642 Proceedings of Royal Society of Edinburgh. [sees. 
The longitudinal section is now the lower quartic curve in the 
figure on p. 639. If we usep, q, r, s, d in the same senses as 
before, and if 
a = 2 tan _1 (p/a) , /3= 2 t£m~ 1 (q/a , 
then the boundary conditions £=0 when x=p and x — q give as 
before 
sin d(a - /8) = 0 . 
In the present case it is obvious that d cannot vanish ; hence 
we must have 
0 = V7 rjh (27) 
where 
k — 2 tan ~ l (p/a) - 2 tan -1 (< 7 /a) . . . (28) 
Hence for the v-nodal seiche 
c„ = a\ 40 2 - 1) = a 2 (4v 2 7r 2 //c 2 - 1) . (29) 
= 2tt/tz = 2t r/a J{gh(4vW/k* - 1)} . . (30) 
§ 9. We find, exactly as in § 6, 
'-VC/ si 1 )' ■ (31 > 
(!2) 
Hence the period of the v-nodal seiche is given by 
= 27 rlly J{gd(±vV/k* - 1)} ; . . (33) 
where 
When the lake is symmetrical, q= —p, r = s ; and (34) and 
(35) take the simpler forms 
