VIBRATION OF BODIES IN GENERAL. 4:7 



and sino-le arch, or which suppose no support but that which our own 

 position supplies, will assuredly never become realities. "We must 

 have a firm basis of intermediate generalizations in order to frame a 

 continuous and stable edifice. 



In the subject before us, we have no want of such points of inter- 

 mediate support, although they are in many instances irregularly 

 distributed and obscurely seen. The number of observed laws and 

 relations of the phenomena of sound, is already very great ; and 

 though the time may be distant, there seems to be no reason to despair 

 of one day uniting them by clear ideas of mechanical causation, and 

 thus of making acoustics a perfect secondary mechanical science. 



The historical sketch just given includes only such parts of acoustics 

 as have .been in some degree reduced to general laws and physical 

 causes ; and thus excludes much that is usually treated of under that 

 head. Moreover, many of the numerical calculations connected with 

 sound belong to its agreeable effect upon the ear ; as the properties of 

 the various systems of Temperament. These are parts of Theoretical 

 Music, not of Acoustics ; of the Philosophy of the Fine Arts, not of 

 Physical Science ; and may be referred to in a future portion of this 

 work, so far as they bear upon our object. 



The science of Acoustics may, however, properly consider other 

 differences of sound than those of acute and grave, for instance, the 

 articulate differences, or those by which the various letters are formed. 

 Some progress has been made in reducing this part of the subject to 

 general rules ; for though Kempelen's " talking machine " was only a 

 work of art, Mr. "Willis's machine, 19 which exhibits the relation among 

 the vowels, gives us a law such as forms a step in science. We may, 

 however, consider this instrument as a phthongometer, or measure of 

 vowel quality ; and in that point of view we shall have to refer to it 

 again when we come to speak of such measures. 



On the Vowel Sounds, and on Reed Organ-pipes. Camb. Trans, iii. 287 



