Halley

Why politicians should drink loose leaf tea

Coffee Corona

Notice the rainbow pattern around the reflected light spot?
The universe is in a cup of coffee but to understand rising sea levels, it’s helpful to look at tea.

The universe is in a glass of wine. So said Richard Feynman. It has been the focus of this website to concentrate instead on the universe in a cup of coffee, partly because it is much easier to contemplate a coffee over breakfast. However there are times when contemplating a cup of tea may be far more illuminating. Such was the case last week: if only a politician had paused for a cup of tea before commenting on rising sea levels.

There are many reasons to drink loose leaf tea rather than tea made with a bag. Some would argue that the taste is significantly improved. Others, that many tea bags contain plastic and so, if you are trying to reduce your reliance on single-use plastic, loose leaf tea is preferable. Until last week though, it had not occurred to me that brewing a cup of tea with a mesh ball tea infuser (or a similar strainer) was a great way to understand the magnitude of our problem with rising sea levels. If a stone were to enter a pond, the pond-level would rise; if a spherical tea strainer (full of loose leaf tea) were to be placed in a cup, the soon-to-be-tea level would rise.

Clearly, because we know our physics, we would not place a strainer of tea into an existing cup of hot water as we know the brewing process relies on diffusion and turbulence, not just diffusion alone. So what we more commonly observe in the cup is actually a tea-level fall as we remove the straining ball. Fortunately, we can calculate the tea level decrease, h:

A schematic of the tea brewing process

My cylindrical tea mug has a radius (d) of 3.5cm. The radius (r) of the mesh ball is 2cm. We’ll assume that the tea leaves completely expand filling the mesh ball so that the ball becomes a non-porous sphere. Clearly this bit is not completely valid and would anyway create a poor cup of tea, but it represents a worst-case scenario and so is good as a first approximation.

Volume of water displaced = volume of mesh ball

πd²h = (4/3)πr³

A bit of re-arrangement means that the height of the tea displaced is given by

h = 4r³/(3d²)

h = 0.87 cm

This answer seems quite high but we have to remember that the mesh ball is not completely filled with tea and so the volume that it occupies is not quite that of the sphere. Moreover, when I check this answer experimentally by making a cup of tea, the value is not unreasonable. Removing the mesh-ball tea strainer does indeed lead to a significant (several mm) reduction in tea level.

Earth from space, South America, coffee

Assuming we are truly interested in discovering more about our common home, we can gain a lot through contemplating our tea.
The Blue Marble, Credit, NASA: Image created by Reto Stockli with the help of Alan Nelson, under the leadership of Fritz Hasler

What does this have to do with politicians? Last week a congressman from Alabama suggested that the observed rising sea levels could be connected with the deposition of silt onto the sea bed from rivers and the erosion of cliffs such as the White Cliffs of Dover. If only he had first contemplated his tea. Using a “back of the envelope” calculation similar to that above, it is possible to check whether this assertion is reasonable. As the surface area of the oceans is known and you can estimate a worst-case value for the volume of the White Cliffs falling into the sea, you can calculate the approximate effect on sea levels (as a clue, in order to have a significant effect, you have to assume that the volume of the White Cliffs is roughly equal to the entire island of Great Britain).

Mr Brooks comments however do have another, slightly more tenuous, connection with coffee. His initial suggestion was that it was the silt from rivers that was responsible for the deposition of material onto the sea bed that was in turn causing the sea level to rise. About 450 years ago, a somewhat similar question was being asked about the water cycle. Could the amount of water in the rivers and springs etc, be accounted for by the amount of rain that fell on the ground? And, a related question, could the amount of rain be explained by the amount of evaporation from the sea?

The initial idea that the answer to both of those questions was “yes” and that together they formed the concept of the “water cycle” was in part due to Bernard Palissy. Palissy is now known for his pottery rather than his science but he is the author of a quote that is very appropriate for this case:

“I have had no other book than the heavens and the earth, which are known to all men, and given to all men to be known and read.”

Reflections on a cup of tea.

Attempts to quantify the problem and see if the idea of the water cycle was ‘reasonable’ were made by Pierre Perrault (1608-80) in Paris and Edmond Halley (1656-1742) in the UK. Perrault conducted a detailed experiment where he measured the rain fall over several years in order to show that the amount of rain could account for the volume of water in the Seine. Halley on the other hand, measured the amount of evaporation from a pan of heated water and used this value to estimate the evaporation rate from the Mediterranean Sea. He then estimated the volume of water flowing into that sea from a comparison to the flow of the water in the Thames at Kingston. Together (but separately) Perrault and Halley established that there was enough water that evaporated to form rain and that this rain then re-supplied the rivers. Both sets of calculations required, in the first place, back of the envelope type calculations, as we did above for the tea-levels, to establish if the hypotheses were reasonable.

If you missed the coffee connection, and it was perhaps quite easy to do so, the question that Halley studied concerned the rate of evaporation as a function of the water’s temperature. This is something that is well known to coffee drinkers. Secondly however, one of Halley’s experiments about the evaporating water was actually performed at a meeting of the Royal Society. It is known that after such meetings, the gathered scientists would frequently adjourn to a coffee house (which may have been the Grecian or, possibly more likely, Garraways). As they enjoyed their coffee would they have discussed Halley’s latest results and contemplated their brew as they did so?

What this shows is that sometimes it is productive to contemplate your coffee or think about your tea. Notice what you observe, see if you can calculate the size of the effect, consider if your ideas about the world are consistent with your observations of it. But in all of it, do pause to slow down and enjoy your tea (or coffee).

Theme on a V60

bloom on a v60

V60 bubbles. There is much to be gained by slowing down while brewing your coffee.

Preparing a coffee with a pour-over brewer such as a V60 is a fantastic way to slow down and appreciate the moment. Watching anti-bubbles dance across the surface as the coffee drips through, inhaling the aroma, hearing the water hit the grind and bloom; a perfect brewing method for appreciating both the coffee and the connectedness of our world. The other week, while brewing a delightful Mexican coffee from Roasting House¹, I noticed something somewhat odd in the V60. Having placed it on the kitchen scales and, following brewing advice, measured the amount of coffee, I poured the first water for the bloom and then slowly started dripping the coffee through. Nothing unusual so far and plenty of opportunity to inhale the moment. But then, as I poured the water through the grind, I noticed the scales losing mass. As 100g of water had gone through, so the scales decreased to 99g then 98g and so on. It appeared the scales were recording the water’s evaporation.

science in a V60

Bubbles of liquid dancing on the surface of a brewing coffee.

It is of course expected that, as the water evaporates, so the mass of the liquid water left behind is reduced. This was something that interested Edmond Halley (1656-1742). Halley, who regularly drank coffee at various coffee houses in London including the Grecian (now the Devereux pub), noted that it was probable that considerable weights of water evaporated from warm seas during summer. He started to investigate whether this evaporating vapour could cause not only the rains, but also feed the streams, rivers and springs. As he told a meeting of the Royal Society, these were:

“Ingredients of a real and Philosophical Meteorology; and as such, to deserve the consideration of this Honourable Society, I thought it might not be unacceptable, to attempt, by Experiment, to determine the quantity of the Evaporations of Water, as far as they arise from Heat; which, upon Tryal, succeeded as follows…”²

Was it possible that somehow Halley’s demonstration of some three hundred years ago was being replicated on my kitchen scales? Halley had measured a pan of water heated to the “heat of summer” (which is itself thought provoking because it shows just how recent our development of thermometers has been). The pan was placed on one side of a balance while weights were removed on the other side to compensate the mass lost by the evaporating water. Over the course of 2 hours, the society observed 233 grains of water evaporate, which works out to be 15g (15 ml) of water over 2 hours. How did the V60 compare?

Rather than waste coffee, I repeated this with freshly boiled water poured straight into the V60 that was placed on the scales. In keeping with it being 2017 rather than 1690, the scales I used were, not a balance, but an electronic set of kitchen scales from Salter. The first experiment combined Halley’s demonstration with my observation while brewing the Mexican coffee a couple of weeks back. The V60 was placed directly on the scales and 402g of water just off the boil was poured into it. You can see what happened in the graph below. Within 15 seconds, 2 g had evaporated. It took just a minute for the 15g of water that Halley lost over 2 hours (with water at approximately 30 C) to be lost in the V60. After six minutes the rate that the mass was being lost slowed considerably. The total amount lost over 12 minutes had been 70g (70ml).

evaporation V60 in contact with scales

A V60 filled with 400g of water just off the boil seemed to evaporate quite quickly when placed directly on the scales.

Of course, you may be asking, could it be that the scales were dodgy? 70g does seem quite a large amount and perhaps the weight indicated by the scales drifted over the course of 12 minutes. So the experiment could be repeated with room temperature water. Indeed there did appear to be a drift on the scales, but it seemed that the room temperature water got moderately heavier rather than significantly lighter. A problem with the scales perhaps but not one that explains the quantity of water that seems to have evaporated from the V60.

control

Hot water (red triangles) loses more mass than room temperature water (grey squares).

Could the 70g be real? Well, it was worth doing a couple more experiments before forming any definite conclusions. Could it be that the heat from the V60 was affecting the mass measured by the electronic scales? After all, the V60 had been placed directly on the measuring surface, perhaps the electronics were warming up and giving erroneous readings. The graph below shows the experiment repeated several times. In addition to the two previous experiments (V60 with hot water and V60 with room temperature water placed directly on the scales), the experiment was repeated three more times. Firstly the V60 was placed on a heat proof mat and then onto the scales and filled with 400g of water. Then the same thing but rather than on 1 heat proof mat, three were placed between the kitchen scales and the V60. This latter experiment was then repeated exactly to check reproducibility (experiment 4).

You can see that the apparent loss of water when the V60 was separated from direct contact with the scales was much reduced. But that three heat proof mats were needed to ensure that the scales did not warm up during the 12 minutes of measurement. Over 12 minutes, on three heat proof mats, 14g of water was lost in the first experiment and 17g in the repeat. This would seem a more reasonable value for the expected loss of water through evaporation out of the V60 (though to get an accurate value, we would need to account for, and quantify the reproducibility of, the drift on the scales).

V60 Halley

The full set: How much water was really lost through evaporation?

Halley went on to estimate the flow of water into the Mediterranean Sea (which he did by estimating the flow of the Thames and making a few ‘back of the envelope’ assumptions) and so calculate whether the amount of water that he observed evaporating from his pan of water at “heat of summer” was balanced by the water entering the sea from the rivers. He went on to make valuable contributions to our knowledge of the water cycle. Could you do the same thing while waiting for your coffee to brew?

Let me know your results, guesses and thoughts in the comments section below (or on Twitter or Facebook).

¹As this was written during Plastic Free July 2017, I’d just like to take the opportunity to point out that Roasting House use no plastic in their coffee packaging and are offering a 10% discount on coffees ordered during July as part of a Plastic Free July promotion, more details are here.

²E Halley, “An estimate of the quantity of vapour….” Phil. Trans. 16, p366 (1686-1692) (link opens as pdf)

Ghosts of Christmas Past, the Devereux

Grecian, Coffee House, London Coffee House

The Devereux now stands where the Grecian once was

The Grecian is steeped in history. One of London’s early Coffee Houses, it counted Isaac Newton and Edmond Halley among its regulars. Today it is the site of a pub, “The Devereux“, owned by Taylor-Walker. The building itself dates from the nineteenth century though it is on the site of the old Grecian (a drawing of which can be seen on a wall inside the pub). In a sense, the Devereux is a continuation of the Grecian that once existed on this spot and it is for this reason that I’ve wanted to enjoy a drink at the Devereux/Grecian for a long time. What better time to do it than for a Christmas themed cafe-physics review?

The Devereux itself is a fairly spacious, comfortable pub, tucked down a little alley just off Fleet Street. It is strange to consider (while sipping on a glass of the 1730 pale ale) that it was here, just over 300 years ago, that the Grecian would host the after-meeting “pub outing” of the (then newly formed) Royal Society. Paintings and photographs of the Grecian and the Fleet St. area surround you, as you sit and enjoy your drink (they do serve tea and coffee too). Indeed, it is possible to almost feel the history of this place. I recalled reading a 1686 paper in the Philosophical Transactions by Edmund Halley in which he described a live demonstration, in front of a meeting of the Royal Society, of just how much water could evaporate from a heated plate of water in two hours. Halley was interested in this as part of the whole question of how rivers formed and where rain came from. I wondered whether Halley and his friends Newton and Sloane, retired to the Grecian after that meeting and sipped on hot coffee as they sat next to the cold windows which started to steam up on the inside.

Vegetable Lamb, Lamb of Tartary

The Vegetable Lamb in the collection of The Garden Museum

Reading about these early frequenters of this drinking establishment, it is hard to avoid the impression that they were driven by an interest in knowledge and knowing things. Of course the term ‘scientist’ had not yet been invented*. Science as in ‘scientia’ was still just Latin for knowledge, the men who gathered at the Grecian (and they were mostly men) were not “scientists” they were Natural Philosophers. Hans Sloane, another regular, was a great collector, finding curiosities from around the world and displaying them in his house. Most of his collection became the start of the British Museum but there is one curiosity of Sloane’s that I came across recently that is not to be found there at all and that is his “Vegetable Lamb”.

Vegetable Lambs were believed, in the seventeenth century to be, genuinely, part vegetable part animal. You can see from the photo that they do look fairly animal-like. According to the Garden Museum, these vegetable lambs originated in the Far East but now only two remain in the UK. The one that belonged to Hans Sloane (which is in the Natural History Museum) and the one that belonged to John Tradescant and that can now be found in the Garden Museum (now sadly closed until refurbishment is complete in 2017). Hans Sloane’s contribution was to show that this vege-animal was in fact purely a plant, a type of fern, which may make vegetarians everywhere breathe a sigh of relief. It was because these people were interested that they worked so hard in trying to understand the world around them. Which brings us, somewhat surprisingly, to one of the more recent famous patrons of what had by that time become, the Devereux.

Chesterton

The festive Chesterton bookshelf at the Devereux

GK Chesterton is not known for his scientific research. However, he did spend a great deal of time thinking and writing about all sorts of things. (It also appears that he spent a fair amount of time in the Devereux where there is an entire bookshelf of his books). A book of Chesterton’s essays “As I was saying” was published in the year of his death, 1936. Within that book is an essay “About the Telephone”. Chesterton was musing on a sentence that he had read in a newspaper that had troubled him: “The time will come when communicating with the remote stars will seem to us as ordinary as answering the telephone”. Chesterton wrote “Now if you could say to me: ‘The time will come when answering the telephone will seem to us as extraordinary as communicating with the remote stars…’ then I should admit that you were a real, hearty, hopeful, encouraging progressive.” I suspect that with our tendency today towards the fragmentation of knowledge and increasing specialisation, we would categorise the work of Newton and Halley, Sloane and then Chesterton in quite different compartments. Yet it seems to me that they share something in their work: an element of wonder and curiosity at the world. As Chesterton continued in “About The Telephone”,  I am not objecting to the statement that the science of the modern world is wonderful; I am objecting to the modern world because it does not wonder at it.

It sometimes seems hard for us to sit in a cafe on our own without using, or at least looking at, our telephones. Checking our email or the latest news on our telephones has become extraordinarily ordinary for us. Maybe this should be our New Year’s resolution: put our phone back into our pocket and consider, with Chesterton, Sloane, Halley and Newton, just how wonderful it is.

Happy Christmas & New Year to all

 

* The word science/scientist was first used in the sense that we now understand it by William Whewell in the nineteenth century.

“As I was Saying – a book of Essays by GK Chesterton” was published by Methuen&Co Ltd, 1936

The Devereux can be found in Devereux Court, just off Fleet Street, WC2R 3JJ

Seeing things at a kopitiam (coffee shop)

Rocky, Bangsar, KL, Malaysia, koptiam

A kopitiam in Bangsar, Kuala Lumpur, Malaysia

One of the great things about travelling is exploring the different cafe and coffee cultures in different countries. Is it the coffee that is important? Or food, alcohol or maybe just the opportunity for socialising? In Singapore and Malaysia, the “kopitiam” (or coffee shop) is a familiar part of each neighbourhood. Each kopitiam serves local coffee (kopi) and a variety of foods which are usually prepared while you wait, from stalls around the edge of the kopitiam. The kopitiam provides a space for socialisation and meeting people over a bowl of steaming noodles. Inside electric fans are blowing continuously in an effort to lessen the heat. Frankly, the local coffee is not to my taste but there are plenty of other things to eat and drink in each kopitiam. A breakfast of “kueh” and black tea for example is a welcome change from toast at home! In many areas of Singapore, and to a lesser extent Malaysia, local kopitiams are closing to make way for the new style cafés which serve a range of freshly roasted, pour over or espresso based coffee. Not being Malaysian or Singaporean I do not want to comment too much on that, I guess it is similar to the decline of the “caffs” in the UK. Mourned by many in the community but welcomed by others for the improved quality of the coffee.

straw, water, glass

An everyday example of refraction. The water refracts the light to make the straw appear ‘broken’.

However, with so much going on in a kopitiam, the temptation to look at a kopitiam-physics review was too great, especially when I started to “see things” at the edge of the shop. Am I going mad? No, it was not that my imagination was playing with my mind; I saw the ingredients for a mirage. You see, at the edge of the kopitiam the hawkers will cook noodles, or rice dishes etc. and this creates heat. Above some stalls there will be clouds of steam rising as the noodles boil in a pan. The clouds appear white because of the scattering of light by reasonably sized water droplets (more info here and here). Above other stalls, there is no steam but the heat created by the cooking makes the air immediately above the stove warmer (and therefore less dense). This less dense air refracts light less than air at room temperature. It is refraction that causes that straw in your iced coffee to look as if it is broken as you look at it (see picture). In the kopitiam, it means that as you look through this region of warm air you see a wobbly or wavy type pattern as the light from outside is refracted by different amounts depending on the temperature of the air that it goes through. It is this that is the primary ingredient for seeing a mirage.

The fact that air at different temperatures refracts light by different amounts is the reason for mirages in the desert. Frequently, warm air is trapped at ground level by a layer of cold air above it. The light is bent as it travels through these layers (see diagram here) and so it may appear as if they sky is on the ground (which the brain will interpret as a pool of water on the ground). Conversely, if there is a layer of cold air trapped beneath a layer of warm air, the light is bent downwards and so objects that are usually below the horizon due to the curvature of the earth can be seen (illustrated by the diagram here).

Edmond Halley, Canary Wharf, Isle of Dogs, view from Greenwich

The view towards the Isle of Dogs (and Canary Wharf) from Greenwich. Things have changed a little since Halley’s time.

Back in 1694 Edmond Halley (who drank coffee with Isaac Newton at the Grecian) was investigating the evaporation of water as a function of temperature. He wanted to see if evaporation alone could explain the rainfall and the quantity of water in the river system. As he did so he noticed that, in still air, there was a layer of water vapour that formed above the bowl of evaporating water. He noticed this because it refracted the light in an unusual manner. At the time, there was reported to be an unusual phenomenon that occurred at high tide near Greenwich. It seems that cows used to graze on the Isle of Dogs in London. Ordinarily the cows could not be seen from Greenwich because they were too far away, but occasionally, at high tide, the cows would be visible. Putting together what he knew about the evaporating water Halley wrote “This fleece of vapour in still weather… may give a tolerable Account of what I have heard of seeing the Cattle at High-water-time in the Isle of Dogs from Greenwich, when none are to be seen at low-water (which some have endeavoured to explain by supposing the Isle of Dogs to have been lifted by the Tide coming under it.) But the evaporous effluvia of water, having a greater degree of refraction than the Common Air, may suffice to bring these Beams down to the Eye, which when the Water is retired, and the vapours subsided with it, pass above, and consequently the Objects seen at the one time, may be conceived to disappear at the other”*. I think that although he had the mechanism correct (in terms of refraction), the cause of this odd refraction was temperature inversion and a layer of cold air immediately above the Thames rather than water vapour but what do you think? Let me know in the comments section below.

 

* Punctuation and capitalisation kept as in original. Taken from Edmond Halley, “An Account of the Evaporation of Water, as It Was Experimented in Gresham Colledge [sic] in the Year 1693. With Some Observations Thereon” Phil. Trans. 18, 183-190, 1694″

From a Caravan to the Grecian

It is a Saturday morning as I write this while sitting in Granary Square in Kings Cross, London. I’ve just enjoyed an Ethiopean filter coffee at Caravan. If only more cafes offered the possibility of sampling single estate coffees rather than the espressos that are otherwise so popular in London.

Caravan, Granary Square, coffee, single estate, good cafes in London

The fountains in front of Caravan

In the square outside, people are laughing (and dancing!) in front of the old warehouses that accomodate Caravan. Amongst them all, four sets of ground-level fountains push jets of foaming water 50cm into the air, in patterns that change as you watch. There is so much physics here to observe: The white colour of the water foam, the dance of the water droplets as they emerge from the main jet of the fountain and then fall back to earth, the fact that the wet concrete around the fountains is darker than the dry concrete nearby.

Consider though one more observation. As the water shoots upwards, it is pushed by occasional gusts of wind from west to east making the fountains appear as loops rather than columns of dancing liquid. Although the direction of the wind is determined by local weather patterns, over the UK the prevailing wind direction is Westerly, that is flowing from west to east.

People have wondered about the origin of the winds from ancient times. The Greeks had four wind Gods who had authority over the winds from each direction: Boreas, god of the North wind, Notus of the South, Euros of the East and Zephryos of the West. Pliny the Elder speculated at length on the causes of the winds and yet the start of the modern conversation regarding the origin of the winds had to wait until 1686 with the publication of a work by Edmund Halley.

Grecian, Coffee House, London Coffee House

The Devereux now stands where the Grecian once was

Halley (1656-1742) is now more famous for the comet that is named after him rather than his meteorological work but, as with many scientists of the time, he had his finger in many pies. He also seems to have been a keen coffee drinker, or at least, he regularly spent time in one of London’s coffee houses, the Grecian, discussing science with Isaac Newton, Hans Sloane and others. A pub, the Devereux, now stands on the site of the old Grecian in a little side street off of Fleet Street.

Did Halley ponder cloud formation, rain and the origin of the winds while contemplating his steaming coffee cup on cold days in 17th Century London? Regardless, Halley did recognise that the heat from the Sun was the driving force for the wind system. Halley surmised that as a parcel of air was heated by the Sun and rose upwards, the cold air surrounding it would have to flow in to its place so as to replace the risen air so “..by a kind of Circulation N.E. Trade Winds below will be attended by a S.W. above, and the S.E. with a N.W. Wind above”* The problem for Halley was that his explanation of the wind system could account for a North-South wind direction owing to the Sun’s heating the air at the equator, but not the Easterly direction of the Trade Winds near the equator nor the Westerly direction of the winds over the UK.

A few years later, George Hadley (1685-1768) suggested that it was the rotation of the earth that was responsible for the east-west component; the mass of air, being detached from the earth, would appear to flow in a particular direction as a consequence of the earth spinning below it. The idea was not new, Galileo had proposed it some years earlier while similar arguments were made later by the philosopher (and scientist) Immanuel Kant (1724-1804). At first sight, such an argument looks appealing but there are problems, as John Herschel (1792-1871) pointed out. If this were the explanation for the wind direction, the effect would be “so great as to produce not merely a wind, but a tempest of the most destructive violence”.

Herschel suggested, as had Hadley before him, that friction could slow the wind to the speeds that we normally observe, but while this may explain the wind speed at ground level, what about the upper circulatory patterns noted by Halley: What friction could slow these down?

Grecian, Devereux, Coffee house London

A plaque outside the Devereux pub

It turns out that this is not the reason for the discrepancy in the wind speed. Hadley’s theory was wrong on a number of issues (if you are interested, I suggest reading this article). The real driving force for the Trade Winds is the Coriolis effect which deflects the warm air rising at the equator towards the right as it travels to the North pole. The majority of this air then cools and descends at about 30 degrees latitude, circling back on itself (as per Halley) as the Easterly trade winds. However the air that continues in the westerly direction north (or south) of 30 degrees latitude becomes those prevailing westerlies of the sort that batter the shores of the UK (see here for more information).

Even if Hadley’s simple model was wrong, its contemplation did lead to an important discovery that is still relevant for us today. The question was: What was it in the upper atmosphere that could cause a friction effect that could slow the winds? The person contemplating this question was taking a walking holiday in the Alps in the first half of September in 1886. Hermann von Helmholtz (1821-1894) observed a layer of clouds which showed “whirls formed by perturbation and rolling up” of the surfaces of two neighbouring layers of air. Helmholtz had observed what became known as “Kelvin Helmholtz clouds”, a beautiful but very rare cloud type, for an example click here. Helmholtz realised that the formation of these clouds required that two layers of air rubbed against each other. In the region between the two layers, the air became unstable, wavy and finally showed the whirls which are actually a series of vortices. As these vortices developed, the two layers of air would get more thoroughly mixed and it was in this way that friction could develop in the upper atmosphere.

Such vortices and “surfaces of discontinuity” are now an important concept in many places including the coffee cup. The video “Coffee Rings” presents another manifestation of the effects of surfaces of discontinuity. So we have returned from contemplation of the wind in a late summer square in London, through a famous Coffee House and back to the coffee.

I have not yet had the opportunity for myself to see a Kelvin Helmholtz cloud. If any reader has been so fortunate please share photos with @thinking_bean. Let me know what you think and what you see around you in the comments section below and most importantly, enjoy your coffee!

*from E. Halley, An Historical Account of the Trade Winds, Transactions of the Royal Society, 1686, p. 133, via “From Watt to Clausius”, DSL Cardwell, Cornell University Press, 1971

†Quotes taken from Anders O Persson, “Hadley’s Principle: Understanding and Misunderstanding the Trade Winds”, History of Meteorology, 3, (2006) p. 17 (linked in article)