10 
ME. G. I. TAYLOR ON TIDAL FRICTION IN THE IRISH SEA. 
keep the water moving straight. The same reasoning applies to the ebb stream 
winch piles itself np against the Irish coast. At the particular section from 
Arklow to Bardsey the flood stream is a maximnm at H.W. and the ebb stream a 
maximinn at L.W. Hence the eflect 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 eflect 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-cliannel 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 2o)pv sin X, where w 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 
2wpv sin X 2(joV sin X 
— - -5 or - 
p 9 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,! = 162 cm. per 
second; w = 0‘()00073 ; in latitude 52°, sin X = 079, g — 981. Hence from (17) the 
slope is 1'9 X 10“” radians. 
Tlie 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"® x 2‘88 x 10® = 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. 1:^ later. 
