ON THE HYDRODYNAMICAL THEORY OF SEICHES. 639 
For large values of v, we have 
T, = 16a/(2v+ 1) /(gh) . - (D. 
And, when 1/2 is negligible, simply 
) T,=8a/v J(gh), 
=41/v /(gh). : : : ; : (88) . 
Hence, as the nodality increases, the periods of the pure seiches tend more and more 
to follow the harmonic law; and ultimately are the same as the periods in a uniform 
lake of double the length. 
If ,2, have the same meaning as before, and ,X, have a corresponding meaning for 
the ventral points, we find 
1 = ,2,/@ =Joya[j? = T,?/Tors § 
in, Xe 72 (27202. ; ; 5 eR 
Hence, if we compare the different nodes of the same seiche, the distances of the nodes 
from the end of the lake are inversely proportional to the squares of the periods of the 
lower seiches of odd nodality. 
If we compare nodes of the same order for different seiches, the distances from the 
end are directly proportional to the squares of the periods of the corresponding seiches. 
It is also easy to see from the above formule that, when the nodality of the 
seiche is high, the wave lengths near the ends of the lake increase at first in 
arithmetic progression. 
If we apply the rule of Du Boys to the present case we get 
al i-44/( ()/2 Fone =a" 
Since T, = 271/7,,/(gh) , we have 
a B= yl 881 5 
that is, Du Boys’ rule gives too great a period, as it does in the case of parabolic 
or quartic concave lakes: the deviation is even greater than in the case of a 
‘symmetric parabolic lake. 
As the present case is an interesting one, serving as a standard of comparison for 
other cases, I add some numerical data. 
Table of Ratios of Periods for a Complete Symmetric Rectilinear Lake. 
T,/T, T,/T, T,/T, T;/T, T,/T, T,/T, T,/T, T,/T, T,,/T, 
6276 | 4357 | 3428 | -2779 | 2365 | -2040 | -1805 | -1609 | 1460 
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 25). 94 
