Proportional Circles on Visualizing.JP

A Country's Extent as the Area of a Circle, the Weight of Its Tax as the Direction of a Dotted Line: Playfair's The Statistical Breviary, Chart 1

Sun, 12 Oct 2025 00:00:00 +0900

In 1801, in Chart 1 of The Statistical Breviary, William Playfair (1759–1823) drew the extent of the countries of Europe as the area of circles. Population and revenue are shown by vertical lines standing on either side of each circle, measured on the same scale. The tops of the two vertical lines are joined by a dotted line. In his text, Playfair writes that which way the dotted line rises shows whether taxes are heavy in proportion to population.

The sources are the book’s preface, pp.13–16, where he explains how to read the chart, and the country-by-country tables. I read the text in the Bodleian Library copy on the Internet Archive. Because the foldout plates were not captured correctly in that scan, I show the chart from the 1802 French translation. How the circles are divided is covered in an article comparing the two circles of 1801 and 1805, and the 1805 chart is covered in an article on the 1805 United States pie chart.

Photograph of the plate of Chart 1 in The Statistical Breviary

Chart 1 in the French translation. Circles are arranged in order of size, from the large Russia at the far left to the United States at the far right. Red and yellow vertical lines stand on either side of each circle, with their tops joined by a dotted line

The whole plate, original drawing by William Playfair, engraved by Adam (French translation, 1802). Source: David Rumsey Map Collection, David Rumsey Map Center, Stanford Libraries / Internet Archive (CC BY-NC-SA 3.0)

Four Charts Born from the Supplement to a Table

According to the preface, it began with helping with someone else’s book. The editor of the English edition of Boetticher’s statistical tables asked him for a table supplying the changes since publication. Partway through that work, he writes, he realized the following (preface p.3).

it occurred to me, that tables are by no means a good form for conveying such information

In short: tables are not at all a good form for conveying this kind of information. On p.4 he says that when proportion and magnitude are at issue, appealing to the eye is the best and quickest way.

The book appeared in London in 1801. According to Chris Pritchard, it runs to 64 pages, most of them tables by country, with four plates. The contents of the four are listed on p.14.

Chart 1: Europe before the French Revolution
Chart 2: Europe as projected by the peace of Lunéville
Chart 3: The populations of the capitals of Europe
Chart 4: The countries of Hindustan

The original wording for Chart 1 is “Exhibits the powers of Europe as they were previous to the French Revolution.” What is drawn is Europe before the Revolution, not Europe as of 1801. 1801 was the middle of the French Revolutionary Wars, and Chart 2 draws the picture after the Treaty of Lunéville in February (Pritchard 2021).

Charts built from lines were not new for Playfair. On p.15 he writes that about fifteen years earlier he had applied lines to commerce and finance; this refers to The Commercial and Political Atlas. The Statistical Breviary came out in Paris the following year, 1802, in a French translation by D.-F. Donnant, and the plates were re-engraved with French text.

The Reading Instructions Are in Two Pages of the Text

Chart 1 has no legend. How to read it is set out in the text, pp.13–14. The key passage about the vertical lines is this.

The yellow lines on the right of each nation represent the revenue in millions of pounds sterling, measured also upon the same divided scale with the population.

The yellow line on the right represents revenue in millions of pounds, measured on the same scale as population. Just before this he writes that the red line on the left represents population in millions, and that the scale, one division per million, is numbered “at both ends.”

Population and revenue are measured on one and the same scale. The numbers appear at the left and right edges of the chart so that either can be read from both sides. It is not a dual axis, with the left for population and the right for revenue.

Turning the text’s explanation into a table of data and appearance gives the following. The example is France (before the Revolution), with figures from the table on p.33.

Data	Appearance	Example: France
Extent of the country (square miles)	Size of the circle; arranged from left in descending order of size	Circle
The extent figure	Number inside the circle	149,000
Population (millions)	Height of the red vertical line to the left of the circle	26
Revenue (millions of pounds)	Height of the yellow vertical line to the right of the circle, on the same scale as population	19
Weight of tax relative to population	Which way the dotted line joining the tops of the two vertical lines rises	Falls to the right
Population density (people per square mile)	Number directly above the circle	174
Maritime or land power	Color of the circle; green for maritime powers, pale red for land powers	—

The number above each circle is population density, not revenue. The text itself gives examples: “5 over Russia, and 14 over Sweden.” If you read France’s 174 as revenue, it is wildly at odds with the table’s £19 million.

In the French translation’s plate, the circles are colored blue and red. France, Spain, Britain and others are blue; Poland, Prussia and others are red. The maritime powers that the English text calls “green” can be read as having become blue in the French translation.

Only the circles for Russia and Turkey are divided inside. In Russia the inner circle is European territory and the outer ring is Asian territory; Turkey is split into sectors by continent. The text does not explain this division. Here the colors stand for continents rather than maritime or land power. It can be read as the colors carrying two different meanings within a single chart.

The circles of the Russian Empire and the Turkish Empire

Making Countries’ Shapes into the Same Circle

Why draw countries as circles? Playfair gives his reason on p.15.

for where forms are not similar, the eye cannot compare them easily nor accurately. From this circumstance it happens, that we have a more accurate idea of the sizes of the planets, which are spheres, than of the nations of Europe which we see on the maps

Where forms are not similar, the eye cannot compare them easily or accurately; so we have a more accurate idea of the sizes of the planets, which are spheres, than of the nations of Europe that we see on maps. In the preface, p.6, he also writes that when the eye sees similar forms it cannot help comparing their sizes.

On how the size of a circle is determined, the text does not say “proportional to area.” The preface’s phrase is “proportional circles.” I measured the plate of the French translation (the image above, 2000px wide): Russia’s circle has a diameter of about 410px and France’s about 68px. Taking France’s diameter as 1, area-proportional circles would give Russia about 5.6, and diameter-proportional circles about 31. The measured ratio is about 6, so the diameter is roughly proportional to the square root of the extent. Even allowing for measurement error, this is a value consistent with area proportionality.

The circles are arranged from left to right in order of size. On p.7 Playfair writes that on seeing this chart one will be struck by the size of Russia and Turkey. He continues that one will also be struck by the smallness of the nations that have moved the world these five hundred years.

He also decides what not to draw. On p.15 he writes that he combined extent, population, and revenue in one chart because they are the foundation of a power that can be accurately measured. He goes on to say that the form of government and the virtue of individuals also affect a nation’s strength, but cannot be shown in a chart.

The Direction of the Dotted Line Divides at “One Pound per Person”

The explanation of the dotted line spans p.13 to p.14.

The dotted lines drawn between the population and revenue, are merely intended to connect together the lines belonging to the same country. The ascent of those lines being from right to left, or from left to right, shews whether in proportion to its population the country is burdened with heavy taxes or otherwise.

The dotted lines are there to connect the two lines belonging to the same country. And which way a dotted line rises shows whether the country is burdened with heavy taxes in proportion to its population. Read only the first half, and the dotted line is merely a connector. It is the second sentence that gives the dotted line meaning.

Because population and revenue are on the same scale, a dotted line rises to the right when the revenue figure exceeds the population figure. That is, it is a country where tax per person exceeds one pound. Let us check against the tables in the text (£1 = 20 shillings).

Country	Population (millions)	Revenue (millions of pounds)	Tax per person in the table	Dotted line
Russia	25	7.3	6s 8d	Falls to the right
France	26	19	14s 8d	Falls to the right
Spain	11	14	£1 5s 5d	Rises to the right
Britain and Ireland	14	27	£1 18s 3d	Rises to the right

The figures are from the tables on pp.19, 33, 35 and 37. In the chart, the dotted line rises to the right for only four countries: Spain, Britain and Ireland, Portugal, and the United States. Those are also the only four countries whose tax per person in the tables exceeds one pound.

The section with Poland, France, Spain, and Britain and Ireland. France’s dotted line falls to the right, those of Spain and Britain rise to the right, and Britain’s rises most steeply

Detail cropped from Chart 1, original drawing by William Playfair, engraved by Adam (French translation, 1802). Source: David Rumsey Map Collection, David Rumsey Map Center, Stanford Libraries / Internet Archive (CC BY-NC-SA 3.0)

It matters that Playfair speaks only of the direction in which the line rises. On a common scale, direction works correctly as a binary split at “one pound per person.” The text’s explanation can be read as promising that much and no more.

The steepness of the slope is a separate matter. The two vertical lines stand touching the left and right edges of the circle, so the horizontal gap between them is the circle’s diameter. The slope of the dotted line is the difference between revenue and population divided by that diameter. Russia has a large difference, but its circle is large, so its dotted line is gentle. Britain has a difference of 13 and a small circle, so its dotted line rises steeply. The country’s extent gets mixed into the steepness of the slope.

How Third Parties Saw the Chart

The David Rumsey Map Collection’s catalog entry for the French translation quotes a comment by Akerman and Karrow. Their view is that the circles for countries’ extent, the sectors of Turkey, and the lines for population and taxes are “a creative combination of different visual forms.”

It was Pritchard (2021) who criticized the slope. He sums up the novelty as three things: the area-proportional circles, the division of Russia and Turkey, and the vertical lines with the sloping lines joining them. He then writes:

a direct comparison of these lines, one country to another, is not possible because each gradient is affected by the radius (and hence the area of the country)

The point is that because the slope depends on the circle’s radius, that is, on the country’s extent, it cannot be compared from one country to another. Jonathan Sachs makes the same point in a note, naming Funkhouser (1937) and others. Incidentally, Pritchard writes that population is read on the left scale and the budget on the right, which conflicts with the text’s “the same divided scale.”

Sachs’s main argument is in the history of ideas. He gives weight to the replacement of irregular national territories with “uniformly scaled circles.” If wealth is measured as revenue, a quantity, then wealth is not the same as the extent of territory. He reads this chart as a rebuttal to those who held that territory and population are wealth.

Juliana Adelman (2018) of The Irish Times focuses on intent. She writes that what Playfair most wanted to show was the advantage of the United Kingdom, which raised large revenue from a small territory and a small population. She then adds that overseas colonies are not counted.

Uses

There are four things to take away from Chart 1.

The first is to put things into the same shape before comparing sizes. On a map, countries’ extents are hard to compare. Playfair replaced them with identical circles and left the work of comparing to the eye.

The second is that putting two quantities on the same scale lets you read the relationship between them. By putting population and revenue, which have different units, on one numerical scale, he made a dividing line of “one pound per person” appear on the chart.

The third is that if you show a derived quantity by slope, you should keep the horizontal gap constant. In Chart 1 the gap is the circle’s diameter, itself data, and the country’s extent got mixed into the weight of tax. If you want to show tax per person, drawing that value directly is more reliable.

The fourth is to put the instructions for reading beside the chart. In Chart 1, the reading instructions exist only in the text. If you cut out the chart alone, you could easily misread the population density above a circle as revenue.

On p.16 Playfair writes that the greatest criterion is what remains in the mind of someone who looks at it for the first few minutes. By my count, Chart 1 tried to show six things in those few minutes: extent, population, revenue, population density, maritime or land power, and the weight of tax. The slope of the dotted line can be read as the awkward part that this cramming produced.

References

Primary sources

William Playfair, The Statistical Breviary; Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe, London, 1801 (Bodleian Library copy, digitized by Google). Internet Archive / Full text / Google Books
William Playfair (trans. D.-F. Donnant), French translation (Paris, 1802), Chart 1, “Carte statistique représentant l’étendue, la population et les revenus des principales nations de l’Europe”. David Rumsey Map Collection. Copy on the Internet Archive

Secondary sources

Chris Pritchard, “Life of Pie: William Playfair and the Impact of the Visual,” Mathematical Association, Presidential Essay No.4, July 2021. PDF
Jonathan Sachs, “1786/1801: William Playfair, Statistical Graphics, and the Meaning of an Event,” BRANCH. Article
Juliana Adelman, “The man with a finger in many pie charts,” The Irish Times, 2018-03-05. Article
Catalog entry of the David Rumsey Map Collection for Chart 1 of the French translation (quoting Akerman & Karrow). Copy on the Internet Archive

Six Circles Around a Country Chart the Growth of Railways: The 1880 Railway Development Map

Mon, 15 Sep 2025 00:00:00 +0900

In July 1880, the French Ministry of Public Works issued the 1880 edition of the Album de statistique graphique (Album of Graphic Statistics). Its last plate, no. 16, shows each country’s total railway length from 1830 to 1878 as the area of blue circles. The circles for each year are spaced 60 degrees apart around the center of the country. Length per 10,000 inhabitants (green) and per 100 km² (yellow) is added as quarter-circles in the middle.

The original title is “Carte figurative du développement des chemins de fer dans les principaux États de 1830 à 1878”. The catalog names Émile Cheysson as its author. What follows draws on the images that the David Rumsey Map Collection has published (legend, data table, sources) and on the preface to the album. The preface was reprinted in the 1881 Journal de la Société de statistique de Paris.

The whole plate: yearly blue circles for each country lined up along dotted circumferences on a map, with a separate box for the United States and others on the right, a line chart at upper right, and a data table at lower right

Source: Ministère des Travaux Publics (1880) / David Rumsey Map Collection. CC BY-NC-SA 3.0

The Last Plate of the 1880 Album

According to the preface, the album is an annual collection of plates established by a ministerial order of March 12, 1878. The order required that statistics on passenger and freight flows on transport routes, and on their construction and operation, be turned into diagrams and published every year. The 1880 edition is the second. The previous year’s edition had 12 plates; the 1880 edition has 16, all of them large-format. Plate 16 is the last of these, a 49 × 62 cm sheet folded into the album.

The person in charge was Cheysson. According to Michael Friendly, the Ministry’s Bureau of Graphic Statistics was created in March 1878 and headed by Cheysson (1836–1910), an engineer of the École nationale des ponts et chaussées (ENPC). How the album came about, and its plate 1, are covered in the statistical map of the breakdown of transport infrastructure, in the same series.

The preface groups plates 1, 2, and 16 as “cartogrammes à foyers diagraphiques”: maps in which a small diagram is placed around a point (foyer) on the map. The preface notes that plates 1 and 2 use sectors, and it describes plate 16 as follows.

Enfin, la dernière planche n° 16 se rapporte à l’accroissement du réseau ferré des grands États de l’Europe, de dix en dix ans, depuis 1830, et le figure par des cercles proportionnels distribués régulièrement sur une circonférence dont le centre est le chef-lieu de chaque État.

The last plate, no. 16, concerns the growth of the railway networks of the major European states, every ten years since 1830. It represents this with proportional circles spaced evenly along a circumference whose center is each state’s capital.

The preface also names the readers. The album is meant “especially” (auxquels il est spécialement destiné) for members of parliament, and it hopes to be read by administrators and economists as well. It adds that each plate comes with its source, a legend stating the drawing conventions, and a table of the underlying figures. Plate 16 has all three.

What the Legend Says About the Encoding

At lower left of plate 16 is a box titled LÉGENDE. Its first paragraph gives the convention for the blue circles.

A box titled LÉGENDE, with handwritten text giving the convention for the blue circles and quarter-circles, the radius formula, an explanation of the separate boxes, and the sources

Source: Ministère des Travaux Publics (1880), legend detail / David Rumsey Map Collection. CC BY-NC-SA 3.0

Ces 6 phases sont représentées par des cercles dont les centres sont distribués uniformément sur une circonférence en trait noir pointillé, et dont les surfaces teintées en bleu sont proportionnelles au développ.nt du réseau.

These 6 phases are represented by circles whose centers are spread evenly along a circumference drawn as a dotted black line. The surfaces tinted blue are proportional to the length of the network.

A radius formula follows. With the length as n km, the radius is “0,01 √(n / 30 000k)”. The denominator is hard to make out in the image, but the use of the square root is clearly legible. If the radius is made proportional to the square root of the value, the area is proportional to the value. Counting the pixels of the circles in the image, the ratio of France’s 1870 and 1878 areas is 0.77, which roughly matches the ratio of the lengths in the data table, 0.73.

Data	Appearance	Basis
Total railway length of each country (1830, 1840, 1850, 1860, 1870, 1878)	Area of a blue circle	Legend text and radius formula
Which year	Position on the dotted circumference, 60 degrees apart, clockwise	Legend “distribués uniformément”, ring printed with the years
Which country	Center of the circumference (the capital, per the preface)	Preface “le centre est le chef-lieu”
Length per 10,000 inhabitants in 1878	Area of the green quarter-circle at center left-bottom	Legend checked against the data table
Length per 100 km² in 1878	Area of the yellow quarter-circle at center right-bottom	Legend checked against the data table
Countries outside Europe	Separate boxes, removed from their map positions (same scale)	Legend paragraph on “cartouches”

A white ring labeled FRANCE with the years printed on it, six blue circles of different sizes along the dotted circumference around it, and green and yellow quarter-circles in the center

Source: Ministère des Travaux Publics (1880), glyph for France / David Rumsey Map Collection. CC BY-NC-SA 3.0

Let us confirm the orientation on the glyph for France. 1830 is at the 2 o’clock position at upper right, 1840 is at lower right, and 1850 is straight down. 1860 is at lower left, 1870 at upper left, and 1878 comes at the top, at 12 o’clock. The circles grow larger as they go clockwise.

About the quarter-circles at the center, the legend says only that “one is yellow, one is green” and that they represent length relative to territory and to population. The text does not settle which is which, so I compare against the data table. Belgium has 7.5 km per 10,000 inhabitants and 13.5 km per 100 km², and in the plate the yellow one is larger. The United States has 33.9 km and 1.7 km, and the green one is larger while the yellow one is very small. Green is per 10,000 inhabitants, and yellow is per 100 km². The two quarter-circles sit side by side and form a semicircle in the lower half.

The separate box for ÉTATS-UNIS D’AMÉRIQUE. The 1878 blue circle is the largest, and in the center the green quarter-circle is large while the yellow one is very small

Source: Ministère des Travaux Publics (1880), separate box for the United States / David Rumsey Map Collection. CC BY-NC-SA 3.0

Placed 60 Degrees Apart: Ten Years and Eight Years

The six years are not equally spaced, and the legend says so itself. From 1830 to 1878 there are “4 périodes décennales consécutives et une période de 8 ans”: four ten-year periods and one eight-year period. Even so, the circles are placed 60 degrees apart. The preface’s “de dix en dix ans” (every ten years) can be read as a rounded way of describing that last eight-year period.

At upper right of the same plate is a line chart of the world’s total railway length. Its title is “Diagramme figurant le développement des chemins de fer du Monde de 1830 à 1878”.

A line chart titled DIAGRAMME, rising to the right from 1830 to 1878, with the years and lengths in thousands of km below

Source: Ministère des Travaux Publics (1880), line chart of the world’s railway length / David Rumsey Map Collection. CC BY-NC-SA 3.0

The horizontal axis here follows the actual intervals between years. The gap between the ticks for 1875 and 1878 is narrower than the others. The value for 1878 is 330.4 (thousand km), so the world’s railways had reached about 330,000 km.

Within a single sheet, time is handled in two ways. The glyphs line up points in time as “phases” at equal angles, while the line chart measures time as length. Since the legend itself points out the eight-year interval, it can be read as the makers being aware of the difference in intervals and still equalizing the angles of the glyph. What the glyph was meant to show was not the length of time but the difference in size from one phase to the next.

Countries Moved Off the Map, and the Data Table

Countries outside Europe cannot be placed on the map. According to the legend, the major ones gave up the map and were moved to separate boxes (cartouches). The legend states that the boxes have nothing to do with position, but that the conventions and the scale are the same as for the European countries.

The United States, British India, and Canada are in the boxes on the right, while Algeria is drawn at its position in North Africa. Because the scale is shared, the circles in the boxes can be compared in size with the circles on the map.

For the data table at lower right, the legend says that “the map is a translation of these figures into a diagram.” A few countries are extracted below (unit: km; “—” means not recorded).

Country	1830	1870	1878	Per 10,000 inhabitants	Per 100 km²
Great Britain and Ireland	279	24,999	27,552	8.6	8.7
France	37	17,924	24,424	6.6	4.6
Germany	—	18,560	31,556	7.4	5.8
Belgium	—	2,979	3,980	7.5	13.5
Europe, total	316	104,120	158,157	5.3	1.7
United States	65	84,637	131,681	33.9	1.7

The United States in 1878 had about 130,000 km, a little over five times France and close to the roughly 160,000 km of all Europe. The sources of the data are given under “Sources” in the legend: Poor’s Manual (1877), the Ministry’s Situation des chemins de fer (1878), and the Annuaire du Bureau des Longitudes pour 1879.

On a map of Western Europe, glyphs for Great Britain, Belgium, Germany, France, and others stand side by side, and large blue circles spill over the sea and neighboring countries

Source: Ministère des Travaux Publics (1880), Western Europe detail / David Rumsey Map Collection. CC BY-NC-SA 3.0

On the map, the glyphs become larger than the countries. The dotted circumference is about the same size for every country; only the blue circles change. The 1870 and 1878 circles for Great Britain and Germany spill over the sea and neighboring countries. The map seems to serve as a backdrop that shows which country each glyph belongs to, with positional accuracy a secondary concern.

How Third Parties Have Viewed This Album

In his 2008 paper “The Golden Age of Statistical Graphics,” Friendly places the album as a whole at the peak of the golden age of statistical graphics.

These volumes can be considered the pinnacle of the Golden Age, an exquisite sampler of nearly all known graphical forms, and a few that make their first appearance in these volumes.

Friendly names “planetary” diagrams among the new forms that appear in the album, and he shows plate 9 of the 1897 edition as an example. He does not discuss plate 16 itself. However, the Rumsey catalog notes this plate as a “multi-circle, planetary design,” so plate 16 can be read as an early example of that form. Friendly also writes that the album was discontinued in 1897 because of its high production cost.

The geographer Gilles Palsky offered a different view in a 2023 talk at the Ruderman Conference on Cartography.

In the end, it appears that the series of albums did not really meet their objectives, and this despite its high financial cost, which no doubt explains its extinction at the beginning of the twentieth century.

Palsky argues that the series fell short of its aims despite its cost, which likely explains why it ended in the early twentieth century.

Palsky views the album not from the quality of the plates but from its aims and readers. Together with the preface’s naming of members of parliament as the intended readers, this suggests that how well the plates are made and whether their aims were achieved are separate questions.

The third is perceptual research on reading proportional circles. In a 1970 presentation, James J. Flannery reported that even for circles whose areas are properly proportional, readers underestimate the differences in size.

map users consistently underestimated size differences

Map users consistently underestimated the differences in size.

Plate 16 makes the areas proportional exactly as the formula says. In light of Flannery’s result, the difference between the United States and France in 1878 may look smaller than the actual factor of a little over five.

Takeaways

What we can take away from plate 16 is that it hands the reader the rules of the encoding inside the chart itself.

The first is to write the formula in the legend. Plate 16 says that area is proportional to length, and even adds the radius formula. If you use proportional circles or bubbles, you can add one line saying that you scaled by area.

The second is to attach the underlying figures to the chart. Differences in area tend to be underestimated. Plate 16 has a data table, so the difference between the United States and France can be checked in numbers. The meaning of the colors of the quarter-circles was also settled with this table.

The third is to separate absolute and relative quantities by color and position. The outer blue circles are the total length, and the green and yellow at the center are per capita and per area. A country like Belgium, whose total length is small but whose length per area is large, can be read in a single glyph.

The fourth is to decide whether to equalize time by angle or to measure it by length, and to say which. Plate 16 equalizes the angles in the glyph, notes the eight-year interval in the legend, and shows the actual intervals in the line chart. Countries that do not fit were moved to separate boxes at the same scale. When you place small graphs on a map, you can likewise write in the legend what you kept and what you gave up.

References

Primary sources

Ministère des Travaux Publics, Carte figurative du développement des chemins de fer dans les principaux États de 1830 à 1878, 1880 (Album de statistique graphique 1880, pl. 16). David Rumsey Map Collection, List No. 12511.022. Detail page / IIIF manifest / Catalog (search API) / Internet Archive mirror
Album de statistique graphique 1880, table of contents (Table des matières). Internet Archive
Album de statistique graphique 1880, preface (Notice). Page 1 / Page 2
“Bibliographie. Notice relative à l’album de statistique graphique,” Journal de la Société de statistique de Paris, 22, 1881, pp. 25–28 (excerpt from the Bulletin de statistique du Ministère des travaux publics, August 1880). numdam / PDF

Secondary sources

Michael Friendly, “The Golden Age of Statistical Graphics,” Statistical Science, 23(4), 2008, pp. 502–535. DOI: 10.1214/08-STS268. Project Euclid / PDF
Michael Friendly, HistDataVis, Chapter 7. Online version
Gilles Palsky, “Legitimizing administrative statistics in XIXth Century France: The ‘Albums de Statistique Graphique’ in Context, their Aims and Audiences,” Ruderman Conference on Cartography, David Rumsey Map Center, Stanford University, 2023. Abstract
James J. Flannery, “The Relative Effectiveness of Some Common Graduated Point Symbols in the Presentation of Quantitative Data,” 1970 (ERIC ED045469). PDF