MR. G. I. TAYLOR ON TIDAL FRICTION IN THE IRISH SEA. 15 



Height of Tide at Section AB. Having now chosen the section AB of the South 

 Channel along which we intend to calculate the average value of \gp \Dhv sin 9ds 



we must return to the discussion of the values of h. In the first place the line AB 

 is practically a co-tidal line, i.e., a line through all points at which it is H.W. 

 simultaneously. On the Irish side it is H.W. at Arklow Bank at 8h. 24m. ; at 

 Arklow at 8h. 25m. ; at Kilmichael Point, where the section AB strikes the Irish 

 coast, at 8h. 25m. ; and at Courtown, about 4 miles south of Kilmichael Point, at 

 7h. 55m. On the Welsh side it is H.W. at St. Tudwall Road at 8h. 2m., at Bardsey 

 Island at 7h. 59m. The time of H.W. all along the line AB may therefore be taken 

 as 8h. 10m., which is the mean of the times at either end. This will only be a few 

 minutes wrong at either end, and the convenience, in evaluating the integral, of 

 assuming a constant time of H.W. along the section, is very great. The value of T, 

 will therefore be taken as 8h. 10m. all along AB. 



In the expression h = H cos-=^(/! + T,) which was adopted to give the height of the 



tide at any point, the value of H varies from point to point. 



It has been shown, however, that H must decrease uniformly from one side of the 

 channel to the other, and that in the case of the section AB, where there is 

 practically no difference between the time of H.W. and the time of the maximum 



flood stream, the sea at H.W. slopes at an angle - - . 



j 



If y is the distance of any point from the central line of the channel measured in 

 the direction perpendicular to the current and towards the Irish Coast, then 



H = H 1 - 2a>t>BinX y, (19) 



(7 



where H! is half the range of tide in mid-channel. We have already seen that 

 the ranges of tide on the two sides of the channel are 4 and 15 feet ; hence 



H! = i( } = 4f feet. If s is the distance measured from the central point, L. 



of AB, then 



siM0 = jy (20) 



Evaluation of the Rate of Transfer of Energy through the South Channel of 



the Irish Sea. 



We are now in a position to evaluate W (/6 , the average rate at which energy enters 

 the Irish Sea across the section AB, 



f /*B 



W^ = average value of < gp \ ~Dhvsm6ds} (21) 



