462 PROFESSOR CHRYSTAL 



During the observations the mean level of Loch Earn varied through a range of 

 nearly 20 inches (over 50 centimetres) ; but a careful examination of the Tables I.— VIII. 

 does not appear to show any correlation between the depth of the lake and the various 

 periods. It follows that in the case of Earn, within the range of our observations, 

 the periods are independent of the depth. 



From the theoretical point of view, there is nothing surprising in the result 

 just arrived at. Let us consider elongated lakes of uniform 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 v =2l/v s /(gh). 

 Hence, since in this case I is constant, as h increases all the periods diminish. If the 

 longitudinal section is parabolic, then T„ = ttIJ <J{v(v+ l)gh}* In this case / is pro- 

 portional to tjh ; 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 bipara- 

 bolic lake. If the longitudinal section be rectilinear and symmetrical, shelving at 

 both ends, then T v = 2Trl/j v0 J(gh)J In this case I is proportional to h, and j„ is a 

 mere number depending only on the nodality ; hence T„ is proportional to fjh — 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 ForelJ and 

 Ebert§ that the Lake of Geneva and the Starberger See belong to the latter category; 

 and Halbfass || has found that the Madii See 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. 



If it be admitted that the periods are independent of the depth, the process of 

 taking means in Tables I. -VIII. is logically unobjectionable ; and, as the identity of 

 the uninodal, binodal, and trinodal seiches was fully established by phase observations, 

 it only remains to select what on the whole appear the probable results of observation 

 for T l9 T 2 , T 3 . Taking all the circumstances into account, I incline to the values 



T 1 = 14-52, T 2 = 809, T 3 = 6-01. 



The identification of the periods in Tables IX. and X. as quadrinodal and quinqui- 

 nodal respectively rests merely on the comparatively close agreement of the numbers 

 in each table with each other and with the quadrinodal and quinquinodal periods 

 deduced from the hydrodynamical theory and from Du Boys' formula. No phase 

 observations were available to assist the identification. 



* H.T.S., p. 622. t H.T.S., p. 638. 



\ he Leman, t. ii., p. 122. 



§ " Periodische Seespiegelschwankungen beobachtet, am Starnberger See," Sitz. Ber. kgl. buyer. Akud. d. Wiss, 

 VA. xxx. (1900), p. 453. 



|| "Stehende Seespiegelschwankungen im Mad usee in Pomnicrn," Zeitschrift fiir Gcwusserkunde, Bd. vi., p. 96, 



