Émile Cheysson on Visualizing.JP

Semicircles for Length and Breakdown, Quarter-Circles for Density: The 1880 Transport Routes Map in the Album de statistique graphique

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

Plate 1 of the 1880 Album de statistique graphique (Album of Graphic Statistics) is a map that places one semicircle on each French département. The area of the semicircle represents the total length of transport routes at the end of 1878. The seven sectors inside the semicircle give the breakdown by type of route, and the two quarter-circles below show length per area and length per inhabitant.

The title is “Carte figurative du développement des voies de communication par département au 31 décembre 1878” (Figurative map of the development of communication routes by département at 31 December 1878). It was made by the Direction des Cartes et Plans (Bureau of Maps and Plans) of the French Ministry of Public Works, and no individual is named on the plate. What follows draws on the plate’s legend and data table, on the album’s preface (reprinted in the 1881 Journal de la Société statistique de Paris), and on the writings of Émile Cheysson, who headed the bureau.

July 1880: An Album of Statistical Charts for Legislators

It began with a ministerial order of March 12, 1878. The order organized the “Bureau of Maps, Plans, Documents and Graphic Statistics,” and Article 2 decided that an album of statistical charts would be published every year. An order of July 3 laid out its contents in detail.

The 1879 edition had 12 plates, and a contemporary review says it was prepared by the Maps and Plans section under Cheysson’s direction. In 1890 Cheysson himself signed as “former head of the Ministry of Public Works’ Bureau of Maps and Plans” and wrote that the 1879 edition was the first application of the order. Some articles mention a “1878 edition” of wall maps, but by his own count the 1879 edition was number one.

This plate is in the second album, the 1880 edition. Its title page reads “July 1880,” and it was published by the Imprimerie nationale in Paris. Of the 16 plates, this map is Plate 1, and Plate 16 depicts the development of railways in the major countries (the article on the railway development map). No source names the author of the 1880 edition; the David Rumsey Map Collection, which holds it, registers the Ministry of Public Works and Cheysson as authors.

A folded plate with a semicircle diagram placed on each département across France, a legend at lower left and a table of figures by département at right

The whole of Plate 1. The legend is at lower left and the table of figures by département is at right

Source: Ministère des Travaux Publics (1880), David Rumsey Map Collection, held at the David Rumsey Map Center, Stanford Libraries (CC BY-NC-SA 3.0)

According to the preface, all 16 plates are large-format, folded in a special way to fit the format of parliamentary documents. The makers dropped lithography in favor of engraving on stone, and shades of the same color are produced by the density of hatching.

The preface ends by naming the readers.

le nouvel album pourra être consulté avec profit par les membres du Parlement, auxquels il est spécialement destiné, par les administrateurs, par les économistes …

In short, the new album is intended especially for members of parliament, and should also be useful to administrators and economists. The reference date of the data is January 1, 1879, and the album was published in July 1880. Cheysson wrote in 1890 that the figures in the albums are normally those of two years before the year of publication.

Reading the Legend: Semicircles, Seven Sectors, Two Quarter-Circles

The conventions are written in the legend at lower left of the plate.

The legend box: explanatory text at the top, a table in the middle matching sector numbers, types of route, colors and scales, and a guide to the data table and the sources at the bottom

The legend (LÉGENDE) of Plate 1

Source: Ministère des Travaux Publics (1880), David Rumsey Map Collection, held at the David Rumsey Map Center, Stanford Libraries (CC BY-NC-SA 3.0)

Chacune de ces longueurs est exprimée par un secteur, qui occupe toujours la même place sur le diagramme, au-dessus du diamètre horizontal, et qui est teinté d’une couleur particulière. L’ensemble de ces secteurs compose un demi-cercle, dont la surface est proportionnelle au développement des voies du Département.

Each length is expressed by a sector that always occupies the same position above the horizontal diameter and is tinted in its own color. The semicircle made of all the sectors has an area proportional to the length of the département’s routes. The legend goes on to say that the two quarter-circles below represent the ratios of length to population and to territory.

The table in the legend, recast as a correspondence between data and appearance, looks like this.

Data	Appearance	Color (as named in the legend)	Scale (legend)
Total length of the département’s transport routes	Area of the upper semicircle	—	Radius 0.025 m = 12,000 km
National roads (Routes nationales)	Area of sector 1 (far left)	Purple	Same as above
Departmental roads (Routes départementales)	Sector 2	Orange	Same as above
Navigable waterways (Voies navigables)	Sector 3	Yellow	Same as above
Railways (Chemins de fer)	Sector 4	Blue	Same as above
Communal roads, long-distance (de grande communication)	Sector 5	Rose, dark	Same as above
Communal roads, common-interest (d’intérêt commun)	Sector 6	Rose, medium	Same as above
Communal roads, ordinary (ordinaires)	Sector 7	Rose, light	Same as above
Total length ÷ area of territory (per km²)	Area of lower left quarter-circle	Blue	Radius 0.005 m = 1
Total length ÷ population (per 100 inhabitants)	Area of lower right quarter-circle	Yellow	Radius 0.007 m = 1
Département	Where the semicircle is placed	—	Within each département

There are seven sectors but only five hues. For the communal roads (chemins vicinaux), the three legal categories are separated by shades of rose. According to a note in the legend, the 12,000 km scale applies to both the semicircle and each sector. Within a département the radius is common, so the angle of a sector is also proportional to its length.

The order is the same in the legend and in the columns of the data table, but the reason is nowhere stated. The base map consists of département boundaries, rivers, coastlines, road and railway lines, and place names, with no depiction of relief. Over the sea, a sample diagram is placed.

A sample diagram of an average département: a semicircle divided into seven colored sectors, with blue and yellow quarter-circles attached below

The sample diagram at sea, “DÉPARTEMENT MOYEN” (average département)

Source: Ministère des Travaux Publics (1880), David Rumsey Map Collection, held at the David Rumsey Map Center, Stanford Libraries (CC BY-NC-SA 3.0)

Below the legend is a column of sources. National roads, departmental roads, and waterways come from the situation tables of the Corps des Ponts et Chaussées (civil engineering corps); communal roads from the situation tables of the Ministry of the Interior; and population and area from the 1879 Annuaire statistique de la France. Only the communal roads have a reference date one year earlier (January 1, 1878). The source of the railway figures is not in this column.

Checking Against the Data Table: National Totals and the Seine Département

The legend also states where the numbers are.

Les chiffres, qui mesurent ces données et dont les diagrammes se bornent à donner la traduction graphique, sont groupés dans un tableau placé à droite de la Carte.

In other words, the diagrams only translate the numbers into pictures, and the numbers are gathered in a table to the right of the map.

The bottom row of the table, “Total and average,” gives national roads 37,279.9 km, departmental roads 38,358.6 km, navigable waterways 13,046.7 km, railways 28,435.0 km, and communal roads 417,264.6 km. The average ratios are 1.01 per km² and 1.45 per 100 inhabitants. Added together, the total is about 534,000 km, of which communal roads are about 78% and railways about 5% (the author’s calculation). Of the semicircle’s 180°, the blue of the railways is only about 10° (the author’s calculation).

Around Paris: below the semicircle of the small Seine département is a large blue quarter-circle, and the yellow quarter-circle is almost invisible. The surrounding départements have large semicircles

Around Paris. The small diagram in the center is the Seine département, and the one at lower left is Seine-et-Oise

Source: Ministère des Travaux Publics (1880), David Rumsey Map Collection, held at the David Rumsey Map Center, Stanford Libraries (CC BY-NC-SA 3.0)

For the Seine département, which includes Paris, the five columns of the table add up to about 1,010 km (the author’s calculation), so the semicircle is small. Meanwhile its length per km² is 2.11, among the highest of all départements, and per 100 inhabitants it is 0.04. Calculated with the scale in the legend, the radius of the blue quarter-circle is about 7.3 mm and that of the yellow about 1.4 mm (the author’s calculation). A large blue attaches below the small semicircle, and the yellow is almost invisible.

In the neighboring Seine-et-Oise, both ratios are 1.29. Even so, the radius of the yellow quarter-circle comes to about 8.0 mm and that of the blue to about 5.7 mm (the author’s calculation), because the scales of the two ratios differ, 0.005 m and 0.007 m. This suggests that the left and right quarter-circles were not made to be compared in size on the same yardstick. What can be compared is left with left and right with right, across départements.

“Fan” and “Foyer”: Reading Through Cheysson’s Words

The preface to the 1880 edition itself explains the type of this plate.

Les planches 1 et 2 ont eu recours aux diagrammes par secteurs diversement coloriés, dont chacun est affecté à la représentation d’un élément distinct et dont l’ensemble constitue une sorte d’éventail.

Differently colored sectors each represent a separate element, and together they form “a sort of fan (éventail).” The preface goes on to say that Plate 1 shows, for each département, progress “in absolute terms and in terms of ratios.”

The preface classifies Plates 1, 2, and 16 as “cartogrammes à foyers diagraphiques” (cartograms with diagraphic foyers). Most of the others are “band cartograms,” in which the width of a band represents the quantity. The name was given by Cheysson in his report on the 1878 Exposition universelle. The method takes the point to be shown as the “foyer” (focal point) and erects a small diagram on it.

In the same 1878 report, Cheysson also touches on the misreading of sectors. A ring diagram from the Marseille Chamber of Commerce represented quantities by the length of the arc.

si la légende n’y mettait ordre, l’esprit serait tenté de faire intervenir dans la mesure des faits, non la largeur des arcs, mais l’aire des secteurs.

His point is that unless the legend set things right, the reader would be tempted to measure by the area of the sectors rather than by the width of the arcs. The legend of Plate 1 makes “area” the convention from the start. It can be read as choosing, as its convention, the quantity that readers naturally look at.

The 1890 commentary cites Plate 34 of the 1886 edition as an example of dividing a semicircle into sectors, saying that the diagram for each département takes the form of a “colored fan.” This can be read as the same construction as Plate 1. The same text also contains a warning.

Il faut surtout se garder de vouloir trop dire de choses à la fois, et de devenir obscur à force d’être complet. … Si un diagramme est touffu au point de n’être plus clair, mieux vaut le tableau de chiffres dont il est la traduction.

Avoid trying to say too much at once and becoming obscure; if a diagram is so dense that it is no longer clear, the table of figures it translates is better. Plate 1 layers four levels on one symbol, yet puts the data table on the same sheet. It can be read as a design that leaves the density to the table.

Cheysson also writes that the purpose of the administration is to prepare material for study and that it has no obligation to draw conclusions. Reading the values of the day from the order of the categories is something the makers themselves held back from, it seems.

How Third Parties Have Viewed This Album

Among contemporary reviews is that of the statistician Toussaint Loua on the 1879 edition. Loua sets length beside average tonnage, writing that waterways, at a third of the length of national roads, carry four times as much in relative terms, and that railway tonnage is nine times that of national roads. This is not a comment on Plate 1, but in a chart of length the railways at about 10° far exceed both waterways and national roads in average tonnage. In the 1880 edition, tonnage is handled by the band maps of Plates 5 to 7 at the same scale.

In his 2008 paper, Michael Friendly places the album as a whole at the peak of the “Golden Age” of statistical graphics. He cites the assessment of Funkhouser (1937).

the Albums present the finest specimens of French graphic work in the century and considerable pride was taken in them by the French people, statisticians and laymen alike.

That is, the albums were the finest specimens of French graphic work of the century, and statisticians and the general public alike took pride in them. Friendly also writes that circles, radial forms, and “pie maps” were favored, but he does not mention Plate 1 itself.

Friendly distinguishes the pie chart as a diagram with “constant radius and varying angle” from the polar area diagram (coxcomb) with “constant angle and varying radius.” The Rumsey catalog annotates this plate with “coxcombs,” but in Plate 1 the sectors share a radius and vary in angle. By Friendly’s definition, it can be read as the semicircle version of a pie chart.

The Rumsey catalog introduces the album as inspired by the work of Charles Joseph Minard. Cheysson himself also begins his 1890 commentary with the name of his predecessor Minard. In 1883 the album, together with the ministry’s statistical bulletin, received the Montyon Prize in Statistics of the Academy of Sciences.

Uses

What we can take away from this plate is how to place conventions when one symbol carries several quantities.

Separate size from breakdown: the size of the semicircle shows the total, and the angles of the sectors show the breakdown.
Fix the positions of the categories: the sectors are placed “always in the same position.” Even if the colors are hard to tell apart, the position lets you read them.
If readers will read by area, say so in the legend: if readers want to measure by area, make that the convention.
If the scales differ, write the scales: when the legend gives numbers, readers can judge which pairs are fair to compare.
Put in a sample: the “average département” becomes a reference that can be applied to the diagram of any département.
Put the data table and sources on the same sheet: even a gap in reference dates (only the communal roads are one year earlier) is written in the legend.

Even so, a chart of length does not show how the routes are used. As Loua set length beside tonnage, quantity and flow have to be handled in separate charts. This presupposes that the title and legend state plainly what was measured.

References

Primary sources

Ministère des Travaux Publics, Direction des Cartes et Plans, “Carte figurative du développement des voies de communication par département au 31 décembre 1878,” Album de statistique graphique, 1880, Pl. 1. David Rumsey Map Collection, List No. 12511.007. David Rumsey Map Collection / IIIF manifest / Internet Archive
“Bibliographie. Notice relative à l’album de statistique graphique [publié par le Ministère des travaux publics en 1880],” Journal de la Société statistique de Paris, 22, 1881, pp. 25–28 (reprint of the preface to the 1880 edition). Numdam
“Notice statistique sur l’album des voies de communication,” Journal de la Société statistique de Paris, 21, 1880, pp. 6–11. Numdam
É. Cheysson, “L’Album de statistique graphique publié par le ministère des travaux publics,” Journal de la Société statistique de Paris, 31, 1890, pp. 11–23. Numdam
É. Cheysson, “Les méthodes de statistique graphique à l’Exposition universelle de 1878,” Journal de la Société statistique de Paris, 19, 1878, pp. 323–333. Numdam
David Rumsey Map Collection, Copyright and Permissions. Terms of use

Secondary sources

T. Loua, “Bibliographie. L’Album de statistique graphique pour 1879,” Journal de la Société statistique de Paris, 20, 1879, p. 308. Numdam
Michael Friendly, “The Golden Age of Statistical Graphics,” Statistical Science, 23(4), 2008, pp. 502–535. doi:10.1214/08-STS268 / arXiv
David Rumsey Map Collection catalog (the plate’s “coxcombs” annotation and the description of the album). Search results

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