666 DR J. HALM 
As regards the constants c, which determine the periods of the various seiches, we 
have the following values : . 
abn eatec Uninodal |. geo eh : Trinodal Quadrinodal 
Lake with ene Binodal Seiche. SEane | Seicnel 
concave parabolic floor, . 3 2-00 6°00 120 20:0 ; 
plain horizontal __,, . | a ine DeSean: 22°25 39 Olam 38) 
convex parabolic _,, ; an PaO <- : WOBBLE DSS ae | Oa. (38) 
convex quartic Es ; aj Z 00 15-00 | 35°0 | 63:0 ; 
and on virtue of the equation T \T, = Were. 
TD, Se ee eee 
concave parabolic : ada, 408 317 2 
plain horizontal : 500 333 250 (39) 
convex parabolic : 472 Bie) ‘234 1 
convex quartic : ‘447 "293 ‘218 
We recognise here, in a more general form, the law found by Professor Curysrat, that 
in concave lakes the ratio T,/T, is greater and in convex lakes smaller than the corre- 
sponding ratio in a lake with plain horizontal floor 
The positions of the nodes may be represented in a convenient graphical form, which 
not only shows clearly their dependence on the curvature of the lake, but at the same 
time enables us to find the nodes for the curves lying between those here discussed, 
which are not amenable to direct analytical treatment. In fig. 1 are shown the halves 
of the vertical longitudinal sections of symmetric lakes. OB represents a, the half- 
length, and O A the central depth, h, of the lake, whereas A B, AC, A D, and A E signify 
the intersections of the vertical plane with the concave-parabolic, the plane-horizontal, th 
convex-parabolic, and the convex-quartic floors. Now, on each of these curves the nodes 
have been marked by the points B,, B,, B,, ete., in such a way that for instance the 
distance of B, from A O agrees with the value of w in (43) which refers to the binodal 
seiche in a lake with concave parabolic floor, t.e. w= = =0°577. Inthe same way H, is 
drawn at a distance 0°447 from A O, thus representing the position of the binode in a 
convex-quartic lake. Having secured the corresponding four points on each of the 
curves A B, AC, AD, and AE, we draw the curved lines B, H,, B,; Ez, and B, Ky, and 
these lines are obviously the doce of the nodes. We recognise at once in all cases the 
displacements of the nodal points towards the shallow water, a phenomenon specially 
marked in concave lakes. Let us now take, for instance, a convex lake whose depth is 
Pee Le: 
Hee 
represented by h,/1 +’ and is indicated in our diagram by the dotted curve AF. The | 
solutions of the corresponding differential equation 
a 
NEL Tyee h ty = =0 
are not known, and hence we are not in a position to compute the nodes and periods of | 
these particular seiches by analytical methods. But approximately the nodes may he 
now directly found from the diagram, being represented by the points of intersection | 
between the Joci BE and the curve AF. It would seem, therefore, that by the preceding | 
