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. 
^(To - Ti) = 87°, so that cos ^ (^o - Tj) = 0'05 
V = 4 knots = 200 cm. per second. 
(Length of EC) x cos (9 is evidently ecpial to the breadth of the North Channel normal 
to the stream. This is 11 nautical miles, or 2 x 10*" cm. 
Dj the mean depth, is about 65 fathoms =10^ cm. Hence the mean rate at which 
energy enters the Irish Sea by the North Channel is 
Wec = ^ x 1'03 X 981 X 10^ x 200 x 61 x 2 x 10® x 0'05 = 6'2 x 1O^'’ergs per second. 
This is only of the energy which enters by the South Channel. It is obvious 
that no 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 Moons Attraction on the Waters of the Irish Sea. 
The attraction of the moon may be expressed by means of a potential function 
Consider the work done by the moon’s attraction on the water contained in an 
element of volume. A, which is fixed to tlie eartli’s surfiice. 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 ] sq. cm. cross-section and stretching from the sea bottom to the 
surface is evidently 
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 
m da. 
(27) 
