*)•> 
MR. G. T. TAYLOR ON TIDAL FRICTION IN THE IRISH SEA. 
Let us assume that tlie tidal phenomena in the South Channel can be represented 
by the superposition of two waves, one of amplit\ide a going in, and the other of 
amplitude ?>, going out. These may be represented mathematically by the formula 
/; = COS^f/'-'^j-/) cos y .(34) 
where the first term represents the wave entering the channel, and tlie second 
represents the reflected wave leaving the channel. 2a and 2h are the ranges of the 
tides due to the two waves separately ; x is the distance measured along the channel 
ill the direction of the Irish Sea ; and c is the velocity of a long wave in water of the 
depth, D, of the channel so that c = 
Our problem is to analyse the observed tidal phenomena so as to find the values of 
a and h, and to show that the various characteristic features of the tidal phenomena 
of the South Channel can be accounted for hy considering tliem as being due to these 
two waves. 
'fhe cui'rent due to tlie entering tidal wave is 
9 
D 
cos 
-it- 
T \ 
X 
The current 
due to the out-going tidal wave is h /y/ ^ cos (^t+ ~ 
Tliey are both positive at x = 0 if a and h are both positive, because the original 
formula (34) assumed for //, gives li as the difierence of two terms and not as the 
sum. 
Hence the tidal current, is 
* It has been suggested that the velocity of the waves into and out of the Irish Sea are not equal to 
sCD, because they are forced waves due to the moon. The moon’s attraction, however, does not appear 
to be capable of exerting sufficient force to alter appreciably the velocity of a free wave of the amplitude 
with which we are concerned travelling down a channel of a depth of about 37 fathoms. 
If / be the horizontal component of the moon’s attraction, the maximum possible value of / is 
8*57 X 10“b/ (see Lamb’s ‘ Hydrodynamics,’ 4th edition, p. 256). 
The maximum value of the horizontal force F, due to the pressure gradient in a free wave of height 2a 
from trough to crest, is F 
where T is the tidal period of 12 Ah. 
It will be seen later that the semi-amplitude of the smaller of the two waves with which we are 
concerned, i.e., the out-going wave, is 145 cm. Taking a = 145, D = 37 fathoms = 6800 cm., it will be 
found that F = 8 x 
It appears therefore that /, the horizontal force due to the moon’s attraction, is only j-Jy''” of F, the 
force due to the horizontal pressure gradient in a free rvave of the height with which we are concerned. 
I he velocity of these waves cannot therefore difter appreciably from that of free waves in the channel, 
t This is the well-known formula connecting the current velocity and tidal range in a tidal wave. 
