Tides and Tidal Currents in the Proximity of Land 347 



allows, through comparison with the corresponding differential equation for £, the computation 

 of the dissipation of the energy E per unit time and unit surface. We have 



E = — oh bir . 

 T 



For a full period of 12 lunar hours, the mean value of m 2 = \U 2 and if we assume again 

 U = H4 cm/sec, q = 103 and for the Irish Sea h = 68 m, and if we take b = 0-2 and according to 

 the previous table (p. 342) then E is nearly exactly 1300 erg per cm 2 /sec in good agreement with 

 Taylor's value. 



Another way of evaluating the friction of tides in adjacent seas has been used 

 by Grace (1931, 1936, 1937). If we assume that, in an oblong-shaped ocean, 

 the tidal motion is completely longitudinal, we can compute from the equa- 

 tion of continuity the mean velocity u at each cross-section for the M 2 tide, 

 and the equation of motion gives then, the only unknown factor, the fric- 

 tional force F. The action of the tide-generating force can be neglected, being 

 very small. The corresponding equations are 



du _ en 



8t~~ g 8x~ ' 



8tj 

 f "= - g 8y-> 



dSu _ ,dt) 

 ~8x~~~ ~ 8t' 



(XI.23) 



if S is the area of the cross-section and b the width at the surface of a cross- 

 section at the point x of the "Talweg". The second equation is used to reduce 

 the values r\ observed on the shores to the "Talweg". If we put 



r\ — Acos(at—y) = r\ x cos at + r) 2 sin at , | ,„_ _.. 



u = u cos (at— a) = UxCOsat + u 2 s'mat I 



we can compute from the third equation ASuJa and ASu 2 /a for the intervals 

 between each cross-section. If we know u at one cross-section (light-ship), 

 the values u x and u 2 can be determined for all cross-sections. Now everything 

 is given in the first equation except 



F =Fcos(at— /?) = fx cos at+f 2 sin at . 



This method has been applied by Grace to the tides of the Gulf of Bristol 

 and of the English Channel between Le Havre — Brighton and Ramsgate — 

 east of Calais, and he obtained for F and /? the values shown in Tables 40 

 and 41. The result is that the phase of friction is in first approximation 

 the same as that of the tidal current, but we see that the frictional constant 

 varies in an irregular way. The mean value for the Bristol Channel is 2-6 x 10 -3 , 

 which is in good agreement with the value 2-4 x 10~ 3 found by Taylor. This 

 value of k corresponds to a b = 1-3, which is also in good agreement with 

 the value assumed by Defant. In the English Channel the phase of the 



