658 DR J. HALM 
The first of Group I. corresponds to Professor CHrysta.’s Seiche Cosine, and the 
first of Group V. to the Seiche Sine. Since for the Seiche-functions a= —}, we have 
Melson e 2 
Seiche Cosine= F (” wise Lae wv?) 
Seiche Sine =wF & Ae Ae w?) 
Se ta ac ae 
or 
; meee ue 1) 2 n(n — 1)[ n(n — 1) - 1.2), 4 Un - 1)[n(m — 1) — 1.2][m(m — 1) - 3.4] 
Seiche Cosine = 1 — Sea ee eam Lix34x56 wee... 
: ¢ pes a = 3 4 Un — 1)[m(m — 1) - 2. 3], 5 — n= 1)[n(m - 1) - 2.3][ n(n — 1) - 4.5), 1 
RES ie a Wms i 2.3.x 4.5 2.3% 4.5 x67 
or finally, if we write for n(n—1), which is the factor of y in the Seiche-equation, the 
symbol c, in accordance with Professor CurysTat’s notation : 
; Meee Op OSI) rhe c(c — 1.2)(¢— 3.4) 
Seiche Cosine = 1 ie? jes ks i Sa eTaae he te tea 
Seiche Sine =w- c¢ Homo re 2.3) ys — he = 2.3) = 4.5) 7 Ae 
23° 2-3 x 4.5 2.3x 45x 6.7 
Let us denote generally 
n n 
Cos, ()) = HE +a,-%,4; uv’) 
, i o@ 1 : \ 
Sin, (w) = wF( 5 soy, 5 3; w?) (18) 
then we have : 
Cos_, (wv) = Seiche Cosine =1 — oie 2 0) w? + (¢+]. O)(e = 1.2) wt — (c+ 1.0)(¢ — 1.2)(¢ - 3.4) wo +. 
1.2 x 3.4 1.2 x 3.4 x 5.6 
n(n — 1) 
Cos, () = Cos(nsinn) = 1 ——— Ba. es Mel (c + 0.0)(¢ — 2.2)(c—4.4) ie 
: 1.2x 3.4 1.2x3.4x5.6 
c=ne 
Cos, (w) = Legendre Cosine = 1 _ (c= 1.0) 1.0) 2 ¢ a LONMe = 3.2) 4 (c— 1.0)(c — 3.2)(¢ — 5:4) w® 
12 Roba T2314 516 ‘ 
c=n(n+ 1) 
Cos, (w) = Stokes Cosine = 1 Gee, 24 (EELS ay 4 5 2.0)e7 See eae 
12 ORB w! 12x BAX I6 . 
— c=n(n + 2) (19) 
Sin_,(w) =Seiche Sine = w — (279-4), , (0 0.1)(e— 2.3), _ (0 0.1)(o — 2.8)(e= 4.5) 
2.3 2.3 x 4.5 2.3 x 4.5 x 6.7 7; a 
c=n(n—1) 
Sin, (w) =sin(nsin wy =» CoD es EI) ys Cb (e=8:8)(0- 5.5) 7 
n 2.3 2.3 x 4.5 2.3 x 4.5 x 6.7 
C=n* 
Sin, (w) = Legendre Sine = w _(=2.1) 3 (c- 2.1)(¢- 4.3) Bee (c= 2.1)(c - 4.3)(¢ = 6.5), 7 
2.3 2.3 x 4.5 2.3 x 4,5 x 6.7 ow 
c=n(n +1) 
Sin, (w) = Stokes Sine =o ee, 3 (c- 3.1)(¢-5°3) Bi (¢- 3.1)(¢- 5.3)(¢- 7.5) MGS 53 
2.3 2.3 x 4.5 2.3 x 4.5 x 6.7 
c=n(n+ 2) 
