VIBRATION OF BODIES IN GENERAL. 367 



lations are only plans of projected structures ; and 

 those plans which exhibit only one vast and single 

 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 intermediate 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 me- 

 chanical 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 calcu- 

 lations connected with sound belong to its agree- 

 able 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 



