SEICHES AND OTHER OSCILLATIONS 
71 
Fionn, and Finglen — which drains into the eastern half. It appears 
from the hmnogram that for some time after the flood commenced 
the level of the whole lake was rising at the rate of '32 mm. per 
minute. In half the period of the uninodal seiche this would give 
a rise of 2'3 mm. Supposing this flood at the very beginning to be 
thrown only on the western half of the lake, there would be a 
disturbance equivalent to an increase of atmospheric pressure of 
4'6 mm. of water. Acting during half the uninodal period, this, by 
the mathematical theory,^ would produce uninodal and trinodal seiches 
having extreme amplitudes of 6*8 mm. and 2*8 mm. If the first 
incidence of the flood were concentrated on, say, the western quarter 
of the lake-surface, the resultant seiche would, of course, be still 
greater. The rise shown at the binode was actually about 5*5 mm., 
which corresponds to an extreme amplitude for the uninodal seiche of 
9*4 mm. It is therefore quite possible that the seiche may have been 
wholly due to the sudden flood on the western half of Loch Earn, 
and there appears to be no other way of accounting for it. 
4. Effect of Rainfall. — In order to obtain an idea of the eflect of 
heavy rainfall in causing a seiche, suppose a cloudburst to fall on the 
eastern half of Loch Earn (idealised into a symmetric parabolic lake). 
If (T denote the rainfall in centimetres per second, v the velocity of 
the rain-drops as they reach the surface of the lake, p the pressure at 
time t after the shower begins, then 
p = (t(v + gt) (dyne/cm.-) 
= crv/g+ at (gm./cm.2) ; 
or, if the pressure be measured in millimetres of water, 
p = 1 Oa-v/g + 1 Oat 
^q + rt, say. 
Suppose that the shower begins when the uninodal seiche 
culminates, and that it lasts for half the uninodal period. Then, if 
dL\ denote the alteration in the amplitude of the uninodal seiche at 
the end of the lake, by the mathematical theory ' 
8^,=t^ + f.T,, 
where is due to the impact, and |7'T^ to the static effect of the 
precipitated water. 
To take an extreme case,^ let o-= -2/60== -1/30, v = 700. Then, 
taking T^ = 15 x 60 as a round number, q = '024, r = l /SO. Hence 
dk^ = -036 4- 22-5 = 23 mm., say. 
1 Trans. Boy. Soc. Edin., vol. xlvi. p. 503. 
2 Ibid., p. 512. 
3 See Hann, Lehrbuch der Meteorologie (1906), pp. 270, 275. 
