VIBRATION OF BODIES IN GENERAL. 365 



bodies. It was formerly held that tense strings and 

 elastic rods could vibrate only in a determinate 

 series of modes of division, with no intermediate 

 steps. But M. Savart maintains 18 , on the contrary, 

 that they produce sounds which are gradually trans- 

 formed into one another, by indefinite intermediate 

 degrees. The reader may naturally ask, what is the 

 solution of this apparent contradiction between the 

 earliest and the latest discoveries in acoustics. And 

 the answer must be, that these intermediate modes 

 of vibration are complex in their nature, and diffi- 

 cult to produce ; and that those which were for- 

 merly believed to be the only possible vibrating 

 conditions, are so eminent above all the rest by 

 their features, their simplicity, and their facility, 

 that we may still, for common purposes, consider 

 them as a class apart; although for the sake of 

 reaching a general theorem, we may associate them 

 with the general mass of cases of molecular vibra- 

 tions. And thus we have no exception here, as we 

 can have none in any case, to our maxim, that what 

 formed part of the early discoveries of science, 

 forms part of its latest systems. 



We have thus surveyed the progress of the 

 science of sound up to recent times, with respect 

 both to the discovery of laws of phenomena, and 

 the reduction of these to their mechanical causes. 

 The former branch of the science has necessarily 

 been inductively pursued; and therefore has been 

 18 An. Chim. 1826, t. xxxii. p. 384. 



