DR. HAROLD JEFFREYS ON TIDAL FRICTION IN SHALLOW SEAS. 
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Magellan Strait and Smith Sound, and when the area of the strait is not insignificant 
the dissipation may be an important part of that in the seas as a whole. 
European Seas. 
1. The Irish Sea. 
This sea has been discussed in detail by Taylor. The rate of dissipation is found 
to be 1040 ergs per square centimetre per second, or 4T x 10 17 ergs per second in 
all, on an average at spring tides. This result is based on the law that the rate is 
proportional to the cube of the velocity. The Irish Sea is remarkable in that the 
maximum current occurs nearly at high water, whereas in ordinary places the water 
is nearly slack then ; though other examples will be given later in this paper. This 
affords the most favourable conditions for an accurate estimate of the rate at which 
energy enters the sea; to this Taylor added the rate at which the moon's attraction 
does work on the sea, and from the fact that all this energy must be dissipated in 
the course of a period (for if it were not, there would be a continual increase of energy 
in the Irish Sea) he found that the mean rate of dissipation at spring tides was 
6‘Ox 10 17 ergs per second. This estimate is probably more accurate than the other, 
as the data involved are obtained from observations in St. George’s Channel, supple¬ 
mented by an accurate theory ; but the former is based on an average of the velocities 
in the Irish Sea itself, which are more difficult to determine. 
2. The English Channel. 
On an average the tidal currents in the English Channel at springs reach about 
2'5 knots. The speed is greatest towards the Straits of Dover and least at the 
entrance to the Channel, and enough data are available in the Admiralty publication, 
‘ The Tides and Tidal Streams of the British Isles ’ to give a very accurate estimate 
of the total dissipation if this were required in the present problem ; but as the errors 
introduced by using only a rough approximation in this case are far less than those 
involved in the best data referring to regions with far larger dissipations, accuracy is 
not here required. 
The rate of dissipation is 0'002pV 3 ergs per square centimetre per second. Here p 
is practically 1 ; and one knot is 51'5 cm. per second. Thus the dissipation per square 
centimetre for a velocity of one knot is 274 ergs per second, and that per square 
kilometre is 274 x 10 12 ergs per second. The area of the English Channel is about 
60,000 sq. km., so that the dissipation when the currents are flowing fastest is 
274 x 10 12 x 6 x 10 4 x 2‘5 3 , or 2‘5 x 10 18 ergs per second. This is of course a maximum, 
while the value obtained for the Irish Sea is the mean over a period ; the average 
rates of dissipation in the two places are perhaps not very different. 
