-27- 273 



Use the same variables A,B as in part II and let 

 D stand for the (fixed) distance of the sea bed from a 

 point 33 ft» above sea level. In place of the equations 

 (2.2), (2.3), (2.4), we have'"' 



(3,1) SnpA"^ [(l+f^)A^ - 2f^AB + (|+f2)B^J 



+ iTrA"^pg(D-B) + G(A) = E, 



where f ,f-,fp are functions of the ratio A/B which 



represent the influence of the rigid wall on the motion of 



4 3 

 the bubble, — n A pg(D-B) represents the gravitational 



potential energy due to the lack of water in the space 



occupied by the bubble, and g is the acceleration due to 



gravity. Explicit expressions for f , f,, fg are derived 



In [5], and will be reproduced in appendix II of this report. 



Introduce non-dimensional quantities as in equations 



(2.5), (2.6) of part II, sections 3 and 4. The energy 



equation becomes 



(3.2) a^Cd+f^)!^ - 2f^ab + (l + f^)^^] 



_, d-b „3 k _ T 



B 



,„Vip-pp d = £ b = — and B is the initial distance of 

 ..liui c '-^ L » "o L ° 

 the bubble from the sea bed. 



The motion of the bubble is determined from (3.2) 

 and one of the Lagrangean equations (2.12), (2.13). Using 



■«• See appendix II for details. 



