Potential Problems connected with the Circular Arc. 277' 



compounded of a rotation about z=—i and a translation 

 parallel to the .r-axis. The application of equation (14) of 

 the preceding paper once more gives equation (8 b). 



Fig. 5. 



§ 4. On the boundary, z— —ie l6 , so that 



9 • 



w = Z(o sin- 



V 2"~ Sln 2 ~ Msm 2 f 



1 



</>=±2a)sin^^/si n 2|_ s i n 2^ f = 2co sin 2 ° 



. (9) 



where the positive value of the root refers to the convex 

 surface. For the energy of the motion, we have 



2T= j"<£di/r taken round the boundary 

 = 2ttg) 2 sin 4 -, upon evaluation. 



Introducing the radius a instead of unity, and the density 

 p or the liquid, J 



L=TrpG> l a* sin -. 



(10) 



