2tt JJ 



212 Mr. C. V. Raman : The Experimental 



plane and on the positive side o£ it, is given by t he integral (d) 

 taken over the whole of the reflecting area. This integral 

 may be written as 



where 6 is the obliquity of the point of observation viewed 

 from the element dY dZ. The point of interest is, that for 

 all points on the continuation of the reflecting sheet, 6 being 



equal to ~ , the value of the integral is rigorously zero and 



the plane is therefore one of silence. This becomes of im- 

 portance experimentally when the angle of incidence is such 

 that the diffraction-pattern is formed near this plane of 

 silence. It is not difficult to understand why the elements 

 of a reflecting surface should be equivalent to double sources 

 and not to simple sources of sound : for, if the reflecting 

 plane be replaced by an indefinitely thin sheet in the same 

 position, every point of which instead of being kept fixed is 

 obliged to follow the vibration in the incident waves, then it 

 is obvious that these waves would be transmitted without 

 disturbance to the far side of the plane. The effect of the 

 reflecting plane must therefore be equivalent to that of the 

 reversed motion of the thin sheet in a medium entirely at 

 rest. This involves periodic compressions and rarefactions on 

 one side of the plane, and simultaneous rarefactions and 

 compressions on the other : i. e., periodic introductions and 

 abstractions of fluid on one side, and simultaneous abstractions 

 and introductions on the other. This is the equivalent of a 

 sheet of double sources. 



Passage of Plane Aerial Waves through an Aperture 

 in a Thin Plate. 



This can be seen to be directly deducible from the pre- 

 ceding : the integral (d) would have to be taken over the 

 reflecting plate (excluding the aperture), and the expression 

 for the velocity potential of a system of plane aerial waves 

 passing through an infinite medium superposed upon it. On 

 the positive side of the reflecting sheet, the integral (d) gives 

 the effect of the reflected waves, and since in the integration 

 the area of the aperture is excluded, the effect of an element 

 of the aperture in any direction on the positive side of the 

 sheet is zero. On the negative side of the plate, the distur- 

 bance passing through the aperture appears as the difference 

 of two quantities : if the integral (d) is taken over the whole 



