58 THE FRESH-WATER LOCHS OF SCOTLAND 
From the theoretical point of view, there is nothing surprising in 
the result j ust arrived at. Let us consider elongated lakes of uni- 
form breadth, and assume that the same normal curve continues to 
represent the lake-basin when the mean level rises or falls. For 
a lake whose longitudinal section is a rectangle T^^^l/p J(gh). 
Hence, since in this case I is constant, as h increases all the periods 
diminish. If the longitudinal section is parabolic, then T„ = 
'ttI/ J{p{i^-\-1)gh}^ In this case I is proportional to Jh; hence all 
the periods are independent of the depth of the lake. It is easy 
to see from the analysis in H.T.S., p. 628, that the same is true for 
a biparabolic lake. If the longitudinal section be rectilinear and 
symmetrical, shelving at both ends, then T^, = ^7rl/j^ J (gh).^ In this 
case / is proportional to /?, smdjv is a mere number depending only 
on the nodality ; hence T^, is proportional to Jh — that is to say, all 
the periods increase when h increases. Generally speaking, we may 
expect the rise of the mean level in a lake to increase its periods if 
the rise greatly increases the horizontal surface of the lake ; and to 
decrease the periods, if the rise increases the horizontal surface very 
little. It appears from the observations of Forel ^ and Ebert ^ that 
the Lake of Geneva and the Starnberger See belong to the latter 
category ; and Halbfass ^ has found that the Madlisee belongs to 
the former. Loch Earn occupies an intermediate position ; the 
constancy of its periods is therefore an indication that the assumption 
of a biparabolic normal curve is a good first approximation. 
The calculated positions of the nodal lines of Loch Earn are 
shown by red lines on the map which accompanies the paper C.P.N. 
The difficulties anticipated *^ in determining the nodes by direct 
observation were more than realised in practice. When the range 
of the seiche is large, there is nearly always a great deal of wind- 
embroidery of an irregular character, which it is impossible to 
eliminate entirely either by damping the limnograph or by residuat- 
ing the limnogram. Also, where the amplitude is small, there is 
almost always sensible disturbance arising from an aperiodic variation 
of the lake level, probably due to the heaping up of the water on 
the shallow shore, an effect which will vary with the slope of the 
beach. The varying slope also affects the range of the seiche at the 
margin of the lake to an extent which it would be difficult to calculate 
o 
1 H.T.S., p. 622. 
2 H.T.S., p. 638. 
2 Le Lemcin, t. 11. p. 122. 
" Perlodlsclie Seesplegelscliwankinigen beobaclitet am Starnberger See," 
Sitzber. kgl. bayer. Ahad. JViss., Bd. xxx. p. 453, 1900. 
^ " Steliende Seesplegelschwankungen Im Madlisee In Pommern," Zeitschr. f. 
Gewdsserhunde, Bd. vi. p. 65, 1902. 
6 C.P.N., p. 850. 
