BY SMALL OBSTACLES OF CYLINDRICAL AND SPHERICAL FORM. 245 



wave-length, presents exactly the same difficulties as occur in the similar problem in 

 connection with the theory of a non-viscous gas. 



We shall also consider especially the case when the viscous gas is the air of the 

 atmosphere; in this case v is a small quantity about "132 in cm. sec. units, and 

 consequently we may regard o-v/c* as a small quantity for all wave-lengths. Since 

 a-v/c 2 is small, we may write very approximately from (9), 2, 



ft = -(l-AioWc*) . (6). 



_ \ l f / \ / 



C- 



We must now obtain approximations to the values of the constants in the expressions 

 for the scattered sound by means of equations (4) and (5). For this we shall need 

 the approximate values of the Bessel functions involved in these equations. For 

 convenience we shall write them down. 



When is small, we have for all values of n>0, 



91 /-, 1 \ | 



I) B () = - - ""+ less important terms 



TT 



2*n ! * 



7T 



J n () = _ . "+ terms containing higher powers of 

 J B ' () = g l ~ l + terms containing higher powers of 



Closer approximations are 



2 , \ i 1 



77 



' W" 



DI() = -{r 1 K (log K+y +&">)} D 2(0 = 



Also we have 



J.(0 = i-iP, J,(0 = K(i-K 2 ), J, (CHini-iW 



Now, on eliminating A n from equations (5), we obtain 



B B [ha . ka D,' (ha) D.' (Jfca)-w 8 D n (Aa) D n (to)] 



= -Wnha { J n (Aa) D,' (Aa)-D. (Aa) J/ (Aa)}. 

 Further 



by a well known result in the theory of Bessel functions. 



