668 DR J. HALM 
we may say quite generally, that the solutions can always be expressed by simple tran- 
scendents if y is an even integer. The Seiche- and LecENnpre-functions, on the other 
hand, belong to differential equations of the same class for which y is an odd integer, 
Hence each equation of the latter class is included between two equations of the former, 
and we have seen that through this remarkable property we were enabled, by studying 
the behaviour of the neighbouring simple transcendents, to form conclusions with regard 
to the far more difficult Seiche-functions. 
In the theory of lakes, the floors of which are composed of two or more parabola 
with different parameters, the evaluation of the two functions C(c,1) and S(c,1) for 
any given value of c becomes important. The calculation of the series 
c(e-2) ee ~ 2)(e— 12) 
1.2.3.4 1.2.3.4.5.6 
€ , e-6) _e-6)(c~ 20) 
“73 9345 ) OE eye” 
Cle, l)=1-,5+ 
sé, e=1 
is always an exceedingly troublesome process, especially for great values of c. In many 
cases even the calculation of 100 terms is not sufficient. But the foregoing investiga- 
tion immediately suggests a rigorous and extremely simple method of computing these 
quantities. Reverting to equations (18) and (20) we find for the two Seiche-functions 
(a = —4) the relations : 
But considering that 
In 7Z 
we find 
Die G) oS 
oe 
Sis we 5 wa a ie | af 
te ae 7 
These expressions are very convenient for computation. Let us take, for instance, 
c= 105°0176, to which corresponds n= 10°76. We have 
(105-0176 ; 1)= - T(5'38) sin 68°-4 
T(5'88) Ja 
1°38 x 2°38 x 3°38 x 4:38 T(1°38) | sin 68°°4 
~ 1°88 x 2°88 x 3°88 x 4°88 T(1'88) Jr 
S(105-0176 ; 1)= 2 1°88 x 2°88 x 3°88 x 4°88 I(1°88) cos 68°°4 
105-0176 1°38 x 2°38 x 3°38 x 4°38 T(1°38) Jr ; 
