Chta-Shun Yth 
Far Te Be SL es (5) 
which is the free-surface condition. 
We shall assume 
P= £ (53) vy) expi (Kec<pont) '4 (6) 
in which k is the wave number and o«@/27 _ is the frequency. Then 
(2) becomes 
RES ERAT 9 Paes a8 (7) 
ax yy 
(3) becomes 
Sit ull 
Snes an ee (8) 
and (5) becomes 
2 
cf = af at the free surface , (9) 
with subscripts indicating partial differentiation. Equations (7), (8), 
and (9) constitute an eigenvalue problem, of which, k?2 being given, 
o? is the eigenvalue to be found. 
Ill) THE DIFFERENTIAL SYSTEM FOR SUPERPOSED LAYERS 
If the fluid system consists of superposed layers, each of 
which is homogeneous, the differential equation for each layer is still 
(2), the boundary condition (3) still holds. The interfacial condition 
at each surface of discontinuity can be derived in a way similar to the 
way in which (5) is derived. The result is 
1400 
