MR. G. T. TAYT.OR ON TIDAL FRICTION IN THE IRISH SEA. 
29 
For this analysis to be correct, the co-tidal line at x = 0, i.e., the line for 8h. lOin. 
should be perpendicular to the direction in which the wave lias been assumed to be 
moTing, i.e., perpendicular to the middle line of the channel. As a matter of fact 
the angle between the co-tidal line AB, and the central line LM, differs considerably 
from a right angle. This is no doubt diie partly to modifications introduced by the 
fact that the channel has not got parallel sides, hut more probably it is due to the 
fact that the tidal wave from the Atlantic does not strike the channel in such a way 
as to allow the co-tidal line for 6h. 15m. to he at such an angle with the direction of 
the middle line of the channel as to allow it to become perpendicular to the channel 
(owing to the co-tidal line travelling faster on the AVelsh side than on the Irish side) 
when it has travelled up the channel as far as the line AB. 
It is worth wdiile, however', to apply equation (40) to find out what angle the 
co-tidal line woidd have turned through, theoretically, in the time from 6h. 15m. to 
8h. 10m. 
The angle, 0, between the co-tidal line for 6h, 15m. and the co-tidal line for 8h. 10 m. 
should be given by 
tan B = .(47) 
ay 
where ^ is obtained by differentiating (46). 
dy 
Turning now to the figures, we have seen (.see equation 44) that 
cot^^ = -0-67. 
Hence (46) becomes 
But 
cot 
'2-TrX 
TT 
= -0-67 
-tl 
/h 
h. 
-1 
ho 
! T 2wy sin X 
a 1 - — -— 
Ml-t 
2(jciy sin X 
(48) 
(49) 
and if we limit ourselves to the consideration of tlie angle tlirough which the co-tidal 
line turns during its passage up the central part of the channel, i.e., up the line ML, 
y may be considered as small. In this case (49) may he written approximately 
tl 
h., 
