DR. HAROLD JEFFREYS ON TIDAL FRICTION IN SHALLOW SEAS. 
251 
The amplitude of >/ reaches a minimum where the coefficient of cosyi vanishes. We 
shall have the least possible tide in the middle, thus satisfying our earlier assumptions, 
if we assume that this minimum is reached at the point where the velocity vanishes. 
In this way we shall underestimate the dissipation, but not by any great amount. 
The value of h that makes this coincidence possible is 6'6 x 10 _6 /1 cm., so that the 
current becomes zero 300 km. from the shore, practically in the middle of the 
entrance. 
Taylor shows ( loc . cit., equation 15) that the average amount of energy 
crossing any line is the average over a period of gp\Dt)U dy in my notation, where D is 
the depth of the water, in this case about 30 fathoms over most of the region in 
which the velocity is greatest, with a range in all of from 20 to 45 fathoms. We 
find easily 
>7 = 147 sin yt — 4‘3 x 10~ 8 Jc (y — 200/k ) 2 cos yt, 
and the average flux of energy across a parallel of latitude is found to be 
1’06 x 10 18 ergs/sec. 
The northward flux on the Chinese side is more difficult to determine, as the 
direction of the currents is variable. Two phenomena are intermingled here. The 
issuing tide from the Yellow Sea comes down this coast, but there is also a definite 
tidal wave that travels into and out of the large bend in the coast whose extremities 
are Shan-tung promontory and Shanghai. This is shown by the fact that along the 
northern part of this bend, on which Tsing-tao stands, the current flows northwards 
while the tide is ebbing both along this coast and in the northern part of the 
Yellow Sea. Thus in this bay the main tide is the local tide of the bay itself and 
not the general tide of the Yellow Sea. The currents produced by these tides are 
rotary, probably an effect of the earth’s rotation ; and it seems that the northward 
component of the velocity is small. Further, it is probably nearly in a phase at 
right angles to the tide, as great divergences from this relation can be produced only 
by great dissipations and accordingly by great velocities in the vicinity. Hence for 
both reasons we infer that the northward flux of energy along the Chinese coast is 
small in comparison with that on the Korean side. 
We also need to know the work done on the water by the moon. If >/ is the 
height of the equilibrium tide, the work done by the moon in a period is 
n 
d 
gyj ~ dt dS, where dS is the element of horizontal surface and the integrals are to 
(a/L 
be taken, in the one case over a period, and in the other over the area considered. 
If the phase of rj is /3 in advance of that of >/', and the amplitudes be h and h', the 
average rate of doing work is — ^g\h-h' y sin ft dS. In the present case h' naturally 
varies little ; h decreases fairly steadily as we travel from the entrance to Port Arthur, 
where it has about half of its value at the entrance. On the other hand (3 varies a 
great deal. The longitude being about 120° E., the moon crosses the meridian at 
full and change at 3h, 43m. It is high water in Shoan harbour, at the southern 
