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XXXI. On Tides and Waves. — Deflection Theory. 

 By Alfred Tylor, F.G.S. 



[With Three Plates.] 

 To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, London, August 15th, 1874. 



I SHOULD be glad if any of your readers will send me a re- 

 ference to any work of authority in which there is any direct 

 statement of the height of the level of the ocean (say the central 

 Atlantic) compared with high-water mark on the east and west 

 coasts of Ireland and England. This is an important point in 

 the general theory of the tides, a subject I am about to dis- 

 cuss. The view I shall advocate is that the level of the ocean is 

 nearly represented by high-water mark on coasts and bays where 

 there is free access of the tide and a channel without a sudden 

 taper. Mr. E. Roberts, of the Nautical Almanac Office, editor 

 of the Reports of the Tidal Committee of the British Associa- 

 tion, informed me last month he was not aware of any statement 

 in print on good authority on this point. The only opinion I 

 have on this subject is from Professor G. G. Stokes, F.R.S. (and 

 that is an imprinted one*), who wrote, " Nobody maintains that 

 the general level of the ocean is that of low water ; it is the 

 mean between high and low, except in shallow channels &c, 

 where it is not the exact mean." In the absence of further 

 authorities I shall give my deflection theory of tides. 



In Plates II. and III. I give a drawing of what I suppose is the 

 relation of high and low water on the coast and in estuaries and 

 channels to that of the sea, I show that the level of the central 

 ocean approximates to mean high- water mark on the coast of 

 Ireland, and is about 4 feet above the English Ordnance Datum, 

 which datum maybe treated as an arbitrary line, being only the 

 mean level of the sea at Liverpool, Penzance, and Falmouth, all 

 places in which the tide is affected by the converging contour 

 of the coast. 



The velocity of the central ocean- stream, if reduced by the 

 inequalities of the sea-bottom at a different ratio to the depth, 

 would cause the water to heap, and vice versa. I do not think 

 it does heap perceptibly until near the coast, and then in very 

 different degrees (see Plates II. and III.). When the increase 

 of velocity exactly balances the decrease of depth ; that is, using 

 V and v for the old and new velocity, and I and i for the re- 

 spective distances from the centre of the earth, 



when I = i. then — = =[ (1) 



v r ' 



* In some remarks about the views expressed in Plates II. and III. sent 

 to him for examination, March 7, 1874. 



