240 TRANSACTIONS OF THE [May 21, 
by the corresponding wave lengths, c the full series, d the odd 
components. ‘The variation in form is striking, and certainly 
affords ground for the suspicion that the perceived quality should 
vary. ‘T'o determine this question experimentally is difficult, 
not only because it requires a trained ear to appreciate such dif- 
ferences in quality as may be imposed, but because in no ordinary 
musical instrument is there any provision for the indication of 
the mode in which harmonic components are combined. 
This problem was first attacked by Helmholtz, and with nega- 
tive results. He used the same apparatus that was employed in 
his masterly analysis of vowel sounds. (A picture of Helm- 
holtz’s apparatus was here shown, and his method of work was de- 
Variation in wave form with change of phase. 
scribed.) ‘To secure variation of phase between any two com- 
ponents of a compound sound produced by a group of forks, he 
narrowed the aperture of oneof the resonators, thus throwing 
it slightly out of tune and weakening the resonance. As the 
result of mathematical investigation, Helmholtz reached the 
conclusion that if the pitch of the resonator is depressed, the 
greatest velocity in periodic motion of the air at its mouth 
slightly precedes that of the fork, producing thus a difference 
of phase. Suppose the resonators of the forks which yield the 
upper partials to remain open, while that of the fork yielding the 
fundamental is partly closed, so as to lower the pitch of the re- 
