_ 1 . 8 (45) 



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



Hence from (41) 



, 2xir 

 cot =r 

 a b _ ci 



a + b L 2Trt,. 0'67 

 cot-^ 



so that 



a 2'44 + 0'67 



1J~ 2'44-0'67 



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, >.c. \ r/T>. 



We then used two totally different methods for rinding 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 question. 

 The depths of course are well known and are marked on all charts. The height of the 

 range of the tide has only been measured 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 the 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 positions of the co-tidal line, one at each end of the South Channel. From 

 measurements of the distance between the mid points of these two lines, and the 

 interval of time between the two H.W's., the ratio of the amplitudes of the two 

 waves in mid channel was found to be 1'8, almost exactly the same result as that 

 obtained by the other method. It is worth noticing that this second method 



* See equation (38). 



