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Boyle’s law is the principle that, at constant temperature, the volume occupied by a gas is inversely proportional to pressure (at least until the pressure gets extremely high). In symbolic terms, PV = k, where k is a constant. The pioneering scientist and amateur theologian Robert Boyle published this law in 1662, in his New Experiments Physico-Mechanical, Touching the Air (2nd edition): Whereunto is added a defence of the authors explication of the experiments against the objections of Franciscus Linus and Thomas Hobbes. The chart above shows the data he collected, together with a diagram of his apparatus and a scan of his original data table (cleaned up from an image in the Wellcome Collection).
Boyle’s apparatus involved an uneven U-shaped tube, sealed at the short end, and with mercury in the “U.” Further mercury was added to the long end, in order to compress the air in the short end to a specified volume. The pressure in each case (in inches of mercury) was the measured amount in the long end of the tube, plus 29.125 inches for atmospheric pressure.
Boyle’s experimental work was excellent, with all errors less than 1% (on my calculation). This is shown visually by the close fit of his experimental datapoints to the line PV = 351.9. His arithmetic was not quite so good – column “E” in his original table showed his predicted pressure, calculated laboriously using fractions. Seven of the 25 entries are incorrect. For example, using his approach, the 7th entry should be 1398 / 36 = 38 5/6, but Boyle has 38 7/8.
Home replications of Boyle’s work generally involve weights, a large syringe, some precarious balancing, and the fact that the air column sitting on a square centimetre weighs about 1.03 kg. Like so:
The Invention of Clouds: How an Amateur Meteorologist Forged the Language of the Skies by Richard Hamblyn (2001)
I recently read The Invention of Clouds by Richard Hamblyn, who also wrote Terra (which I reviewed some years ago). The present volume focuses on the Quaker pharmacist Luke Howard, who produced a taxonomy of clouds in 1802. Essentially the same classification is still used today (but not, as Hamblyn points out, without considerable debate during the 1800s):
The main types of cloud (image: Christopher M. Klaus, Argonne National Laboratory)
Although the focus is on Howard’s work and life, Hamblyn in fact provides a brief history of meteorology (or at least of the study of clouds), and there is a chapter on the Beaufort scale. Contemporary literature referred to includes:
- Luke Howard, Essay on the Modifications of Clouds, 1803 (much of this is quoted by Hamblyn)
- Luke Howard, The Climate of London, 2nd edition, Volume 1, 1833 (these detailed observations by Howard are still of modern interest, and the hyperlink points to a modern edition from the International Association for Urban Climate)
- Abraham Rees, The Cyclopædia; or, Universal Dictionary of Arts, Sciences, and Literature, Volume 8, 1819 (the article on clouds was written by Howard)
- John Dalton, Meteorological Observations and Essays, 1793
- Societas Meteorologica Palatina, Ephemerides, 1789
- Bram Stoker, Dracula, 1897 (an early use of the Beaufort scale: “The wind was then blowing from the south-west in the mild degree which in barometrical language is ranked ‘No. 2: light breeze.’”)
- Hugo Hildebrand Hildebrandsson, Albert Riggenbach, and Léon Teisserenc de Bort, International cloud-atlas, 1896 (illustrated in colour)
- World Meteorological Organization, International Cloud Atlas, 2017 (the latest version, online, containing a nice identification flowchart)
Google Ngrams plot for three of the cloud types (with and without hyphens). The words “cirrostratus” and “cirrocumulus” first appear in reprintings of Howard’s pioneering essay, while the word “cumulonimbus” is introduced around 1887. There is a renewed spike of interest in cloud types beginning in the early 1940’s.
The Invention of Clouds also has some interesting comments on clouds in art and on how to get an education at a time when the two English universities banned non-Anglicans from attending. However, the book does have a few small errors. For example, cloud droplets are not “a mere millionth of a millimetre across,” but in the range 0.005 to 0.05 mm. However, that does not stop the book from being both enjoyable and informative (although I did wish for colour images). See also this review from the NY Times.
Above is an analemmatic sundial. The idea is to orient the sundial facing south, and then place a vertical pointer on the central figure-8 track, in a position corresponding to the date. The sundial above shows a simulated shadow for 2:15 PM yesterday. It can be seen that the sundial tells the time reasonably well, thanks to the inbuilt adjustment for variation in solar position.
For large-scale analemmatic sundials, like the one below, people can stand on the central figure-8 track and act as a human pointer. A sundial like this is fun to have in the garden.
Here are blank sundials for some Southern Hemisphere cities:
- Adelaide, Australia
- Brisbane, Australia
- Canberra, Australia
- Melbourne, Australia
- Sydney, Australia
- Johannesburg, South Africa
The ShadowsPro software will also generate sundials like these, if anyone is particularly enthusiastic.
Because of my interest in social statistics, I’ve been exploring county-level results from the US 2016 presidential election. The map below (click to zoom) summarises the results (blue for Democrat and red for Republican, coloured according to how strongly counties voted one way or the other). Nine of the more extreme counties are highlighted.
Most of the variance in this data can be explained by demographic factors such as race, age, education levels, local unemployment, rural-urban continuum code, and median household income. The latter is particularly interesting, and the chart below provides a summary.
On a scale from −0.5 being 100% Republican to +0.5 being 100% Democrat, the curve shows the average vote of counties by 2016 median household income (where the averages are weighted by county population sizes, and LOESS smoothing is used to draw the curve). Overlaid on the diagram is a bar chart for the total population of different median household income groups (the scale for this bar chart is on the right).
It can be seen that, at the very poorest end, votes are balanced between Democrat and Republican. For example, here are the 7 poorest counties in the United States, by median household income. They are all rural:
- Holmes County, MS: $22,045 (mostly Black, strongly Democrat)
- Buffalo County, SD: $22,500 (mostly the Crow Creek Indian Reservation, Democrat)
- Owsley County, KY: $23,115 (mostly White, strongly Republican)
- Wilcox County, AL: $24,216 (mostly Black, Democrat)
- McDowell County, WV: $24,460 (mostly White, strongly Republican)
- Clay County, KY: $24,901 (mostly White, strongly Republican)
- Stewart County, GA: $24,945 (mostly Black, Democrat)
Above that bottom end, votes trend Republican, with the peak Republican vote occurring at median household incomes around $40,000. Above about $56,000, counties swing Democrat, and the Democrat vote increases with increasing wealth. For example, here are the 4 richest counties in the United States, by median household income. They are all part of the Baltimore–Washington metropolitan area:
- Fairfax County, VA: $115,518 (Democrat)
- Falls Church, VA: $118,035 (strongly Democrat)
- Howard County, MD: $119,386 (Democrat)
- Loudoun County, VA: $134,609 (Democrat)
Essentially, the Republican Party seems to have become the party of the poor, particularly the rural poor. Indeed, the (population-weighted) median of 2016 median household incomes for Democrat-majority counties was $61,042; while for Republican-majority counties it was $52,490 ($8,552 less). For a visual perspective, the map below limits the previous one to counties with a 2016 median household income below $56,000. It is precisely because the Republican Party has become the party of the rural poor that these maps are mostly red. I had not fully appreciated this before analysing the data (although others have), but it certainly explains much of recent politics in the US. However, predicting the results of the next presidential election would require some solid demographically linked polling data as well as a good voter turnout model.
Here is my calendar for November (click for hi-res image). We are thankful for the end of Word War I a century ago.
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National Geographic recently reported an interesting story about the Wondiwoi tree-kangaroo (Dendrolagus mayri). Until recently, this arboreal marsupial was known only from a single specimen collected in the Wondiwoi Peninsula of West Papua in 1928. It was thought to be extinct, and was listed on the “25 most wanted lost species” at lostspecies.org. But when an amateur expedition visited the dense mountain forests of the Wondiwoi Peninsula, there it was, living happily in the trees. A good-news story from the animal kingdom, for once.
Surprised to find kangaroos living in trees? There are a number of related species that do this, in the rainforests of New Guinea and northern Australia. In fact, members of the kangaroo family live in a range of different habitats (the rock-wallaby would be a less dramatic example).