1875.] Notices of Books. 525 
defined as being due to non-periodic motions—that is to say 
motions which do not return to the same condition after equal 
intervals of time; while the latter are due to periodic motions— 
that is, motions which do return to the same condition at the 
end of equal intervals of time. The production and propaga- 
tion of sound is discussed, and the distinguishing features of 
musical tones—to wit, force or loudness, pitch or relative height, 
and quality ; also the various means of indicating and examin- 
ing these distinctive features. The musical tones which can be 
used with advantage are stated to be between 40 and 4000 vibra- 
tions in a second—a range of seven octaves ; while the limits of 
audibility ranges over 11 octaves, from 20 to 38,000 vibrations a 
second. The range of the eye, on the other hand, scarcely exceeds 
one octave. Many terms are explained and definitions given, 
also a minute account of vibrations and of their graphic repre- 
sentation. 
In the second chapter the composition of vibrations is dis- 
cussed. As an analogy, the various simultaneous waves pro- 
duced on water are exemplified, and we are told that we must 
imagine the same kind of action as taking place in the air. In 
a crowded ball-room, for instance, we have the various sounds of 
the musical instruments, the rustling dresses, the voices of men 
and women, and so on, and here ‘ we have to imagine that from 
the mouths of men and from the deeper musical instruments 
there proceed waves of from 8 to 12 feet in length; from the 
lips of the women, waves of two to four feet in length; from the 
rustling of the dresses, a fine small crumple of wave, and so on: 
in short, a tumbled entanglement of the most different kinds of 
motion, complicated beyond conception.” It is then shown that 
such composite masses of tone may be regarded as, and re- 
solved into, simple tones. In the next chapters we plunge at 
once into the more complex technicalities of the subject, and 
the analysis of musical tones is discussed; first, by sympathe- 
tic resonance; secondly, by the ear. The whole structure of the 
ear is minutely discussed, and the functions of its various parts 
are described. Some new woodcuts, from Heule’s *‘ Manual of 
Anatomy,” illustrate this part of the subject. An elaborate 
treatment of the Cortian fibres, and the office of the Cochlea, 
conclude the first part of the book. 
The second part is ‘“‘On the Interruptions of Harmony ;” the 
third ‘‘ On the Relationship of Musical Tones.” Here we have 
an account of the development of musical style, and a division 
of all music into three parts, viz., the homophonic, or unison music 
of the ancients ; the polyphonic music, with several parts, extend- 
ing from the roth to the 17th century; and, finally, harmonic or 
modern music, the special characteristic of which is the signifi- 
cance attributed to the harmonies. 
The primitive form of music with all nations appears to be 
simple melody sung by a single voice, and it still remains 
