MR. a. 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 |gfp|T)Ar) sin Ods! 
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.AV. 
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.AV. at St. T\idwall Hoad 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. lOm., 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 Ti 
will therefore be taken as 8h. lOm. all along AB. 
27r 
In the expression /? = H cos —(^-t-Tj) 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 ^ . 
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 
TT Tj 2te)e sin A 
H = Hi-//, 
fj 
(19) 
where Hi 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 
Hi 
15 + 4' 
= 4f feet. If s is the distance measured from the central point, L, 
of AB, then 
s sin 0 = y. 
( 20 ) 
Evaluation of the Rate of Transfer of Energy th rough the South Channel oj 
the Irish Sea. 
We are now in a position to evaluate W„j„ the average rate at which energy enters 
the Irish Sea across the section AB, 
! .'B 
■pJ. 
= average value of' fjt) 1 DA a sin 0 ols I. . . 
( 21 ) 
