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Tides in rivers

To Mary Stevenson

My dear Friend, London, Sept. 13. 1760

I have your agreable Letter from Bristol, which I take this first Leisure Hour to answer, having for some time been much engag’d in Business.

Your first Question, What is the Reason the Water at this Place, tho’ cold at the Spring, becomes warm by Pumping? it will be most prudent in me to forbear attempting to answer, till, by a more circumstantial Account, you assure me of the Fact. I own I should expect that Operation to warm, not so much the Water pump’d as the Person pumping. The Rubbing of dry Solids together, has been long observ’d to produce Heat; but the like Effect has never yet, that I have heard, been produc’d by the mere Agitation of Fluids, or Friction of Fluids with Solids. Water in a Bottle shook for Hours by a Mill Hopper, it is said, discover’d no sensible Addition of Heat. The Production of Animal Heat by Exercise, is therefore to be accounted for in another manner, which I may hereafter endeavour to make you acquainted with.

This Prudence of not attempting to give Reasons before one is sure of Facts, I learnt from one of your Sex, who, as Selden tells us, being in company with some Gentlemen that were viewing and considering something which they call’d a Chinese Shoe, and disputing earnestly about the manner of wearing it, and how it could possibly be put on; put in her Word, and said modestly, Gentlemen, are you sure it is a Shoe? Should not that be settled first?

But I shall now endeavour to explain what I said to you about the Tide in Rivers, and to that End shall make a Figure, which tho’ not very like a River, may serve to convey my Meaning. Suppose a Canal 140 Miles long communicating at one End with the Sea, and fill’d therefore with Sea Water. I chuse a Canal at first, rather than a River, to throw out of Consideration the Effects produc’d by the Streams of Fresh Water from the Land, the Inequality in Breadth, and the (Diagram omitted) Crookedness of Courses. Let A, C, be the Head of the Canal, C D the Bottom of it; D F the open Mouth of it next the Sea. Let the strait prick’d Line B G represent Low Water Mark the whole Length of the Canal, A F High Water Mark: Now if a Person standing at E, and observing at the time of High water there that the Canal is quite full at that Place up to the Line E, should conclude that the Canal is equally full to the same Height from End to End, and therefore there was as much more Water come into the Canal since it was down at the Low Water Mark, as could be included in the oblong Space A. B. G. F. he would be greatly mistaken. For the Tide is a Wave, and the Top of the Wave, which makes High Water, as well as every other lower Part, is progressive; and it is High Water successively, but not at the same time, in all the several Points between G, F. and A, B. — and in such a Length as I have mention’d it is Low Water at F G and also at A B, at or near the same time with its being High Water at E; so that the Surface of the Water in the Canal, during that Situation, is properly represented by the Curve prick’d Line B E G. And on the other hand, when it is Low Water at E H, it is High Water both at F G and at A B at or near the same time; and the Surface would then be describ’d by the inverted Curve Line A H F.

In this View of the Case, you will easily see, that there must be very little more Water in the Canal at what we call High Water than there is at Low Water, those Terms not relating to the whole Canal at the same time, but successively to its Parts. And if you suppose the Canal six times as long, the Case would not vary as to the Quantity of Water at different times of the Tide; there would only be six Waves in the Canal at the same time, instead of one, and the Hollows in the Water would be equal to the Hills.

That this is not mere Theory, but comformable to Fact, we know by our long Rivers in America. The Delaware, on which Philadelphia stands, is in this particular similar to the Canal I have supposed of one Wave: For when it is High Water at the Capes or Mouth of the River, it is also High Water at Philadelphia, which stands about 140 Miles from the Sea; and there is at the same time a Low Water in the Middle between the two High Waters; where, when it comes to be High Water, it is at the same time Low Water at the Capes and at Philadelphia. And the longer Rivers have, some a Wave and Half, some two, three, or four Waves, according to their Length. In the shorter Rivers of this Island, one may see the same thing in Part: for Instance; it is High Water at Gravesend an Hour before it is High Water at London Bridge; and 20 Miles below Gravesend an Hour before it is High Water at Gravesend. Therefore at the Time of High Water at Gravesend the Top of the Wave is there, and the Water is then not so high by some feet where the Top of the Wave was an Hour before, or where it will be an Hour after, as it is just then at Gravesend.

Now we are not to suppose, that because the Swell or Top of the Wave runs at the Rate of 20 Miles an Hour, that therefore the Current or Water itself of which the Wave is compos’d, runs at that rate. Far from it. To conceive this Motion of a Wave, make a small Experiment or two. Fasten one End of a Cord in a Window near the Top of a House, and let the other End come down to the Ground; take this End in your Hand, and you may, by a sudden Motion occasion a Wave in the Cord that will run quite up to the Window; but tho’ the Wave is progressive from your Hand to the Window, the Parts of the Rope do not proceed with the Wave, but remain where they were, except only that kind of Motion that produces the Wave. So if you throw a Stone into a Pond of Water when the Surface is still and smooth, you will see a circular Wave proceed from the Stone as its Center, quite to the Sides of the Pond; but the Water does not proceed with the Wave, it only rises and falls to form it in the different Parts of its Course; and the Waves that follow the first, all make use of the same Water with their Predecessors.

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 20 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, occasion’d 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 20 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 call’d the Tide; thus we say, the Tide runs strong, the Tide runs at the rate of 1, 2, or 3 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, occasion’d by its Gravity, will explain to you why the Water near the Mouths of Rivers may be salter at Highwater 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 5 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 Highwater Mark. Which is but a fourteenth Part of what would be necessary to fill all the Space between Low and Highwater Mark, for 140 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 farther 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 6 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 agreable 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 something that means nothing, and is merely civil and polite. But being naturally awkward 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 allow’d to subscribe my self Your affectionate Friend