ON THE HYDRODYNAMICAL THEORY OF SEICHES. 607 
Earn, which is asymmetric, the uninode is very near the middle; but in Treig this is 
not so nearly the case: in neither is the trinode coincident with the uninode. In both 
these lakes the deep binode is not far from the point of greatest depth; in both the 
shallow binode is nearer the end than a fourth of the leneth of the lake ; but, whereas 
in Harn the binodes are on opposite sides of the deepest point, in Treig they are on the 
same side. In neither lake are the binodes equidistant from the uninode. It remains 
to be seen how far these results of theory will agree with observation. 
§12. When the breadth and the form of the transverse section of a lake vary as 
well as the depth, provided these variations are not too abrupt, it can be submitted to 
calculation by introducing two new variables, viz., ¢, which is the product of the area of 
the transverse section by the breadth of this section at the surface ; and v, which is the 
area of the surface of the lake between the trace on the surface of the transverse section 
corresponding to c, and any other similar line chosen for reference. In order to submit 
the lake to calculation, its line of maximum depth is taken and laid out straight ; and 
practically the lake is treated as if it were a lake of uniform breadth and rectangular 
eross section, whose longitudinal section is the curve, the abscissa and ordinate of any 
point on which are v ando respectively. This curve | call the normal curve of the 
lake. If we may judge by our results for Treig and Harn, these assumptions are 
sutliciently correct for ordinary concave lakes at least. 
§ 13. In my calculations no account is taken of the dissipative forces which damp 
the seiche oscillation. In some cases the damping is hardly sensible during the period 
for which a seiche is observed to be pure, or even simply dicrote. Foret quotes an 
observation of Puianramour’s, in which a pure uninodal seiche in Léman, whose 
maximum double amplitude was about 169™™., lasted for seven and a half days, and 
consisted of 148 oscillations. The mean double amplitude of 20 oscillations was at 
first 167™™, and at the 140th, 80™™. It was finally disturbed by the appearance of 
a binodal component, which turned it into a dicrote seiche ; otherwise Foret calculates 
that it might have lasted two days more.* In other cases the damping of some of 
the pure seiches seems to be considerable, owing probably to the fact that the lake 
is, so to speak, not well tuned for particular periods. This is seen by studying the 
form of the limnograph trace, by the elegant method suggested by Sorer.t <A serious 
difficulty is thus raised if we attempt to determine the seiche periods from the dicrote 
trace; and it is not unlikely that some of the divergence between the results of 
observations at different times on the same lake may be due to this cause. Calcula- 
tion and observation alike have led me to the conclusion that the best way to 
determine with final accuracy the seiche constants for a lake is to deduce 
approximately the periods and the positions of its uninode and binode beforehand 
_ ~~ Itis just possible that this seiche may have been maintained by ‘some continuing but partly intermittent 
external cause. The limnogram given by Fore. seems to show traces of the interference to which ENpRos has 
called attention. 
t Arch. de Sc. Phys. et Nat. Genéve, 3™¢ Pér, t. iii. p. 1, 1880. The method has been elaborated and used with 
great effect by EnpRés, l.c., p. 15. 
TRANS. ROY. SOC. EDIN., VOL. XLI. PART IIT. (NO. 25). 90 
