ON LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 675 
Fic. 2. 
An extension of Table IV. beyond c=30 is probably unnecessary for practical 
purposes. That the approximate formule for G(c,1) and G(c,1) are still valid 
for c>30 may, however, be concluded from the fact that the higher roots of the 
equations 
cos [Vc + 0°438 x 50°-458]=0 and 
sin [/c + 0°438 x 50°-458]=0 
agree very closely with those of the corresponding Seiche-equations G(c,1)=0 and 
G(c,1)=0. We find for the former 79°099 and 50°465, whereas the corresponding 
roots of the latter were previously found to be 79°053 and 50°466. As regards the 
lower roots which are included in Table III. we have in the case of the hyperbolic 
Seiche Cosine 
1:19942 cos [n/c + 0°438 x 50°-458]—0:0004=0; c= 2-742 
1:19942 cos [s/c + 0°438 x 50°-458] — 0:0034=0; c= 28-230 
and for the hyperbolic Seiche Sine 
CC ay 
Jex0438 sin [,/¢ + 0°438 x 50°'458]+0:0024=0; c=12°341. 
These roots agree almost exactly with those previously found by an entirely 
different approximative method (see (35) ). 
In conclusion, I wish to express my great indebtedness to Professor Curysrat for the 
interest he has taken in this investigation, and especially for having kindly permitted 
me to publish this mathematical discourse on the differential equations of his Seiche- 
problem along with his own physical and mathematical researches. The general type 
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 26). 99 
