PART IV. : EXPERIMENTAL VERIFICATION OF HYDRODYNAMICAL THEORY. 637 



Kid 1 - ' 



pit' + phi 1 - 



and (4) a rectangle. 



In the case represented h = h'. We know from Professor Chrystal's investigations 

 that the periods of the seiches which have the normal curves (l), (2), and (4) are in the 

 ratio* of 2 7r/j\ : tt/^2 : 2, i.e. approximately r306 : I'll : 1"00. Thus the period alters 

 very slowly as we pass from the parabola to the rectangle, and the period corresponding 

 to curve (3) can be interpolated with considerable accuracy. 



Fig. 6. 



§ 39. Another correction requires to be applied where, as in our experiments, h 

 and h' are not small compared with I. The general equation for the velocity of a 



surface wave is 



o qk , , 2irh 



c l = ^— tanh — — ..... 

 2tt A 



and for a wave at the surface of separation of two liquids 



o 9 X P- P 



(3) 



2tt , 2-n-h , , 2tt1i 



p coth -z — I- p coth — r — 



(4) 



§ 40. The following are experiments determining the period of the ordinary seiche 

 in a deep parabolic trough, the period being calculated by the empirical formula 



7*1 



(5) 



tanh 



I. 



cm. 



h. 

 cm. 



t observed. 



t calculated. 



30-54 

 42-98 

 52-73 

 60-68 



7-65 

 15-15 

 22-8 

 30-2 



•859 ± -002 

 •908 ±-003 

 •964+005 

 •997 + -004 



•857 



•914 



•975 



1 -023 



* H.T.S., p. 638. 



