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



in some other way. With this end in view, we shall discuss the movement of the 

 co-tidal lines in the South Channel. 



First, let us consider the theoretical aspects of the case. A co-tidal line is a line at 

 all points of which it is H.W. at the same time. In a progressive wave the co-tidal 

 lines are the positions of the crest of the wave at a series of successive times. The 

 distance apart of the co-tidal lines corresponding with a series of times, separated by 

 intervals of lh., will be a measure of the velocity of the wave. In drawing a 

 map of co-tidal lines, therefore, one is apt to think that they represent the successive 

 stages of advancement of a progressive tidal wave. This idea is incorrect. In the 

 case of two superposed waves moving in opposite directions, for instance, it will be 

 found that the co-tidal line moves in the same direction as that one of the two waves 

 which has the greater amplitude ; but that it does not move at the same speed. 



In certain places the line moves faster than the wave, while in others it moves more 

 slowly, and a knowledge of the relationship between the velocity of the co-tidal line 

 and the velocity of the wave will enable us to determine the ratio of the amplitudes 

 of the two waves. 



The height of the tide above mean sea-level at any time is 



c, 

 This may be written in the form 



fc = Aco8?jZ(*-0 (39) 



where 



^' (40) 



and 



, 2vt x ab , 2-7TJC 



- = C 



The co-tidal line, therefore, moves in time t f , through the distance .r, from the 

 place where the phases of current and tide are the same, x and t x are related by the 

 equation (41). 



The velocity, V t , of the co-tidal line is therefore obtained by differentiating (41) 



/a -6V , 2 7r 

 V = J1-. " [ 



At the point x = where the tidal heights' of the two waves oppose, and the tidal 



streams concur, the velocity of the co-tidal line is therefore a fraction a ~ b of the 



a + b 



