ON THE SEICHES OF LOCH EARN. 505 



In particular, the maximum disturbance of amplitude for the y-nodal seiche is 

 given by 



dk y = \2q r am~£\ ..... (30). 



It is of special interest to notice that the disturbance of the y-nodal seiche is due 

 solely to the v th harmonic term in the zonal harmonic expansion of f{w). It follows 

 that a disturbance of pressure which is proportional to Q, f „( w ) affects the v-nodal 

 component of the lake oscillation and leaves all the others wholly unaltered. 



6. Example 1. — Consider the effect of a uniform gradient of pressure suddenly 

 generated over the whole length of the lake, and causing a difference dp between the 

 two ends. Such a disturbance will be represented by \dpw ; i.e. by q^Q'^w), where 

 </i = h^P- This will give dk 2 = 0, dk s = 0, etc., and 



dk x = I dp sin {%-) , 



if we suppose the uninodal seiche in such a phase when the disturbance commences 

 that the maximum effect is produced. 



The greatest effect of all results when T = Trjn 1 =^T 1 ', i.e. when the disturbance 

 lasts during half the uninodal period. We have then 



dk 1 = dp . 



It thus appears, as a result of our analysis, that a uniform pressure gradient 

 established over the whole of a symmetric parabolic lake can only generate or destroy 

 a pure uninodal seiche. If the oscillation of the lake have any other components, they 

 are unaffected. This conclusion, which might have been expected a priori, seems to 

 confirm the soundness of the assumptions on which we have based the present theory. 



7. Example 2.- — If we suppose the pressure disturbance given by ^dp(3iv 2 — 1) 

 = q 2[ Q' 2 (w) (g , 2 = ^P)) which gives a parabolic distribution with a turning-point at the 

 middle of the lake, and suppose the disturbance to catch the seiche in the most 

 favourable phase, i.e. at a maximum, when the disturbing pressure tends to drive the 

 water in the direction which it would follow if undisturbed, and if we further suppose 

 the disturbance to last for half the binodal period, then we get 



dJc 2 = 2q 2 = 2dp 



for the increase of the extreme amplitude of the binodal seiche, all the other seiche 

 components being unaltered. 



8. Example 3. — In like manner we see that the pressure disturbance which 

 generates a pure trinodal seiche in a symmetric parabolic lake must have the cubic 

 distribution ^q s (5w s — 3>w) ; and so on. 



9. Effect of a, Disturbance of Pressure which varies both in Space and in Time. 

 — Let us suppose that the pressure, measured in centimetres of water, at time t, at 

 any point w ( = x/a) of the parabolic lake, is given by 



9p=/0, t) (31). 



