1888. | NEW YORK ACADEMY OF SCIENCES. 241 
sonator; then the waves from this resonator gain part of a 
wave length on those of the other resonators, which still vibrate 
synchronously with their forks. To allow for diminution of in- 
tensity in the sound of the fundamental resonator, the others 
may be withdrawn slightly from their forks. Helmholtz failed 
to detect the slightest difference in quality as a consequence of 
this variation in phase. His conclusion, therefore, was that the 
‘‘ differences in musical quality of tone depend solely on the 
presence and strength of partial tones, and in no respect on the 
differences in phase under which these partial tones enter into 
composition.” If this unexpected conclusion be wrong, then 
either there was some fault in the mathematical deduction from 
the theory of resonators, or the mere fact of throwing a resonator 
out of tune so alters the conditions as to mask completely the 
change of quality that might otherwise be rendered sensible. 
The first of these alternatives is not very probable, for Helm- 
holtz’s skill as a mathematician is unquestioned. ‘The second 
may be substantiated if an independent method of experiment 
is devised, by which the effect of change of phase is actually 
made perceptible. 
As early as 1868 M. Rudolph Koenig constructed a wave siren 
which he employed in his investigations on the beats producible 
by combination of sounds of known interval. This instrument 
was subsequently modified and improved, and was applied by its 
inventor to the investigation of musical quality. (Pictures 
were here shown of two forms of wave siren, including the one 
containing the Jatest improvements, and their mechanism was 
explained by the speaker.) The wave siren may be described 
briefly as an apparatus in which a blast of air is forced through 
a narrow cleft against the edge of a moving plate or disc on 
which a series of determinate wave forms have been cut. Hach 
sinuosity, as it passes the cleft, interrupts the egress of air, so 
that a series of compound pulses are propagated, whose group- 
ing is determined by the form of the curved edge. The pitch is 
determined by the wave length cut in the metal, through either 
the convex surface of a cylinder which rotates on its axis or the 
edge of a disc which rotates about its centre. A number of such 
wave forms, each with its own wind-cleft, may be operated at 
the same time, with the same speed, and with the same pressure 
of air at each cleft. ‘They may be arranged to either coincide or 
differ in phase to any required extent. In 1881 Koenig pub- 
lished the result of his experiments with this instrument, which, 
for the specific object he had in view, is far more satisfactory 
than that employed by Helmholtz. His conclusions may be ex- 
pressed as follows (Quelques Haupériences d’Acoustique, p. 
242) :-— 
