28 
MR. G. I. TAYLOR ON TIDAL FRICTION IN THE IRISH SEA. 
The amplitude due to the iii-goiiig wave is therefore greater on the Welsh Coast 
tlian on the Irish Coast. In the case of the out-going wave, the right-hand side of 
the channel is the Irish Coast. The amplitude due to the out-going wave is therefore 
greater on the Irish Coast. The result of this is that the ratio of the amplitudes of 
the two waves is very much greater on the Welsh Coast than it is on the Irish side 
of the channel. The consequence is that the rate of travel of the co-tidal line near 
the point where the two waves oppose, he., near the section AB. is much less on the 
Irish Coast than it is on the Welsh Coast. 
This explanation can be verified quantitatively. • Let y be the distance of any 
point from the central line of the South Channel, he., from the line LM (fig. 3) joining 
the mid points of the two sections AB and TS. x and y are then co-ordinates of any 
point in the South Channel. 
Since the tidal currents in the South Channel fiow straight backwards and forwards 
without any appreciable circulatory motion, the increase in the height of the tidal 
oscillation on tlie right-hand side of the advancing wave can be expressed 
approximately in the form 
« I — 2 
wy 
sm X cos 
C! 
while the out-going wave is 
h l-t- 
2(ay sin X 
2x/,, X 
cos TiT U+- 
I c 
Tlie height of the tide at the point (,r, y) and at time, t, is therefore given by 
// = a 1 — 
2wy sin X 
cos 
^TT 
T 
2a)?/ sin X\ '1-w 
c 
It is evident that all tlie analysis given above respecting the rate of travel of the 
co-tidal line still applies for any fixed value of y provided we use « 1 — 
instead of a, and 6^1-1- sin X ^ instead of 6. The actual values of a and h which 
we found apply to the middle line, y = 0. 
Denoting « ^ 1 — j by /q, and h yl+ ^ ) by / 12 , where and are 
functions of y, the equation for the co-tidal line for 6h. I5ni. is evidently found from 
( 41 ) by replacing a and h by h-^ and /r,. The equation in question is 
cot 
q —/q 
i + h 
‘IwX 
“aT 
(46) 
where C is constant but /q, /q and x vary. 
* This is evident from the analysis given on p. 10, but reference may also be given to Lamb’s 
‘ Hydrodynamics,’ p. 304, 1906 edition, where the expression ( = cos K(e5-.'r) occurs for the height 
of a long wave in a long rotating canal. The above expression is an obvious modification of this. 
