SIMPLE -HAKMONIC WAVES. DIFFRACTION 253 



the conditions postulated, exactly opposite to that transmitted 

 by an aperture of the same dimensions. This is a familiar 

 fact in Optics ; but the preceding considerations shew that it 

 may be utterly wide of the mark when the wave-length is no 

 longer small compared with the linear dimensions concerned. 



It need hardly be said that there are acoustical phenomena 

 where, as in the case of large reflecting or obstructing surfaces, 

 optical relations are approximated to. The results are then 

 analogous, the resemblance being more complete the higher 

 the pitch of the note sounded. By the use of a source of very 

 high pitch, and of a sensitive flame as a detector, Lord Rayleigh 

 has succeeded in imitating some of the most delicate phenomena 

 of physical optics. 



In the above theoretical investigation we have been obliged 

 to rely to some extent on intuitive considerations, as e.g. in the 

 assumed distribution of velocity over the area of an aperture 

 when the wave-length is relatively small. It is therefore 

 desirable that such assumptions should be tested if possible by 

 exact calculation. The only instance, at present, where this has 

 been successfully carried out is that of waves incident on a 

 plane screen with a straight edge. The reflection by the screen, 

 the transmission past the edge, the formation of a shadow 

 behind the screen, and the diffraction phenomena near the 

 boundaries of the respective regions, all come out in practical 

 accordance with the usual theory. The investigation was 

 published by Sommerfeld in 1895*. 



* A simplified version is given in the Proc. Lond. Math. Soc. (2), vol. iv. 

 (1906). 



