J'me 29, 1882] 



NATURE 



205 



difference of phase = \ is a reversed copy of that for 

 whio the difference of phase = o ; while the curves for 

 phast-difference 5 and f are reversed copies of one an- 

 other Now, according to Helmholtz's theory, all these 

 formsof vibration should yield identical sounds in the 

 ear. Kcenig finds, on the sontrary, the startling result 

 that th» sounds are perceptibly different in quality. His 

 proof is extremely simple. The curve, calculated graphi- 

 cally with great care, is set off upon the circumference of 

 a cylindrical band of thin metal, the edge being then cut 



away leaving the shaded portion, the curve being repeated 

 half a dozen times, and meeting itself after passing round 

 the circumference. For convenience the four curves to 

 be compared are set out upon separate rims of metal, all 

 of which are mounted upon one axis to which a rapid 

 motion of rotation can be imparted. Against the indented 

 edges of these rims wind can be blown through an appro- 

 priate slit ; the whole combination forming a variety of 

 the Wave-Siren described a few months ago in the 

 columns of Nature (p. 358, vol. xxiv.). It will be 



Fig. 3.— Resultant wave-form for odd members of serits of upper partial t 



ofpha 



I J 



obvious that as these indented curves piss in front of 

 the slit the maximum condensation will result when the 

 slit is least covered, or when the point of greatest depres- 

 sion of the curve crosses the front of the slit. The 

 negative ordinates of the curves correspond therefore to 

 condensations, the positive ordinates to rarefactions. 

 Now, according to Kcenig's experiment, the sound is 

 louder and more forcible, with a difference of phase of \, 

 than in any other case, that with J difference being the 

 most gentle and soft in tone ; whilst the curves of phase 



o and \ yield intermediate qualities of tone. Kcenig also 

 finds that by combining simply a note and its octave, the 

 loudest resultant sound occurs when the phase of com- 

 bination is j, a difference of phase of \ again yielding 

 the feeblest resultant. In Fig. I, b, four curves are shown 

 corresponding to the combination of the odd members, 

 1, 3, 5, 7, 9, of the harmonic series, taken as before as of 

 equai intensity. In this case the form of the waves is 

 identical for the phases o and A and also for the phases j 

 and j. The latter yield a loud" and strident tone as com- 



