ON THE SEICHES OF LOCH EARN. 



component seiches are k v & 2 , . . . . and the phases r lt r 2 , . . 

 position the general solution for the motion when 0T : 



£ = 1[k v cos n v (t - r„) +f v { - (1 - cos n v T) cos nj, + sin w„T sin n v t}]Q,' v (w) , j 



= 2[{flv cos n F T,, -^(1 -cosw„T)} cos w„i+ {A„ sin. w„t„ +jf sin ra„T}sin«„f]Q',,( 



503 

 , we get by super- 



■■ 2/c'„ cos w„(i; - X")Q,'A W ) > 



(25), 



where 



/£„ sin w„t„ +y^, sin n„T 

 taD VvXv = Av cos «„,-,, -/(l- cos h„T) ' 



tanre„(x„-T„) = 



2/„ sin ( ? V) cos W "( T " ~ ^ T ) 



*, + 2f v sin (^T) sin W ,(t„ - |T) 

 A-', 2 = A-„ 2 + 2Kf v (cos «„(t, - T) - cos w„t„ } + 2/; 2 (l - cos n v T) ., 

 = k? + UcJ, sin (^) sin n r (r p - JT) + 4/ v 2 sin 2 (<T 



(26). 



The maximum value of AY, for a given value of T is therefore given by taking 

 sin u v (t v - ^T) = ± 1. We then have 



'n„T\ 



k'„=k p + 2 



/•-(¥ 



The phase disturbance is then zero. 



4. Particular Cases. — Suppose T = 7r/n 1 = ^T 1 , ^ = 0, X = 0, /u.= + l, which gives 

 us a disturbance extending over the positive half of the lake, and beginning when 

 the uninodal seiche is at its maximum extreme amplitude and lasting for half the 

 uninodal period. 



Then 



Hence the seiches of even nodality are all unaffected ; and, if we denote the uninodal, 

 trinodal, etc. components by ^ £ 3 , . . . . , we have 



£i = ( A 'i + FiOQ'iW cos V ; 



£ 2 = hQli™) C0S ^ " T 2) ; 



£3 = { h - W sin (ff ) } QW cos w 3 (* - T z) . 



where we have determined r 3 so that the disturbance of the trinodal component shall 

 be the greatest possible. 



Since n % \n x = a/(c 3 /c 1 )= ^6 = 2*450, and sin (n 3 7r/2n 1 )= '687, we have in the case 

 of maximum disturbance 



£ 3 = (h + ^0^p)Q,' 3 ( w ) cos »»(* ~ T s)- 



It is unnecessary to set down more formulae, but the following table will give an 

 idea of the effect of various kinds of uniform pressure disturbances on the uninodal, 

 binodal, and trinodal seiche components. B and B' denote the two binodes, U the 

 uninode, T the trinode, and A the positive end of the lake. dk„ denotes the increase 



TRANS. ROY. SOC. EDIN., VOL. XLVI. PART III. (NO. 20). 76 



