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reflected wave may readily be found. As the calculation is extremely easy after what precedes, it seems sufficient to give

the result. Let therefore, here, μ, also e, e, and 6 as be

1

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fore, then e, -e, and the accurate value of e is given by

tan e = μ √μ3 tan2 0 — sec2 - (u2 - 1) tan ✪

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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 sup. p. 114, Art. 133.]

NOTE

ON THE

MOTION OF WAVES IN CANALS*.

* [From the Transactions of the Cambridge Philosophical Society, 1839.1 [Read February 18, 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 y as well as the breadth ẞ of the canal being small compared with the length of a wave. For greater generality, ẞ and y are supposed to vary very slowly as the horizontal co-ordinate increases, compared with the rate of the variation of , 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 Russel 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 as

With regard to the effect of the breadth 6, this is expressly stated by Mr Russel (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 formulæ,

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