Vol. 6, 1920 
PHYSICS: G. W. STEWART 
167 
3 (242)). They found that, for a frequency of 256 d.v., if the difference 
of phase at the ears was kept zero but the ratio of intensities varied, there 
appeared a moving phantom source having a position in front, for an in- 
tensity ratio of unity, and rotating horizontally about the observer, its 
angular displacement from the median plane being proportional to the 
logarithm of the ratio of the intensities at the two ears, the constant of 
proportionality varying for the individual and for the frequency. This 
logarithmic law has now been further tested for frequencies of 512 and 
1024 d.v., and has been found to be correct for displacements from the 
median plane, less than 90°, excepting that for the 1024 d.v. some individ- 
uals do not get a moving phantom source of the fused sound. It would 
thus appear that intensity might have an important influence in localiza- 
tion. But such a conclusion must involve a quantitative test. Assume 
a source of sound at a distance of five meters from the observer and carried 
in a circle about him. It is possible, by means of theory (Stewart, Physic. 
Rev., 33, 1911 (467)), to compute the ratio of intensities at the ears produced 
by such a source at different angular displacements from the median 
plane. But one can, by means of the experiments already mentioned, 
ascertain what apparent angular displacements would be produced by the 
computed intensity ratios. Do these computed displacements agree with 
the actual? If they do, obviously intensity is an important factor in the 
actual case. But they do not agree quantitatively. For example, if 
the displacement of the source was 60°, the computed displacements for 
one observer were as follows: for 256 d.v., 6.1°, for 512 d.v., 13.8°, and 
for 1024 d.v., 11.2°. For a second observer, and the last two frequencies^ 
the computed angles were 9.1° and 9.1°. A careful examination of all 
angular displacements up to 90° showed a similar lack of correspondence. 
Obviously the intensity effect cannot account for the ability to locate 
sounds. It does not appear to be even an important factor. 
Experiments showed that for some people (two out of four observers) 
the intensity effect disappeared entirely in a certain frequency region. 
With each of four observers the intensity effect in a relatively large fre- 
quency region involved not only a moving phantom source of sound, but 
also an additional one stationary and in front, or in a position correspond- 
ing to the difference of phase. 
The logarithmic law of Stewart and Hovda appears not to be merely 
an extension of Weber's Law, as at first announced. 
Phase. — ^That phase difference affects the localization of a sound source, 
has been known for a number of years. (Review of literature; Stewart 
Physic. Rev., 9, June, 1917 (502).) Hartley {Physic. Rev., 13, 1919 (373)), 
has produced evidence in favor of the conclusion that the phase differ- 
ence of a pure tone at the ears is the controlling factor. The present re- 
port presents a considerable addition to this evidence and that of a quan- 
titative character. In the experiments, frequencies from approximately 
