368 POPULAR LECTURES AND ADDRESSES. 



t\vo in the cases we arc about to consider more 

 particularly, but is applicable to flexible or elastic 

 bodies and fluids ; and to complex systems pre- 

 senting a finite number of independent variables, 

 on account of solid bodies or material particles, and 

 infinite numbers of variables, due to flexible, 

 elastic, or fluid matter, influenced by them. It 

 includes, for example, the well-known dynamical 

 theory of the vibrations of a stretched cord, of air in 

 an organ pipe, or of water in an open basin of any 

 shape. In the first two of these cases the periods 

 arc all sub-multiples of the gravest fundamental 

 modes ; whence the explanation of the harmonics 

 of musical cords and of wind instruments ; whence 

 also the fact that a stretched cord struck or 

 disturbed in any manner takes a perfectly periodic 

 motion, and gives a true, although not a pure and 

 simple, musical sound, with the peculiar character 

 of the violin, pianoforte, or harp, depending on the 

 way in which the vibration is excited. lUit the 

 fundamental modes of vibration of an elastic 

 solid for instance a stiff metal bar, or a stiff spiral 

 wire (as the " bell " of an American clock), a sheet 



