262 Prof. A. Steinhauser on the Theory 



It is possible, for example, to conduct researches upon pure 

 direct hearing, uncomplicated by effects of reflexion, by means 

 of a watch removed to as great a distance as is convenient and 

 held by some person in any place he chooses, whilst the ob- 

 server attempts with closed eyes to discover its direction by 

 its ticking. Moreover the direct action of the sound will not 

 be injuriously affected by effects due to reflexion, provided 



for then 



(h + Pi)-(h + p2 ) _ (h — h) + (pi—P2) _ h—h . 



(h + pi) + (h + P2) (h + h) + (pi + p 2 ) h + k' 

 and therefore, if we substitute in equation (3) the value thus 

 found for 



ft— h) + (pi— P2) 



we again obtain the equation 



tana = -^ — ^tan (3, 



h + h 



in which « indicates the direction in which the source of 

 sound is actually situated. 



But from the proportion stated above we may deduce 



hh + hpi = hh + hp2, 

 or 



i 2 p 1 = i 1 p 2 ; 

 therefore the proportion holds good, 



Pi' P2 = h- h* 

 Hence the power of estimating the direction is not affected by 

 the effects of reflexion, provided the increments of intensity 

 thereby occasioned in the two ears are respectively proportional 

 to the intensities produced by the sound directly. 



It will now be considered in the calculations which follow 

 whether effects of reflexion produced by a single plane surface 

 (say, for example, a vertical wall) can in certain cases fulfil 

 the conditions mentioned above — that is to say, whether a 

 position of the wall can be discovered in which the increments 

 of intensity p 1 and p 2 arising from reflexion are respectively 

 proportional to the intensities directly produced. 



As in the previous figures, let A A' in figure 7 represent 

 the line of sight, f x and f 2 the effective surfaces of the pinnse, 

 each including with it the angle /3, a the angle included be- 

 tween the line of sight and the direction of the rays of sound 

 S, which impinge upon both the reflecting wall W and the two 



