98 



LOED RAYLEIGH ON THE ACOUSTIC SHADOW OF A SPHERE, 



in which we may put 



= 2-1925., 



= 2-1711, &c. 



Thus 



$ (o) _ 



... = + 1-0962 + -0054 -f- "0004 = 1-1020, 



and for the actual remainder this is to be taken negatively. The sum of the infinite 

 series for = 180 is accordingly 



- -0225 + -1785 t 



(25), 



from which the intensity, represented by ('0225)- -f ('1785) 2 , is proportional to 

 03237. Referring to (17), we see that the amplitude of i/ is in this case 



(26). 



X v/('03237) 



4TTC 



We may compare this with the amplitude of the vibration which would occur at 

 the same place if the sphere were removed. Here 



(27), 



477?' 



47TC 



since r = 2c. The effect of the sphere is therefore to reduce the intensity in the 

 ratio of -25 to "03237. 



In like manner we may treat the case of = 90, i.e., when the point of 

 observation is on the equator. The odd P's now vanish and the even P's take signs 

 alternately opposite. The following table gives the values required for the direct 

 summation, i.e., up to n = 21 inclusive : 



