, or percepts, result from these sensations. The physical 

 and mathematical basis of auditory sensation forms the subject 

 of a later very interesting work, which is, however, intelligible 

 only to mathematicians, while the physiological factors in 

 audition, along with the psychological and aesthetic considera- 

 tions, are submitted to a remarkable, and, for the most part, 

 easily intelligible analysis in the work itself. 



Part I, which treats of the composition of vibrations, the 

 theory of over-tones, and that of timbre or quality of sound, 

 presents, along with Part II, which deals with interference in 

 harmony, combinational tones and beats, consonance and 

 dissonance, an admirable and masterly treatise, popular in the 

 best sense, with a penetrating analysis, and an exposition, 

 illustrated by a wealth of new experiments, of the results 

 already published by Helmholtz in his separate papers. He 

 gives a precise account of the theory and construction of his 

 harmonium with naturally just intonation, and shows how the 

 siren of Cagniard-Latour, perfected by Dove, had now de- 

 veloped into his polyphonic siren. The first two parts of this 

 unique work accordingly deal with such phenomena as are 

 mechanically determined by the construction of the ear, and 

 are therefore independent of volition, so that it is possible to 

 determine the exact laws by which they are governed. Part 

 III, which is eminently original, magnificently planned, and 

 admirably carried out, deals with the relationship of musical 

 tones, and with scales and tonality, and enters the region of 

 aesthetics in order to establish the elementary rules of musical 

 composition. 



1 The relations between the physiology of audition and the 

 theory of music/ he said on a later occasion, ' are particularly 

 clear and striking, because the elementary forms of musical 

 composition depend far more essentially on the nature and 

 individuality of our sensations than is the case with the other 

 arts, in which the kind of material utilized and the objects to 

 be represented have a much greater influence.' 



Starting from the conviction acquired in the course of his 



