154 Lord Kayleigh on the Passage of 



to amount to a considerable multiple of the length of a 

 wave. 



An effective test on these lines of! the escape of sound 

 through a narrow slit seeming hopeless, attention was turned 

 to the opposite extreme where the length of the slit is re- 

 garded as a small, in place of a large, multiple of the wave- 

 length. The expression replacing (2) is now* 



co* ( nt — kr) 

 ^ = M- — , .... (o) 



where M denotes the electrical capacity of a plate having tha 

 size and shape of the aperture, and situated at a distance 

 from all other electrified bodies. So far as I am aware, M. 

 has not been calculated for a rectangular aperture ; but for 

 an ellipse of semi-major axis a and eccentricity e 



M = -- r - x (4) 



4 (e) ' 



F being the symbol of the complete elliptic function of the 

 first kind. When e = 0, F(e)=^7r; so that for a circular 

 aperture M = 2a/7r. 



If the ellipse be very elongated, 



F w= Ib g v /(fe) =log T' • • • (5) 



if b be the semi-axis minor, so that in this case 



M =io g( l ( //;/ ■■'•,:■■ c«> 



The introduction of this value into (3) shows the same com- 

 parative independence of the magnitude of the width of the 

 small aperture as was manifested in (2). It is understood 

 that the longer dimension 2a of the ellipse, as well as the 

 shorter, is to be a small fraction of A- 



In the earlier experiments the latter condition was but 

 imperfectly fulfilled. The source of sound was a bird-call f 

 giving a wave-length of 44 inch or 30 mm. The wave- 

 length is ascertained in the usual way by placing a high- 

 pressure sensitive flame in the stationary system compounded 

 of the direct waves and of those reflected perpendicularly 

 from a movable reflector. The displacement of the reflector 

 required to pass from a maximum to a maximum or from a 



* See equations (14), (15) of memoir cited, or 'Theory of Sound, 

 §292. 



f < Theory of Sound/ § 371, 2nd edition. 



