44 
THE FRESH-WATER LOCHS OF SCOTLAND 
Again, for a lake whose longitudinal section (or normal curve) is a 
certain quartic curve, Tv = p/ e), where p and e depend on the 
dimensions of the lake, and e may be positive or negative, according to 
circumstances. 
4. Hence it follows that the ratio of the binodal to the uninodal 
period may be less than, equal to, or greater than J, according to 
circumstances — a fact which seems to have puzzled seiche observers 
considerably. Indeed, I have shown that quartic lakes can be 
imagined in which the periods T^, Tg, T3, . . . may be as nearly all 
equal as we please. 
5. The positions of the nodes are given by the roots of certain 
equations xX^) = ^ ^ and the ventral points by the roots of certain 
other equations (pX^') = 0. The roots of these equations interlace 
with each other; but the quarter wave lengths are not, in 
general, equal, as in the case of the lake of uniform breadth and 
depth. 
6. The following tables, founded on calculations partly by myself 
(H.T.S.), partly by Dr Halm, will convey a clear idea how the ratios 
of the periods and the positions of the nodes may vary in lakes of 
uniform breadth but different shapes of floor : — 
Lake with 
T,/T,. 
T4/T,. 
concave parabolic floor . 
•577 
•408 
•317 
plain horizontal . 
•500 
•333 
•250 
convex parabolic , , . 
•472 
•312 
•234 
convex quartic • 
•447 
•293 
•218 
Positions of Nodes 
Lake with 
Uninodal 
Seiche. 
Binodal 
Seiche. 
Trinodal 
Seiche. 
Quadrinodal 
Seiche. 
concave parabolic floor . 
plain horizontal • 
convex parabolic . 
convex quartic • 
w = 0 
0 
0 
0 
+ •577 
+ -500 
+ -473 
+ -447 
0 ; +-775 
0; ±-667 
0 ; + •632 
0 ; ±'600 
+ -340 ; +-S62 
+ •250; +-750 
+ -224 ; + ^717 
+ ■202 ; +^684 
where is the distance of a node from the centre of the lake, half the 
length being taken as unity. 
7. A shallow or other obstruction, or a deep near a node, greatly 
affects the corresponding period, a shallow increasing the period, a 
deep decreasing it. Also a shallow attracts the node towards itself, 
and a deep repels it. Thus, for example, the bin odes in a parabolic 
lake are nearer the ends than in a rectangular one. 
