10 MR. G. I. TAYLOR ON TIDAL FRICTION IN THE IRISH SEA. 



keep the water moving straight. The same reasoning applies to the ebb stream 

 which piles itself up against the Irish coast. At the particular section from 

 Arklow to Bardsey the flood stream is a maximum at H.W. and the ebb stream a 

 maximum at L.W. Hence the effect of the slope of the sea surface, which is 

 necessary to keep the stream straight against the deflecting force due to the earth's 

 rotation, is to add to H.W. and to subtract from L.W. on the Welsh side, thus 

 increasing the range above the mean range for the section. The effect on the 

 Irish side is exactly the reverse, so that the tidal range is diminished there. Though 

 this explanation is given in general terms it is a simple matter to express the forces 

 and slopes concerned in a quantitative manner. 



The application to the present question follows directly. If it can be shown by 

 observation that the tidal currents move straight up and down the channel without 

 being deflected across it, then the slope of the sea surface must everywhere correspond 

 with the velocity of the current. If the current is nearly uniform right across the 

 channel, then the sea will slope down uniformly from one side of the channel to the 

 other. It will be shown later, in discussing the tidal currents, that both these 

 conditions are satisfied. Dynamical considerations therefore enable us to say what 

 the tidal range in mid-channel is, when we know it at either side. 



Confidence in the correctness of this view is greatly strengthened by calculating 

 the difference to be expected in the tidal ranges on the two sides of the channel, and 

 showing that it is in close agreement with the observed difference. 



The deflecting force due to the earth's rotation which acts on each cubic centimetre 

 of the sea is 2wpv sin X, where &> is the angular velocity of the earth's rotation, and X is 

 the latitude. 



The slope of the surface, in a direction perpendicular to the stream, which will just 

 balance this force, is therefore 



2tapv sin X , 2vsinX , , 



pg g 



The measured maximum velocity of both the flood and the ebb stream at spring 

 tides across the section, AB, from Arklow to Bardsey* is 3 '2 knots, t =162 cm. per 

 second ; o, = 0'000073 ; in latitude 52, sin X = 079, g = 981. Hence from (17) the 

 slope is T9 x 10~ 5 radians. 



The distance across the channel in a direction perpendicular to the current from 

 Bardsey Island to Arklow, on the Irish coast, is 48 nautical miles = 288,000 feet. 

 Hence the difference in level at time of the maximum current between the sea surface 

 at Bardsey Island and at Arklow should be 1'9 x 10~ 5 x 2'88 x 10 5 = 57 feet. 



Now, as has been mentioned already, the streams in this part of the Irish Sea have 

 their maximum velocities at H.W. and L.W. The curves shown in fig. 2 represent 



* See map, fig. 3. 

 t See p. 12 later. 



