Secondat: London awash and the King returning to power

I've been reading letters of John Wallis, an English mathematician of the seventeenth century who had some insights which led to the revolutionary development of the calculus. He did not confine his interest to math, having administrative responsibilities as keeper of archives at Oxford University and the varied interests typical of members of the Royal Society in his time. One of these was a study of tides, specifically the causes of the exceptionally high tides which occur near the vernal and autumnal equinoxes each year.

From his home in Oxford he wrote frequently to Henry Oldenburg, the Royal Society's secretary on the probable causes of these tides. Kepler and Gallileo had also studied this phenomenon and Newton would later take it up. Galileo thought the main cause to be variations in the speed of the earth's rotation at different points on its surface. Wallis suggested that the main cause was the combined pull of gravitation exerted by sun and moon. He visualized a common center of gravity which changed position as the earth and moon moved in their orbits. The explanation given today largely reaffirms this hypothesis.

All this came to mind on reading an account in the Guardian about the yearly highest of high tides that are expected in England today and Monday and then again on October 7 and 10. These dates are conjunctions of two major astronomical events, one set occuring about every two weeks (the new and full moons, when the moon, earth, and sun are aligned with one another) and the other occuring twice a year when the sun crosses the equator (the equinoxes). On these times tide-producing gravitational forces are at their greatest. The tides are highest in years when the equinox and a new or full moon are timed as they are now. Click image to enlarge. Its caption, from BBC News, reads: "Shading shows likely extent of flooding from overflowing rivers and exceptionally high seas if there were no flood defences (Environment Agency). Spring tides expected in September and October may be highest for next 20 years in some areas. But Environment Agency says most flood defences should be able to cope unless they coincide with particularly severe weather."

There are quite a few factors that affect the actual tide height (mostly weather conditions, curvature of the shorline, the shape of the ocean floor, atmospheric pressure, and some special conditions affecting tidal rivers and inlets) so the semi-yearly high tides are not entirely predictable. The caption on this image from BBC News reads: "Prevailing SW winds carry depression to NW Scotland. Mean current forces surge to right of wind direction. If low also moves east, surge is forced southwards.
Shallower seabed means surge elevations higher in southern parts of North Sea."

Wallis didn't have the benefit of our full understanding of all the forces and conditions that affect tides. Newton's insight into the law of gravity was, in fact, still in the future. So his intuition and inductive reasoning are, I think, pretty admirable. And it's therefore surprising that his evidence did not support what we now know as fact concerning the conjunction of equinox, on the one hand, and alignment of sun, earth, and moon, on the other. In fact, though he understood that the matter was complicated, he didn't have enough evidence to grasp how many and varied were the causes of exceptional high tides.

Here is his account of the observations that caused him to develop the common-center-of-gravity hypothesis.

This comes from an article he wrote for Philosophical Transactions, the periodical (first of its kind) published by Oldenburg for the Royal Society. It is An essay of Dr. John Wallis, exhibiting his hypothesis about the flux and reflux of the sea (Issue no. 16, Monday, August 6, 1666, London, John Martin). The full title is "An Essay of Dr. John Wallis, exhibiting his Hypothesis about the Flux and Reflux of the Sea, taken from the Consideration of the Common Center of Gravity of the Earth and Moon."

Here are his observations. I like particularly his memory of the high water of November 1660 in London.

It having been observed (grosly) that those high Tides have used to happen about the Spring and Autumn; it hath been generally taken for granted (without any more nice observation) that the two quinoxes are the proper times, to which these Annual high Tides are to be referred; And such causes sought for, as might best sute with such a Supposition.

But it is now, the best part of twenty years, since I have had frequent occasions to converse with some Inhabitants of Rumney-marsh in Kent; where the Sea being kept out with great Earthen walls, that it do not at high water overflow the Levell; and the Inhabitants livelyhood depending most on grazing, or feeding Sheep; they are (as you may believe they have reason to be) very vigilant and observant, at what times they are most in danger of having their Lands drowned. And I find them generally agreed, by their constant Observations, (and Experience dearly bought) that their times of danger are about the beginning of February and of November : that is, at those Spring Tides which happen near those times; to which they give the names of Candlemass-stream and Allhallond-stream : And if they scape those Spring-tides, they apprehend themselves out of Danger for the rest of the year. And as for March and September (the two quinoxes ) they are as little solicitous of them, as of any other part of the year.

This, I confess, I much wondred at, when I first heard it; and suspected it to be but a mistake of him, that first told me, though he were indeed a person not likely so to be mistaken, in a thing wherein he was so much concerned: But I soon found, that it was not onely his, but a general observation of others too; both there, and elsewhere along the Sea coast. And though they did not pretend to know any reason of it, (nor so much as to enquire after it;) Yet none made doubt of it; but would rather laugh at any that should talk of March and September , as being the dangerous times. And since that time, I have my self very frequently observed (both at London and elsewhere, as I have had occasion) that in those months of February and November , (especially November ) the Tides have run much higher, than at other times: Though I confess, I have not been so diligent to set down those Observations, as I should have done. Yet this I do particularly very well remember, that in November 1660. (the same year that his Majesty returned) having occasion to go by Coach from the Strand to Westminster , I found the Water so high in the middle of King-street , that it came up, not onely to the Boots, but into the Body of the Coach; and the Pallace-yard (all save a little place near the West-End ) overflow'd; as likewise the Market-place; and many other places; and their Cellars generally filled up with Water. And in November last, 1665. it may yet be very well remembred, what very high Tides there were, not onely on the Coasts of England , (where much hurt was done by it) but much more in Holland , where by reason of those Inundations, many Villages and Towns were overflow'd. And though I cannot so particularly name other years, yet I can very safely say, that I very often observed Tides strangely high about those times of the year. This Observation did for divers years cause me much to wonder, not only because it is so contrary to the received opinion of the two quinoxes ; but because I could not think of any thing signal at those times of the year: as being neither the two quinoxes, nor the two Solstices , nor the Sun's Apogeum and Perigeum ; (or Earths Aphelium and Perihelium ;) nor indeed, at contrary times of the year, which at least, would seem to be expected. From Alhollandtide to Candlemass being but three months; and from thence to Alhollandtide again nine months.