388 Prof. S. P. Thompson on the Pseudophone. 



and, developing the sines, 



m _/\ sin 6 cos <£ + cos 6 sin $ 

 n f 2 sin d> cos 6? — cos (/> sin 6? 

 Divide by cos 6 cos $>, and reckon f l =if a . 

 m tan 6 + tan . 



whence 



and 



But 



n tan <£ — tan # 



77i + ?i tan c/> 



m — n "~ tan 



tan = — ; — tan 

 m +72 



h /I 



... tan (^^—^ tan 



? 1 + h 2 



Or the difference of the intensities as compared with their sum 

 affords a means of comparing the angle between the line of 

 vision and the direction in which the sounds come, with the 

 angle made by the effective surfaces that receive the rays of 

 sound*. 



Such an estimate as we are therefore able to make of the 

 position of a source of sound, judging solely by the relative 

 intensities of the sensation in the two ears, depends upon our 

 previous perceptions and upon our possession of a constant 

 amount of effective auditory surface, and a constant angle 

 subtended between the ears and the line of vision. 



In the Pseudophone these angles are variable, and the 

 amount of effective surface can also be varied, and this with- 

 out any knowledge, on the part of the person experimenting 

 with the instrument, as to how much they may be varied. 

 Hence the acoustic illusions which are now to be described. 



* This equation, which is the starting-point of Steinhauser's theory, 

 ought more strictly to he interpreted thus : The ratio between the differ- 

 ence of the intensities and their sum is the same as the ratio between the 

 tangent of the angle between the line of vision and the direction in which 

 the sounds come and the tangent of the angle made by the effective sur- 

 faces that receive the sound with the line of vision. Steinhauser assumes, 

 as it is assumed in the paragraph above, that the ratio between the tan- 

 gents of the angles will be the same in our perception as the ratio between 

 the angles themselves. This is, of course, only true when the angles are 

 very small. Only, unfortunately, for very small angles the perception 

 ceases to be very accurate. No experimental determinations of the degree 

 of accuracy of perception have yet been published. 



