SIMPLE-HARMONIC WAVES. DIFFRACTION 245 



though large as compared with the linear dimensions of S, 



are small compared with X. Let two surfaces be drawn, on 



the two sides, at some such distance from 0, each abutting 



on the screen in the manner indicated by the dotted lines 



in the figure. Within the region thus bounded, the fluid 



oscillates backwards and forwards almost as if it were in- 



compressible, and the total flux ( 67) through the aperture 



will therefore bear a constant ratio to the difference of the 



velocity-potentials at the two surfaces. This will perhaps be 



understood more clearly if we have 



recourse to the analogy of electric 



conduction. Suppose we have a / 



large metallic mass, severed almost / 



in two by a non-conducting parti- / 



tion occupying the place of the ;,' 



screen. If this mass form part of \ 



an electric circuit, there will be \ 



little variation of potential in it \ x 



except in the neighbourhood of the Xv 



narrow neck which connects the two 



portions. The electric potentials Fig" 74 



at a distance on the two sides being 



<>! and <f>. 2 , the current through the neck will be 



*(*.-&) ......................... (3) 



where K may be called the " conductivity " of the neck, the 

 specific conductivity of the substance being taken to be- unity. 

 In the hydrodynamical question, also, the quantity K may 

 appropriately be called the conductivity of the aperture. It is 

 easily seen that it is of the nature of a length. 



At the two surfaces shewn in the figure we have ^ = 2(7, 

 <f> 2 0, approximately, and the total flux through the aperture 

 is therefore 2KC. If an equal flux were directed symmetrically 

 from the aperture on the left-hand side, the combination would 

 be equivalent, in an unlimited medium, to a simple source of 

 strength 4>KC. Hence, by 76 (12), 





