46 
THE FRESH-WATER LOCHS OF SCOTLAND 
would have after it has fallen from rest through a distance equal to 
half the depth at that point. 
This formula is exact for a lake of uniform breadth and depth, 
but errs in excess for a lake having a concave, and in defect for a 
lake having a convex, bottom. But the approximation becomes 
better as the nodality rises ; and, for that and other reasons, his rule 
is very useful in limnographic calculations. 
Experimental Verification of the Hydrodynamical Theory. — 
In order to satisfy myself of the applicability of the theory of long 
waves to seiches in an elongated lake, I asked Messrs White and 
Watson, two of Professor Macgregor's students, to make for me a 
series of experiments on waves in a tank fitted with various longi- 
tudinal sections. The conditions in the laboratory experiments were 
very much less favourable for the theory than in actual lakes. For 
example, the ratio of the depth to the wave length in the experiments 
ranged from 1/40 to 1/4, as against 1/4500 in the case of Loch Earn. 
Nevertheless, for the lower nodalities the observed and calculated 
periods agreed within the limits of experimental error, as will be seen 
by the following tables : — 
1. Seiches ix a Concave Symmetric Complete Parabolic Lake (§ 27, H.T.S.) 
JSf. B. — All linear measurements are in centimetres ; the periods are given in seconds. 
A a O a A 
[ft = 70 cm. ; h = l0-9 cm.] 
Position of 
T 
2 
T4 
Binode - . 
h 
a 
obs. calc. 
obs. 
calc. 
obs. 
calc. 
obs. 
calc. 
obs. 
calc. 
obs. 
calc. 
10-9 
2-98 2-99 
1-72 
1-73 
1-24 
1-22 
•98 
•95 
•80 
•77 
•567 
•577 
9-4 
2-98 1 2-99 
1-72 
1-73 
•566 
•577 1 
6-2 
2-98 2-99 
r72 
1-73 
•573 
•577 
