252 
DR. HAROLD JEFFREYS ON TIDAL FRICTION IN SHALLOW SEAS. 
end of Korea, at lOh. 33m., so that /3 is here —199°, or more conveniently +161°. 
The tide lags more and more on the way up the sea, and at Port Arthur it has lost 
practically a whole period, the high water at full and change occurring there 
at llh. 7m., making /3 = —216°. Positive elements will be added to the integral 
by the places where /3 is from 161° to 0°, negative elements where /3 is from 0° to —180°, 
and positive again where it is from —180° to —216°. These values are however 
weighted according to the values of h and according to the extent of the areas for 
which they are correct. Now (3 is zero near the Conference Islands, only about O'4 of 
the way to the narrowest part, so that on this account the area for which it is 
positive would appear to be less than that for which it is negative. The sea becomes 
much narrower farther north, however, which must reduce the ratio of the weights 
somewhat, and the tides are only about two-thirds of the height. Thus it seems that 
the weights to be attached to ,the positive and negative values of sin /3 are nearly 
equal, and its average over the sea is unlikely to be more than 0'2. The area of the 
sea as far as Port Arthur is about 300,000 sq. km. ; taking the average of h as 240 cm., 
and that of li' as 20 cm., we find the energy imparted by the moon to be not greater 
in absolute magnitude than 2 x 10 17 ergs per second on an average. That entering up 
the Korean coast is far greater. 
In the discussion of the work done by the moon the Gulfs of Pe-Chili and Liau-tung 
have been ignored. There are two reasons for this : their united area is about a 
third of that of the main part of the sea, and the tides recorded at the sides are also 
about a third of those on the Korean coast. It seems to me, however, that these two 
gulfs afford an example of a special type of tidal problem different from any previously 
discussed. For, let us suppose if possible that the recorded amplitudes, of the order 
of 90 cm., were typical of the whole area. The average depth is about 2000 cm., and 
a tidal wave in water of such a depth would give rise to a current of maximum 
velocity about h (g/ D) 4 , which in this case is 65 cm./sec. The corresponding 
dissipation would be 550 ergs per square centimetre per second. On the other hand 
the average energy present is about \gph 2 , or 4 x 10 6 ergs per square centimetre. Thus 
if the above assumption were correct the whole energy of the tide would be dissipated 
in about 7000 seconds, or two hours. This is absurd, and we must suppose, in order 
to avoid the result that energy is dissipated faster than it enters the region, that 
the tides in the greater part of the gulfs are much less than the recorded ones. 
Their height may be only a few inches ; while the recorded heights are the result of 
great magnification in the very shallow water around the edge. Accordingly the 
work done by the moon on this region may be neglected. The whole work done on 
the Yellow Sea by the moon is therefore small in comparison with the energy entering 
with the tide, and even its sign is uncertain. Thus the average dissipation in the 
whole of the sea is not very different from l'l x 10 18 ergs per second. 
An alternative estimate may be deduced directly from the formula for the 
dissipation, with a suitable hypothesis on the distribution of velocity. At the 
