28 MR. G. I. TAYLOR ON TIDAL FRICTION IN THE IRISH SEA. 



The amplitude due to the in-going wave is therefore greater on the Welsh Coast 

 than 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, i.e., 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, i.e., 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 flow straight backwards and forwards 

 without any appreciable circulatory motion, the increase in the height of the tidal 

 oscillation on the right-hand side of the advancing wave can be expressed 

 approximately in the form 



while the out-going wave is 



l Cl 



The height of the tide at the point (.<, ?/) and at time, t, is therefore given by 



It is evident that all the analysis given above respecting the rate of travel of the 



co-tidal line still applies for any fixed value of y provided we use ail Z<ay Sm M 



c I 



instead of a, and b(l + 2ft>y sm X ) instead of 6. The actual values of a and 6 which 



\ 



we found apply to the middle line, y = 0. 



Denoting a l- 2*01^) by h lt and b l + ^H^) b y },,, where J h and h 2 are 



functions of y, the equation for the co-tidal line for 6h. 15m. is evidently found from 

 (41) by replacing a and I by /;, and Ji 2 . The equation in question is 



, 2irf. x _ h l h 2 , 2-n-x 



where t x is constant but hi, h, 2 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 f = ae~^ cos K (cb - x) occurs for the height 

 of a long wave in a long rotating canal. The above expression is an obvious modification of this. 



