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reflected wave may readily be found. As the calculation ia extremely easy after what precedes, it seems sufficient to give
the result. Let therefore, here, /* = -^. also e, e, and 0 as before, then e, = — e, and the accurate value of e is given by
tan e - /* VyW0- sec»0 - ^~}Lpl.
The first term of this expression agrees with the formula of page 362, Airy's Tracts*, and the second will be scarcely sensible except for highly refracting substances.
* [Airy, ubi tup. p. 114, Art. 133.]
MOTION OF WAVES IN CANALS*.
* [From the Transactions of tke Cambridge Philosophical Society, J839,] [Read February j8, 1839.]
NOTE ON THE MOTION OF WAVES IN CANALS.
In a former communication* I have endeavoured to apply the ordinary Theory of Fluid Motion to determine the law of the propagation of waves in a rectangular canal, supposing % the depression of the actual surface of the fluid below that of equilibrium very small compared with its depth; the depth 7 as well as the breadth ft of the canal being small compared with the length of a wave. For greater generality, ft and 7 are supposed to vary very slowly as the horizontal co-ordinate as increases, compared with the rate of the variation of J, due to the same cause. These suppositions are not always satisfied in the propagation of the tidal wave, but in many other cases of propagation of what Mr Eussel denominates the "Great Primary Wave," they are so, and his results will be found to agree very closely with our theoretical deductions. In fact, in my paper on the Motion of Waves, it has been shown that the height of a wave varies aa
With regard to the effect of the breadth ft, this is expressly Btated by Mr Eussel (vide Seventh Report of the British Association, p. 425), and the results given in the tables, p. 494, of the same work, seem to agree with our formula as well as could be expected, considering the object of the experiments there detailed.
In order to examine more particularly the way in which the Primary Wave is propagated, let us resume the formulae,
* Supra, p. 22?