MR. G. I. TAYLOR 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. 10m. 

 should be perpendicular to the direction in which the wave has been assumed to be 

 moving, 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 due partly to modifications introduced by the 

 fact that the channel has not got parallel sides, but 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 be 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 Welsh side than on the Irish side) 

 when it has travelled up the channel as far as the line AB. 



It is worth while, however, to apply equation (46) to find out what angle the 

 co-tidal line would have turned through, theoretically, in the time from 6h. 15m. to 

 8h. 10m. 



The angle, 9, between the co-tidal line for 6h. 15m. and the co-tidal line for 8li. l()m. 

 should be given by 



tan fl = ^ (47) 



dy 



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 



2<ai/ sin X\ 



i ( 1 - - 



(49) 



( 2ay sin \ 



and if we limit ourselves to the consideration of the angle through 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 be written approximately 



_ 

 h, b 



