116 REPORT— 1842. 



then we have at the low waters, Li and L 2 an elevation, and two depressions of an 

 equally anomalous 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 show the effect of form of channel on the wave. 



Mr. Russell then proceeded to his explanation of these anomalous phenomena. 

 He referred to the very great progress which had recently been made in our know- 

 ledge of the laws and phsenomena of the tides. Mr. Lubbock had succeeded in deriving 

 all the principal phenomena of the tides most accurately from the equilibrium theory 

 of Bernoulli ; Mr. Whewell had constructed, from the discussion of a multitude of 

 simultaneous 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 anoma- 

 lous 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 represented by 

 the wave which he has called the great wave of translation ; 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, exhibits the following pheno- 

 mena : — First, a velocity varying as the square root of the depth of the channel ; second, 

 an increase of height with the diminution in breadth and in depth of the channel ; 

 third, a dislocation of the centre, which is transferred forwards in the direction of 

 transmission according to a simple and well-established law. And these changes ex- 

 actly correspond to the epoch of high water, the law of rise and fall, and the exag- 

 geration 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 o'clock at spring tides. This wave is the 

 same which brings to the whole of the Firth of Forth the normal high water, and of 

 the double tides the later of each pair corresponds exactly with the time as predicted 

 by the excellent tables of Mr. Lubbock. But if we conceive the great southern wave, 

 which comes up the English Channel, to continue its course northwards in the oppo- 

 site direction to the normal tide, it would enter the Forth at ten o'clock, being two 

 hours previous to the normal tide, due to the succeeding transit of the moon, or 

 the tide E at Leith will consist of the normal tide due to transit B and the abnormal 

 tide due to transit A. Now the double tides are in exact correspondence with these 

 conditions, the abnormal tide being generally about two hours in advance of the nor- 

 mal tide. 



But the circumstance which most perfectly fixes the identity of the tides, as due to 

 the successive transits A and B, is found in the character of their diurnal irregu- 

 larities. If the theory adduced be correct, the normal and the abnormal tides will 

 have opposite inequalities. The observations made exactly correspond with this view ; 

 and, so far as they go, establish the soundness of the view which has been adduced 

 for their explanation. 



Another remarkable confirmation of this view is derived from the examination of 

 the diurnal inequality of places on opposite coasts at the mouth of the Forth, the 

 diurnal inequality on the south side being that due to the northern or normal tide, 

 and that on the northern coast being that due to the abnormal or southern tide-wave. 

 At Leith both waves meet, and the inequalities nearly neutralize each other, and 

 give only the difference of the inequalities. By the same process, using the wave 

 of translation as a type of the tide-wave, some further anomalies of the tide-wave 

 were explained, and the absence of all tide frequently observed on opposite and adja- 

 cent coasts, as at the north of Scotland and the opposite coast of Norway. These are 

 explained by the fact that the lateral transmission of the wave is slower than its trans- 

 mission in the direction of its amplitude, so that the rapid advancement of one por- 

 tion of the wave gives divergence to the branches, which thus separate and leave an 

 interval of diminished tide or of no tide. 



