504 



PROFESSOR CHRYSTAL 



of the extreme amplitude of the v-nodal seiche in the case where the phase is such 

 that the increase (due to the disturbance of pressure dp lasting for a time T) is a 

 maximum. 



T 



Extent. 



2j\/d P 



2fjdp 



2/ 8 /3p 



dkjdp 



dkjdp 



dkjdp 



Fi 



UA 



- 1 500 







•875 



1-500 







•601 



*t, 



BA 



- 1-000 



- -962 



•388 



•787 



•962 



•309 



}y 



UB 



- -500 



•962 



1-264 



•394 



•962 



1-006 



!! 



B'B 







-1-925 











1-925 







AT 



2 X 3 



TA 



- -600 



- -775 



-•700 



•359 



•695 



•700 



>) 



UT 



- -900 



- -775 



1-575 



•538 



•695 



1-575 



5. Disturbance caused by a suddenly generated Distribution of Pressure, given by 

 the Law 3p = f(w), lasting from t = to t= T. — The only supposition we shall make is 

 thaty(w) is expansible in a series of zonal harmonics ; so that we have 



dp = 2q„Q' v (w) . ... (27), 



where 



j„=i(2v + l)|dM/fa)Q'»* 



The addition to the potential energy 33 due to this distribution of pressure is 

 given by 



ga I dwbpt,=g rIw{'2g v Q\(w)}{'Zcf> y Q\(w)}. 



+i 



Now, since | dwQ,' l A[iv)Q f v (w) = if m + i/, we have 



ga | divdpt, = 2e„<£„ , 



where 



e> = gq„\ rfw{Q',(w)} 2 , 

 = 2gqJ(2v+l) (28). 



It follows that the formulae (22), (24), (25), (26) are all applicable to the general 

 case now under discussion, the only difference being that f v is now given by the 

 equation 



f'—st— i&lsh --*--«%+ 1) P^»)Q» • w 



* See Whittaker's Modem Analysis, ch. x., § 128. 





