PHYSICS NINETEENTH CENT. SOUND. 541 



comparing this apparatus with a monochord (page 14), he found that 

 when each sounded the same note, the number of blows given to the 

 card was equal to the number of complete, double, or to-and-fro vibra- 

 tions of the cord. A comparison of the toothed wheels with Cragniard 

 de Latour's instrument showed that exactly the same sounds were ob- 

 tained by the two methods of communicating impulses to the air. The 

 toothed wheels could indeed be employed after the manner of the 

 revolving discs in the syren, by directing a current of air against the 

 teeth of the wheel, perpendicularly to its plane, from the orifice of a 

 small tube ; so that as each tooth passed the current of air was inter- 

 rupted. The notes thus yielded by the wheels were identical with 

 those produced by the shocks given to the piece of wood or card- 

 board. Savart endeavoured to ascertain the limiting number of vibra- 

 tions per second at which the ear ceases to have any perception of 

 these vibrations as sounds. With a wheel 9 inches diameter, however, 

 the tones lost their clearness when 4,000 impulses per second were 

 given. But when a wheel 18 inches in diameter, with the same number 

 of teeth, was used, sounds up to 15,000 vibrations per second were 

 audible. With a still larger wheel the number of vibrations producing 

 an audible sound was carried to 24,000 per second. It would appear, 

 therefore, from these experiments that, had the diameter of the wheel 

 been further increased, while the number of teeth remained the same, 

 a greater number of shocks than 24,000 per second might have been 

 made audible. This shows that an increase in the intensity of the 

 impulses extends the limits of audibility. In fact, Despretz afterwards 

 proved that sounds may be heard corresponding with the rate of 

 38,000 vibrations per second. The whole range of musical tones dis- 

 tinguished by the human ear extends, therefore, over nearly seven 

 octaves. 



The most interesting inquiries belonging to the science of acoustics 

 are undoubtedly those relating to musical tones. We have seen that 

 the ancient Greeks were accurately acquainted with the relative lengths 

 of vibrating strings which yield harmonic intervals. But these ratios 

 were by them, and by others down to comparatively recent times, 

 considered as significant of some recondite^relation between whole 

 numbers and musical sounds. When the investigations of the eigh- 

 teenth century brought to light the laws of vibrations in strings, it was 

 of course perceived that the simple ratios belonged essentially to the 

 vibration rates, and that they applied to the tones of all musical in- 

 struments. Very curious, however, were the explanations given of the 

 pleasure derived by the ear from concordant tones. Even Euler en- 

 tertained a notion that the listener was thus pleasurably affected be- 

 cause the mind easily comprehends simple ratios, whereas, as a matter 

 of fact, no numbers or ratios are presented to the consciousness of 

 the hearer, but are associated with musical harmonies in the minds of 

 the scientific inquirer only. It has been reserved for a distinguished 



