Elementary Theory of the Tides: the Fundamental Theorems Demonstrated Without Mathematics, And the Influence On the Length of the Day Discussed

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It is easy to deduce from this construction the cor- responding formulae. For, if OB = r, we have Bp=r{l-oos'w). Bntps=^r-Bp=lr{2oos^b)-l)=}rooB2b).
And since sB is proportional to the mean height, the defect 14 THE TIDES.
from this height is proportional to ps, and therefore to cos 2a).
The effect of pressure with such a tide will be extremely small. As it operates to send the water away from its position of greatest elevation, it will so far assist the moon's force without changing the place
...of high water.
To estimate the effect of friction, the moon's force being = - H sin 2(0, the velocity ®, undisturbed by friction = V cos 2(1) {V being the greatest velocity). If the dis- placement caused by friction is very small, we may take this value of » as a sufficient approximation. The friction, assumed proportional to velocity = Vf cos 2aj, and the velocity begins to be checked when py cos 2a) = - fl'sin2aj , _ Vf 366000. _.. . .
or, tan 2bj = - ^ = ^ — /= - 7000/ nearly.
When the displacement (which we shall call S) is sensible!


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