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



for the rate of flow of energy into the Irish Sea, across the section EC, the numerical 



values of the terms are 



H = (4 feet) = 61 cm. 



(T - T,) = 87, so that cos ^ ( T o - T i) = ' 05 



V = 4 knots = 200 cm. per second. 



(Length of EC) x cos 6 is evidently equal to the breadth of the North Channel normal 

 to the stream. This is 11 nautical miles, or 2 x 10 6 cm. 



DI the mean depth, is about 65 fathoms = 10 4 cm. Hence the mean rate at which 

 energy enters the Irish Sea by the North Channel is ' 



WHO = x 1'03 x 981 x 10 4 x 200 x 61 x 2 x 10 8 x 0'05 = 6'2 x 1 18 ergs per second. 



This is only riV 1 f the energy which enters by the South Channel. It is obvious 

 that DO high degree of accuracy is aimed at in obtaining this figure. It is merely 

 intended to show that the amount of energy which enters the Irish Sea by the North 

 Channel is quite insignificant compared with the amount which enters by the South 

 Channel. In the work which follows, I shall neglect it altogether, and shall consider 

 merely the South Channel. 



Amount of Work Done by the Moon's Attraction on the Waters of the Irish Sea. 



The attraction of the moon may be expressed by means of a potential function Q. 

 Consider the work done by the moon's attraction on the water contained in an 

 element of volume, A, which is fixed to the earth's surface. If the element contains 

 water during two complete tidal periods, i.e. till it comes back to its original position 

 relative to the moon, no work will be done on it. If on the other hand, the element, 

 A, is situated within the space which is filled with water at high-tide and is empty at 

 low-tide, work may be done on the water contained in A. 



If p be the density of sea-water, h the height of the tide above mean sea-level, the 

 work done by the moon's attraction during two complete lunar semi-diurnal tides, on a 

 column of sea of 1 sq. cm. cross-section and stretching from the sea bottom to the 



surface is evidently 



r 

 m = \hp dQ, (26) 



the integral extending over all the changes in Q which occur during the complete 

 cycle. Evidently the total energy communicated by the moon's attraction during two 

 periods is 



E M = JJmdtr, (27) 



E 



