ON THE SEICHES OF LOCH EARN. 513 



where a is the difference of pressure between the ends of the lake generated in unit 

 of time. 



Then we get from (46) 



dk v = |a(2v +1)1 dwQ' v (w)w dt n v t sin n v (t - t„) . 



Since w = Q/(w), and awQ „(w)Qi (M>) = , unless v=l, in which case the value is 



2/3, it follows that a pressure disturbance of the kind under consideration can only 

 generate a uninodal seiche in a symmetric parabolic lake ; and we have, putting 



)i 1 r 1 = (p for shortness, 



ck x = 2«(U cos (j> - sin (j>) , 

 where 



U = dt n-J sin n-f , 



= -{mi 6-6 cos 6} , 

 if = i h T ; and 



r 



V = \ dt nj cos n-J , 



= l{0sin0-(l-cos0)}. 



n i 



If we take the special case where the pressure disturbance begins when the uni- 

 nodal seiche is at its culmination, (p = ; and we have 



dk, = — (sin 6-6 cos 6) . 

 1 2»V 



It is easy to see that sin 6 — 6 cos has a maximum value when 6 — tt, i.e. when 

 T = x/rij = ^-T 1} as might be expected. The greatest possible disturbance under the 

 present supposition regarding the phase would therefore be given by 



In other words, the alteration in the range of the seiche (23^) would be equal to 

 the number of millimetres (Aq.) of difference in pressure between the two ends of the 

 lake generated in half the uninodal period. 



If the initial phase be not given, but so chosen as to give the maximum effect to 

 the disturbance, then 



^ = ^v/(U 2 + V*), 



= " J(6' 2 - 26 sin 6 - cos 6 + 2) . 



2?? 1 



This has a maximum value when = 2tt, viz. : — 



