But a wave in water is not indeed in all circumstances exactly like that in a cord; for water being a fluid, and gravitating to the earth, it naturally runs from a higher place to a lower; therefore the parts of the wave in water do actually run a little both ways from its top towards its lower sides, which the parts of the wave in the cord cannot do. Thus, when it is high and standing water at Gravesend, the water twenty miles below has been running ebb, or towards the sea for an hour, or ever since it was high water there; but the water at London Bridge will run flood, or from the sea yet another hour, till it is high water, or the top of the wave arrives at that bridge, and then it will have run ebb an hour at Gravesend, &c. &c. Now this motion of the water, occasioned only by its gravity, or tendency to run from a higher place to a lower, is by no means so swift as the motion of the wave. It scarce exceeds perhaps two miles in an hour.
If it went as the wave does twenty miles an hour, no ships could ride at anchor in such a stream, nor boats row against it.
In common speech, indeed, this current of the water both ways from the top of the wave is called the tide; thus we say, the tide runs strong, the tide runs at the rate of one, two, or three miles an hour, &c. and when we are at a part of the river behind the top of the wave, and find the water lower than high-water mark, and running towards the sea, we say, the tide runs ebb; and when we are before the top of the wave, and find the water higher than low-water mark, and running from the sea, we say, the tide runs flood; but these expressions are only locally proper; for a tide, strictly speaking, is one whole wave, including all its parts higher and lower, and these waves succeed one another about twice in twenty-four hours.
This motion of the water, occasioned by its gravity, will explain to you why the water near the mouths of rivers may be salter at high water than at low. Some of the salt-water, as the tide wave enters the river, runs from its top and fore side, and mixes with the fresh, and also pushes it back up the river.
Supposing that the water commonly runs during the flood at the rate of two miles in an hour, and that the flood runs five hours, you see that it can bring at most into our canal only a quantity of water equal to the space included in the breadth of the canal, ten miles of its length, and the depth between low and high-water mark; which is but a fourteenth part of what would be necessary to fill all the space between low and high-water mark, for one hundred and forty miles, the whole length of the canal.
And indeed such a quantity of water as would fill that whole space, to run in and out every tide, must create so outrageous a current, as would do infinite damage to the shores, shipping, &c. and make the navigation of a river almost impracticable.
I have made this letter longer than I intended, and therefore reserve for another what I have further to say on the subject of tides and rivers. I shall now only add, that I have not been exact in the numbers, because I would avoid perplexing you with minute calculations, my design at present being chiefly to give you distinct and clear ideas of the first principles.
After writing six folio pages of philosophy to a young girl, is it necessary to finish such a letter with a compliment?—Is not such a letter of itself a compliment?—Does it not say, she has a mind thirsty after knowledge, and capable of receiving it; and that the most agreeable things one can write to her are those that tend to the improvement of her understanding?—It does indeed say all this, but then it is still no compliment; it is no more than plain honest truth, which is not the character of a compliment. So if I would finish my letter in the mode, I should yet add some thing that means nothing, and is merely civil and polite. But being naturally aukward at every circumstance of ceremony, I shall not attempt it. I had rather conclude abruptly with what pleases me more than any compliment can please you, that I am allowed to subscribe myself
Your affectionate friend,