ON THE HYDRODYNAMICAL THEORY OF SEICHES. 627 
SEICHES IN A CONVEX SYMMETRIC PARABOLIC LAKE. 
h(x) =h x (1+2’/a’). 
A @) G@ 2 A 
Fr. 5. 
oP n 
B- Oe gos py 
Ou? zs gh( 1 + «/a?) 
w= c/a, 
: (a= ; 37 
j (l+w ae Os : : (37), 
c=a/g, _- : : : : : (38). 
e therefore 
EA(1 +?) =u= {A O(c, w) + B S(c, w)}sin ne ; 
C= ani G'(c, w) +B Sc, w)}sin nt. 
ust vanish at the vertical ends corresponding to w= +1, we have, although 
erent reason, the same boundary conditions as before, viz.— 
A CG(c,w) +B Se, w) =0, 
A @(c, w) - BG, wv) =0. 
is before, we arrive at the two sets of solutions 
Be A G(¢,,_1, w)sin ,,_, ¢ 
~ fh Leu? ; 
(39) ; 
C= =U cai 1D) SI Py geal! B 
cB Sloss) sin ny, 
=F) 1+? 
(40) ; 
B a . 
€ ais S (Eqs W) SIN Nog ; 
js, - --- ,m%1,....- are the roots of the equation 
O(c. 1)=0; 
Mee... - » %, -.. - are the roots of 
Sle, 1)=0. 
1,W) and G(‘,,,w) are, of course, no longer polynomials, but transcendental 
ns of w. 
