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



therefore all the terms in the second integral of (13) are small compared with those 

 of the first. 



We shall therefore neglect 



P v sin d dt (2gh 3 + D v 2 + hv a ) ds 



in comparison with 



pgdt, {l)kvshi6ds .......... (14) 



Taking account of the conservation of energy, this must be equal to^the sum of the 

 increase in kinetic energy of the sea included in the area enclosed by s, the energy 

 dissipated during the time dt by tidal friction, and the work done by the moon's 

 attraction during the same time. It has already been pointed out that since there 

 is no continual increase in the kinetic energy of any portion of the sea, the first of 

 these will vanish when we come to consider the mean rate of dissipation of energy 

 over a complete tidal period. 



If W is the average rate at which energy is dissipated by tidal friction in the 

 portion of the sea enclosed by .s, and W m is the average rate at which work is done 

 on it by the moon's attraction, it will be seen from (14) that 



W W m = average value of \gp Dhv sin 0dsk v . . . . (l 5) 



Application t thf, fn's/i Saa. 



In applying this expression to the Irish Sea, it will be necessary to evaluate the 

 integrals across sections of the North and South Channels ; and in choosing the 

 exact positions of these sections, it is clear that those parts of the channels must be 

 selected where the greatest number of observations of the rise of tide and the 

 strengths of the currents have been made. 



The only observations of tidal currents in the Irish Sea to which I have had access 

 are contained in the Admiralty publication ' Tides and Tidal Streams of the British 

 Islands.'* The observations on the rise and fall 'of tide are contained in the 

 'Admiralty Tide Tables ' and the ' Irish Coast Pilot.' 



Height of the Tide. The Tide Tables give the time of H.W. at full and change of 

 the moon. They also give the range of tide at spring tides and at neaps. They 

 afford no indication, as a rule, of the height of the tide at the intermediate hours, 

 except when there is some marked peculiarity such as the long- continued H.W. 

 at Poole, or the bore in the Bristol Channel. The principal tidal phenomenon is, 

 however, the semi-diurnal rise and fall of tide, with a period of 12h. 25m., and in a 



* First edition, 1 909. 



