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V11L Tidal Friction in Shalloiv Seas. 
By Harold Jeffreys, M.A., D.Sc., Fellow of St. Johns College , Cambridge. 
Communicated by Sir Napier Shaw, F.R.S. 
Received April 7,—Read June 24, 1920. 
The astronomical importance of the dissipation of energy that goes on in shallow seas 
has been shown by G. I. Taylor’s recent estimate^ of the amount in the Irish Sea, 
which is enough to account for about one-fiftieth of the secular acceleration of the 
moon. It also produces a considerable effect on the tides themselves, and there are 
probably many places where it must be taken into account before any satisfactory 
theory of the local tides, or even their empirical prediction, can be achieved. It is 
indeed very well known that there are bays and straits where the height of the 
tides, or the speed of the currents, or both, are greater than in the Irish Sea, and a 
careful examination of such places, with a view to finding the dissipation in them, is 
needed. There are other places where the dissipation for an equal area is less than in 
the Irish Sea, but which may actually contribute much more altogether on account of 
their greater size. The object of this paper is to discuss what regions are capable of 
producing notable parts of the secular acceleration ; to estimate as accurately as 
possible from the data available the dissipation in these ; and to compare this with 
that calculated from the secular acceleration, so as to find out whether it is necessary 
to assume the existence of any other important cause to account for the latter. 
The horizontal force of the skin friction of water over the sea bottom is 0'002/3V" 
dynes per square centimetre, where p is measured in grammes per cubic centimetre 
and V in centimetres per second. The difficulty of the problem is in the estimation 
of Y. The available observations of the velocities of tidal currents are given in the 
Admiralty Sailing Directions; hut they are never uniformly distributed, and are 
usually confined to the neighbourhood of the coasts, and they must be supplemented 
by theory before the velocities remote from the coast can be found. A few 
theoretical considerations that have been found useful in this process will now be 
mentioned. 
Take first the case of a bay or strait long in comparison with its width, and 
consider a wave entering it whose period is much longer than the time needed for a 
* ‘Phil. Trans.,’ A, vol. 220, pp. 1-33, 1919. 
2 L 
YOL. CCXXI.- A 589. 
[Published November 5, 1920. 
