242 TRANSACTIONS OF THE [MAY 21, 
‘The complex sound obtained by the composition of a series 
of harmonics, of even as well as of odd orders, quite independ- 
ently of their relative intensity, has always its maximum of 
strength and its greatest acuteness of quality for a difference of 
phase of a fourth of a wave length; the minimum of strength 
and the softest quality for a difference of phase of three-fourths 
of a wave length; the sounds corresponding to differences of 
phase zero and a half wave length lie between these two ex- 
tremes in regard to both intensity and quality. 
‘¢The composition of a series of harmonics, taken in the order 
of the odd numbers, gives the same sound for differences of 
phase one-fourth and three-fourths, and also the same sound for 
differences zero and one-half; but in the first case the sound is 
stronger and more brilliant than in the second. 
‘“<Tf, then, quality depends indeed principally on the number 
and relative intensity of the harmonics into which it can be de- 
composed, the influence of the difference of phase of these har- 
monics is not so small that it can properly be neglected. It 
may be said that if changes in the number and relative in- 
tensity of the harmonics produce differences of quality such as 
are observed in instruments belonging to different families, or 
such as the human voice shows in the different vowels, the 
changes due to difference of phase between the same harmonics 
are yet capable of producing differences of quality at least as 
sensible as those which are noticeable in instruments of the same 
kind, or in the same vowels sung by different voices.” 
These conclusions expressed by M. Koenig have not yet re- 
ceived the general credit to which they are entitled. ‘The cause 
of this is found partly in the overmastering authority of Helm- 
holtz’s splendid researches, which preceded Koenig’s investiga- 
tions on this topic, and partly in the fact that but few persons 
have had the opportunity personally to test the subject 
experimentally. The present writer, while spending a few weeks 
in Paris during the last summer (1887), enjoyed the privilege of 
using the wave siren in company with M. Koenig, and with 
satisfactory results. He noticed a distinct change of quality 
with change of phase. The chief object of the present paper is 
to add his confirmation to the conclusion reached by M. Koenig, 
and to call attention to what is due an acoustician whose me- 
chanical skill in the construction of apparatus is more than 
equalled by his originality, care, and patience in investigation. 
