SEICHES AND OTHER OSCILLATIONS 
45 
If the obstruction at a node is very great, it may render the cor- 
responding seiche unstable, or prevent its occurrence altogether. 
This explains the absence in certain particular lakes of certain seiches 
of the theoretically possible series. 
8. When the breadth and the form of the transverse section of an 
elongated lake vary as well as the depth, provided these variations are 
not too abrupt, it can be submitted to calculation by introducing two 
new variables, viz., o", which is the product of the area of the transverse 
section by the breadth of this section at the surface ; and which is 
the area of the surface of the lake between the trace on the surface of 
the transverse section corresponding to cr, and any other similar line 
chosen for reference. In order to submit the lake to calculation, its 
line of maximum depth is taken and laid out straight, and practically 
the lake is treated as if it were a lake of uniform breadth and 
rectangular cross section, whose longitudinal section is the curve, the 
abscissa and ordinate of any point on which are v and cr respectively. 
This curve I call the Jiormal curve of the lake. 
Judging by the results for Lochs 'J'reig and Earn, these assump- 
tions are sufficiently correct for ordinary concave lakes at least. 
9. It will be obvious that a seiche, properly so called, differs 
essentially from an ocean tide. The origin of a seiche, and the 
absolute and relative magnitudes of the pure seiches of which it is 
composed, no doubt depend on external circumstances ; but the 
periods and the positions of the nodes of the component seiches 
depend merely on the configuration of the lake-basin, and on the 
surface-level of the water at the time. In a tide, on the other hand, 
the periods are dependent on external disturbing agencies, chiefly the 
sun and moon. In the language of physicists, a seiche is a free 
oscillation ; a tide deforced oscillation. 
Du Boys' Theory. — My predecessor in the mathematical theory of 
seiches, M. Du Boys, gave, seventeen years ago, in his interesting 
" Essai theorique sur les Seiches,"' an approximate method for calculat- 
ing the periods of a seiche. He treats the seiche as the interference of 
two solitary waves travelling backwards and forwards in the lake, the 
velocity of propagation being at each section that due to the greatest 
depth there. He thus arrives at the formula 
The symbol ^ simply means the time that a man would take 
jo Jigh) 
to travel from one end of the lake to the other along the line of 
greatest depth, his speed at each point being that which a stone 
