Proceedings of the British Association. 547 



These diagrams exhibit the following changes produced in the tidal 

 course. First of all, we have the tide rising to high water at h } fal- 

 ling to a low water at p lf rising to a second high water at Hj with a 

 very small low water at p h between them; then we have at the low 

 waters L j and L 2 an elevation, and two depressions of an equally ano- 

 malous kind. It also appears that the range or rise and fall of tide in- 

 creases as it travels, instead of diminishing. As these observations 

 were reduced to the same level, it further appeared that the high water 

 mark at Stirling was higher than high water mark at Leith, by ten to 

 fifteen feet. These diagrams, being compared with the plan of the 

 Firth, serve to shew the effect of form of channel on the wave. Mr. 

 Russell then proceeded to his explanation of these anomalous pheno- 

 mena. He referred to the very great progress which had recently been 

 made in our knowledge of the laws and phenomena of the tides. Mr. 

 Lubbock had succeeded in deriving all the principal phenomena of the 

 tides, most accurately from the equilibrium theory of Bernouilli ; Mr. 

 Whewell had constructed, from the discussion of a multitude of simul- 

 taneous observations, empirical formulae by which the progress of the 

 tide wave had been represented with a high degree of accuracy, and the 

 theory of the tides had attained a high degree of perfection. But there 

 still remained a multitude of anomalous facts for which received theory 

 could not account, and amongst this number were these refractory 

 double tides. Mr. Russell's theory is this : that the tidal wave is a 

 compound wave of the first order ; that its phenomena are correctly re- 

 presented by the wave which he has called the great wave of transla- 

 tion — that this tide's motion along our shores is correctly represented 

 by this type. Now the wave of translation in ascending a channel 

 whose breadth and depth vary, exhibit the following phenomena : — First, 

 a velocity varying as the square root of the depth of the channel ; se- 

 cond, an increase of height with the diminution in breadth and in 

 depth of the channel ; third, a dislocation of the centre, which is trans- 

 ferred forwards in the direction of transmission according to a simple 

 and well-established law. And these changes exactly correspond to 

 the epoch of high water, the law of rise and fall, and the exaggeration 

 of range in the Firth of Forth. Of the four successive high waters of 

 each day, he has ascertained the latter tide of each pair to be normal 

 and the earlier the abnormal tide. It is well known that the tide 

 which brings high water to the east coast of Britain, as far at least as 

 the Thames, comes round the north of Britain, and bringing high water 

 to Aberdeen about noon, Leith about two, and London about twelve 



