( 629 ) 
XXV. — Theoretical Determination of the Longitudinal Seiches of Lake Geneva. 
By A. T. Doodson, R. M. Carey, and R. Baldwin, Tidal Institute, University 
of Liverpool. Communicated by Dr E. M. Wedderburn. 
(MS. received November 11, 1919. Read January 12, 1920. Issued separately April 2, 1920.) 
1. The theoretical determination of the longitudinal seiches of a lake was reduced 
by Professor Chrystal # to the finding of those solutions of the differential equation 
*Y+A_v-o 
dor? p(x) 
( 1 ) 
which vanish at x = 0 and x = a. 
Here x denotes the area of the surface of the lake from one end up to any trans- 
verse section, and ranges from 0 to a, a being the total area of the surface of the 
lake ; p(x) denotes the product of the area of the transverse section at x and its 
breadth at the free surface ; ^ = <r 2 /g, & being the “ speed ” of the periodic motion and 
g the acceleration due to gravity ; V denotes the total volume of water which has 
passed the section up to the time t. 
If £ denotes the elevation of the free surface at the transverse section corre- 
sponding to x, we have 
£= - 
3V 
dx 
( 2 ) 
An inverted graph of the function p(x) was called by Chrystal the “ normal 
curve” of the lake, and it can be constructed from the results of a bathymetrical 
survey. By approximating to the normal curve by geometrically simple curves, 
Chrystal showed how to find the required solutions of (l), and he and E. M. 
Wedderburn applied the method to Lochs Earn and Treig.f The normal curves of 
these lakes are fairly regular, and results were obtained closely in agreement with 
observation. 
In a recent paper by J. Proudman, \ a general solution of the problem has been 
given which does not involve approximations similar to those of Chrystal, and the 
object of the present paper is to give details and results of the application of this 
solution to Lake Geneva. The normal curve of Lake Geneva had been constructed 
some years ago by Wedderburn ; he suggested that the present method should first 
be applied to this lake, and very kindly supplied his data and calculations. A glance 
at the diagrams illustrating the normal curve will show how complex the curve is ; 
the approximate methods introduced by Chrystal were not easily or satisfactorily 
• “ Hydrodynamical Theory of Seiches,” Trans. Roy. Soc. Edin., vol. xli, p. 599. 
f “Calculation of the Periods and Nodes ot' Lochs Earn and Treig,” ibid., p. 823. 
\ “ Free ami Forced Longitudinal Tidal Motion in a Lake,” Proc. Lond. Math. Soc., series 2, vol. xiv, p. 240. 
TRANS. ROY. SOC. EDIN., VOL. LII, PART III (NO. 25). 97 
