26 
MR. G. I. TAYLOR ON TIDAL FRICTION IN THE IRISH SEA. 
Hence from (4l) 
so that 
The agreement between this and the previous result ^ = 2'0,* is remarkable, 
because they are based on quite different data. 
At this point it is worth while to look back at what we have done. We began by 
assuming that the tides in the South Channel of the Irish Sea can be represented by 
two tidal waves moving in opposite directions and with the velocity appropriate to 
the depth of the channel, i.e. (/D. 
We then used two totally different methods for finding the ratio of*the rise and 
fall of tide due to each of the two waves. 
The first of these methods depends on the relationship between the tidal currents, 
the depth and the rise and fall of tide across the section where the tidal current and 
tidal height are in the same phase. 
The tidal currents have been measured at four points across the section in (piestion. 
The depths of course are well known and are marked on all charts. The height of the 
range of the tide has only been ineasured at points at, and near the ends of, the 
section. The fact that the tidal current moves backwards and forwards in a straight 
line and that it is practically uniform across the section, is however a strong reason 
for believing that the tidal range decreases uniformly from the Welsh to the Irish 
shore. It is worth pointing out, however, that the mean rise and fall of tide across 
the section is not a measured quantity ; it is a deduction, based on dynamical con¬ 
ceptions it. is true, but still a deduction, from the measured amounts of the rise 
and fall of tide at each end of the section, and tlie measured tidal currents across it. 
The ratio of the amplitudes of the in- and out-going tidal waves was found by this 
method to be 2‘0. 
The second method of determining the ratio of the amplitude of the in-going tidal 
wave to the out-going wave depends on the ratio of the rate of movement of the 
co-tidal line to the velocity of the tidal wave. It was possible to get two well 
determined pc^sltioiIS of the co-tidal line, one at each end of the South (Jhannel. From 
measurements of the distance between the mid points of these two lines, and the 
interval of time lietween the two H.W’s., the ratio of the amplitudes of the two 
waves in mid channel was found to be I’8, almost exactly the same result as that 
obtained by the other method. It is worth noticing that this second method 
* See equation (38). 
a — h 
Cl-\-h 
cot 
2.'r7r 
2-44 
cot 
0'67 
a 
2-44 + 0'67 
2-44-0‘67 
= 1 - 8 . 
( 45 ) 
