Mr Sharpe, On the Reflection of Sound at a Paraboloid. 119 

 As far as this goes the terms in the bracket are accurate. To 

 y 



OF '=7i/2 



Fig. 3. 



get further in the direction of (56) we must approximate, when we 

 shall get 



where 



r<t>i 

 I = I cos [v — \A log v + Cj — v<f) 2 ] d<f>, 

 J -$, 



G^Alog^Ah-i) 



.(59). 



.(60), 



The final result will be that in (56) 



B = 2-iTr-i (e^ A + e~^ A ) (cos G 1 + sin C,) 

 G = 2^tt-^ (e^ A + e~i" A ) (cos G x - sin G x ) 



where G x is given by (59). Here of course the exponential factor, 

 if A be large (as it may be, provided that A 2 /v be small) indicates 

 the magnification of the sound at the point considered. As in 

 Art. 12 so (56) indicates stationary vibration and we have two 

 equal and opposite waves, which are continually reflected at OL 

 fig. 2. The amplitude is (B 2 + G 2 fjv^ or if A be large, 



amplitude = e^/2* ttM (61). 



(61). 



25. We will now compare together the two solutions (46) and 



Remembering (Art. 5) that the original A and so the present 



