204 Mr Gookson, The Oscillations of a Fluid 



These series are absolutely convergent but are not very con- 

 venient for numerical work: it was necessary to include terms up 

 to </, 7 . 



We have also 



V ' — V —- V 

 - 1 n — - 1 n— 1 „.-*».> 

 X 



an equation required in the calculation of B n (/cr). 

 The formula 



J -^J -J 



X 



was occasionally used as a check. 



Large-scaled graphs were drawn of J x (x) and of y, ,. Y 1 (x) 



and the values of these functions read off them. The contour 

 lines were traced by assigning a value to the constant G in the 

 equation 



f(r) . cos nd — C, 



and by finding the values of corresponding to an assumed r. 



Numerical Application. 



Let a the inner radius of the trough be 1 2 inches, 

 „ b the outer „ „ „ 20 „ 



„ h the depth be \ inch. 



Then p = - = ~ . 



r a 3 



The first thing to do is to find k from equation (9): the first 

 two roots for the cases n = 0, n = 1 will suffice. 



I. n = : 



^w = 4-758 : tf < 2 > = 9-449. 



II. n = 1 : 



x x u = 4-824: a^w = 9-481. 



We have therefore 



^ o (i)-'|_ = 0-396: * < 2 > = 0-787, 



^d) = ^L_ = 0-402 : Kl ® = 0-790. 

 12 



