IV. On the Acoustic Shadow of a Sphere. 

 By Lord KAYLEIGH, O.M., F.fi.8. 



With an Appendix, (jiving the } r alnes of LEG END UK'S Functions from P to P 20 

 at Intervals of 5 degree*. By Professor A. LODGE. 



Received December 28, 1903, Head January 21, 1904. 



IN my book on the ' Theory of Sound,' 328, I luive discussed the effect upon a 

 source of sound of a rigid sphere whose surface is close to the source. 



The question turns upon the relative magnitudes of the wave-length (X) and the 

 radius (c) of the sphere. If kc he small, where k 'lir i X, the presence of the sphere 

 has but little effect upon the sound to be perceived at a distance. 



The following table was given, showing the effect in three principal directions of 

 somewhat larger spheres : 



Here F J + Gr' : represents the intensity of sound at a great distance from the sphere 

 in directions such that //, is the cosine of the angle between them and that radhis 

 which passes through the source. Upon the scale of measurement adopted, 

 F 2 -+- G'' = ^ for all values of fj., when kc = 0, that is, when the propagation is 

 undisturbed by any obstacle. The increased values under /JL = 1 show that the 

 sphere is beginning to act as a reflector, the intensity in this direction being already 

 more than doubled when kc = '2. " In looking at these figures, the first point which 

 (362.) 9-3.04 



