666 Professor George CkrijstaJ [May 17, 



From the tlieoiy it appears that — 



1. In any given lake, pure seiches of all degrees of nodality, i.e. uni- 

 nodal, binodal, trinodal, etc., are possible ; and any actual seiche is 

 either one of these or a superposition of several of them. A compound 

 seiche, which is a superposition of two pure seiches, we call a dicrote 

 seiche ; and so on, following the nomenclature of Forel. 



2. When the lake is of uniform breadth and depth, the periods are 

 proportional to — 



1111 ., • X 



-, ^, -, -, . . . (harmonic series) 

 1' 2 3 4 ^ ^ 



and the quarter-wave length, i.e. the distance from each node to the 

 next ventral point, is the same all over. 



3. When the depth or breadth, or both, varies, the periods are no 

 longer commensurable. Thus, for a complete jmraholic lake the v-nodal 

 period is given by T,, = tt / / V \v (7+ I) gli] ; that is to say, the 

 periods are proportional to 



1 1 1 



V (1 X 2) V (2 X 3) -v/ (3 X 4) 



Again, for a lake whose longitudinal section (or normal curve) 

 is a certain quartic curve T^ = p / ^f (^,^^^) where p and e depend 

 on the dimensions of the lake, and c may be positive or negative, 

 according to circumstances. 



4. Hence it follows that the ratio of the binodal to the uninodal 

 period may be less than, equal to, or greater than J, according to 

 circumstances — a fact which seems to have puzzled seiche observers 

 considerably. Indeed, I have shown that quartic lakes can be 

 imagined in which the periods Tj, T2, T3 . . ., may be as nearly all 

 equal as we please. 



5. The positions of the nodes are given by the roots of certain 

 equations Xv (x) = \ and the ventral points by the roots of certain 

 other equations (^^ {x) = 0. The roots of these equations interlace 

 with each other ; but the quarter wave lengths are not, in general, 

 equal, as in the case of the lake of uniform breadth and depth. 



6. A shallow or other obstruction, or a deep near a node, greatly 

 affects the corresponding period ; a shallow increasing the period, a 

 deep increasing it. Also a shallow attracts the node towards itself, 

 and a deep repels it. Thus, for example, the binodes in a parabolic 

 lake are nearer the ends than in a rectangular one. 



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. 



Du Boys'' Theory. — My predecessor in the mathematical theory 

 of seiches, M. Du Boys, gave, sixteen years ago, in his interesting 



