ON LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 667 
investigation we have gained considerable freedom in the selection of curves representing 
the curvature-conditions of the lake floors, so that we may, by the suggested interpola- 
method, assign approximate values to the nodes, and by means of (38) also to the 
| ods, even under conditions which are unmanageable from the rigorous mathematical 
point of view.* 
Fie, 1. E 
' the advantage of the preceding analysis of Professor CurysTat’s Seiche-equations lies 
» fact that they belong to a class which includes cases where the solutions are 
ible by means of simple transcendents. If we write the general differential equa- 
in their most symmetric form : 
Py dy ( - 
Ae) iz ade 2_ I \y — (0) 
Gea Gy ets (n2+T)y 2) 
dw? dw 4 
* In § 45 of his Hydrodynamical Theory, Professor CHRys?aL investigates the case of a rectilinear lake, the floor 
ch would be represented in the above diagram by the straight line AB. The directions of the nodal loci E B in 
suggest that the nodes in rectilinear lakes should be more displaced towards the shallow water than in any 
ses here considered, and this conclusion is indeed supported by the numerical results given in § 49 of Professor 
[RYSTAL’S paper.—(Note added on June 30.) 
TRANS, ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 26). 98 
