Maps on Visualizing.JP

Drawing a Boston Merchant's Day as a Single Line: Allan Pred's Space-Time Path (1984)

Sat, 11 Oct 2025 00:00:00 +0900

In 1984, the geographer Allan Pred used Torsten Hägerstrand’s space-time path notation to draw a single diagram. The vertical axis is the time of day, and the base is a street map of Boston. It shows the day of a “typical” Boston merchant between 1783 and 1812, from midnight to midnight, as one line.

The diagram appeared in the paper “Structuration, Biography Formation, and Knowledge: Observations on Port Growth during the Late Mercantile Period” (Environment and Planning D: Society and Space, vol. 2, no. 3). The paper was reprinted in the 1990 collection Making Histories and Constructing Human Geographies. I have not been able to read the body of the 1984 paper. What follows rests on the paper’s bibliographic record, abstract and reference list, and on the figure in the reprinted version. I checked the reprinted figure against a photograph of the book’s page posted by Jeremy Norman on HistoryofInformation.com.

Space-time path diagram of a Boston merchant’s day

One Diagram in a Paper on Port Growth

Pred (1936–2007) was a professor of geography at UC Berkeley and served as department chair from 1979 to 1988. The paper appeared in Environment and Planning D: Society and Space, vol. 2, no. 3, pp. 251–275.

According to the abstract, the paper discusses the growth of ports in the late mercantile period from three sides: a reassessment of Braudel’s account of commercial capitalism, Pred’s own theory that sees place as a “historically contingent process,” and the case of Boston.

Finally, the interplay of biography formation, knowledge acquisition, and the growth of Boston, Massachusetts, between 1783 and 1812 is considered.

In other words, the paper’s last topic is how biography formation, knowledge acquisition and the growth of the city interacted in Boston between 1783 and 1812. These years fall after independence, not in the colonial period. The “Structuration” in the title refers to Anthony Giddens’s structuration theory, and the reference list includes several works by Giddens.

The title of the figure is “Daily path of a ’typical’ Boston merchant capitalist.” It does not record the day of one real merchant. It is a day assembled as a type. The quotation marks around “typical” can be read as a signal that the figure is a constructed image.

Time Upward, a Street Map at the Base

An oblique view of a cylinder. The left and right posts carry a time scale from midnight to midnight; a single thick line rises from a street map of Boston on the base to an ellipse on the top, bending as it passes locations 1 to 6

Source: a figure in Allan Pred, Making Histories and Constructing Human Geographies (Westview Press, 1990), first published in the 1984 paper. Taken from a photograph of the book’s page on HistoryofInformation.com (Jeremy Norman); the figure has been cropped and the show-through from the reverse side of the paper has been lightened.

The diagram has the form of a cylinder seen obliquely. The posts on the left and right are the time scale, with midnight at the bottom and at the top. The ellipse at the base is a street map of central Boston, and the ellipse at the top carries only the location markers.

Visual element	Data or meaning it stands for	Concrete example in this figure
Vertical scales at the left and right edges	Time of day (from midnight at the bottom to midnight at the top)	Evenly spaced, every 3 hours
Ellipse at the base	A street map of central Boston, seen obliquely	Markers and numbers for locations 1 to 6
Ellipse at the top	The same plane, placed at midnight at the end of the day	Markers 1 to 6 sit at the same left-right positions as on the base
Black markers and numbers	Places the merchant visits	(1) home, (2) Faneuil Hall, (3) counting-house, (4) coffee house, (5) ‘Change on State Street, (6) club-meeting site
Thick line	The space-time path of one merchant	Just one
Vertical sections of the line	Staying in the same place	Home from 2:00 to 5:45, for example
Slanted or nearly horizontal sections	Moving from place to place	5:45 to 6:00, for example; roughly 7 to 20 minutes
Numbers at the bends	Times of arrival and departure	8:30, 9:20, 11:30, 12:03, 1:07 and others, 12 in all
Color, changes in line width	Not used	Monochrome

The correspondence between numbers and places comes from the legend printed below the figure in the reprinted version. The ellipse at the top does not stand for “distance,” which is separate from time. It is a lid: the plane of the map, lifted by one day’s worth of height.

Following the line from the bottom, the merchant’s day can be read as follows.

Time of day	Location
Midnight to morning	(1) Home
8:30 to 9:20	(2) Faneuil Hall
9:30 to 11:30	(3) Counting-house
Between leaving the counting-house at 11:30 and returning at 12:03	(4) A stop at a coffee house
12:03 to 1:00	(3) Counting-house
1:07 to 1:40	(5) The ‘Change (exchange) on State Street
2:00 to 5:45	(1) Home
6:00 to 9:00	(6) Club meeting site
Just after 9:00 to midnight	(1) Home

The morning goes back and forth between workplaces, early afternoon brings a stop at the exchange, the afternoon is at home, and the evening is at the club. This timetable was read off the line in the figure. It has not been checked against records of daily life at the time.

Height Alone Does Not Give the Time

This diagram has a point where readers can lose their way. Because the map is seen obliquely, the height on the page mixes two things: the time and the depth of the map.

Location 6 lies farther back on the map than home (location 1). The “6:00” where the line reaches location 6 sits, on the left-hand scale, above 6 PM, at about the height of 8 PM. It is lifted on the page by the amount of the depth.

Pred addresses this in the explanatory note for the reprinted figure.

Thus, the time-scales at the two outermost edges hold only for the corresponding perimeter points that they connect, and one must imagine a separate time-scale line connecting each of the six locations visited.

That is, the time scales at the two outer edges apply only to the perimeter points they connect, and the reader has to imagine a separate time-scale line for each of the six locations visited. The same note also says that 0.44 inch along a vertical line corresponds to 3 hours, and that corresponding points on the base and the top are 3.5 inches apart. I have not confirmed whether the figure in the 1984 paper carried the same note.

Writing a time at each bend of the line can be read as a response to this difficulty. It lets the reader take the numbers directly instead of measuring time from height. The division of labor is this: the scale shows the approximate time of day, and the labels carry the exact times.

The Notation Comes from Hägerstrand

Pred did not invent the way this diagram is drawn. It is the notation of time geography, set out by the Swedish geographer Hägerstrand.

Hägerstrand presented it in 1969 at the European congress of the Regional Science Association in Copenhagen, and published it in 1970 as the paper “What about people in regional science?” Wikipedia quotes the following line from it (pp. 10–11 of the original).

In time-space the individual describes a path

In time-space, in other words, an individual traces a “path.” The notation includes the aquarium, which takes the map as its base and time as its height; the prism, which shows the area that can be reached; and the bundle, in which several paths gather. Drawings are made in axonometric projection. Pred’s diagram consists only of the aquarium and a single path.

The link between Pred and Hägerstrand can be traced through the bibliography.

Year	Pred’s work
1967	Translated Hägerstrand’s doctoral thesis (1953) into English: Innovation Diffusion as a Spatial Process (with Greta Haag)
1977	“The Choreography of Existence,” a commentary on time geography (Economic Geography, vol. 53, no. 2)
1981	Edited the festschrift Space and Time in Geography: Essays Dedicated to Torsten Hägerstrand
1981	Published a diagram of the daily paths of a family of four in Journal of Historical Geography, vol. 7
1984	The Boston merchant diagram. The reference list includes Hägerstrand 1970 and 1974, Lenntorp 1976 and others

Two rectangular boxes stacked vertically. The vertical axis is Time, 0 to 24. In the upper box (a), four lines run almost bundled into one; in the lower box (b), the lines separate and enter different posts

Source: a figure from Allan Pred, Journal of Historical Geography 7 (1981), as reprinted in Making Histories and Constructing Human Geographies (1990). Taken from a photograph of the book’s page on HistoryofInformation.com (Jeremy Norman); cropped in the same way, with the show-through lightened.

The title of the 1981 figure is “Daily paths of a hypothetical family of four under (a) the artisan mode of production and (b) the factory and large-scale shop mode of production.” It compares the days of a hypothetical family of four under an artisan mode of production and under a factory and large-scale shop mode of production. According to Norman, the four black lines running vertically are the movements of each family member.

So the 1984 diagram is not an “early example” of time geography. It applies a notation that Pred himself had already used three years earlier to the history of a port town. The base of the 1981 figure has only place names such as TAVERN and HOME, and no streets. The 1984 figure lays a street map of a real city on the base and writes times to the minute at the bends. It can be read as moving, with the same notation, from a schematic diagram to specific times in a specific city.

How Others Have Seen This Diagram

The first view comes from the side of information history: Jeremy Norman of HistoryofInformation.com.

What interested me was not so much the well-analyzed data discussed in the paper, but the way that Pred mapped the movement of the “merchant” within the 24 hour period.

He says that he was drawn less to the data in the paper than to how Pred mapped the merchant’s movement within 24 hours. Comparing it with the 1981 family diagram, Norman writes that the merchant diagram is “perhaps easier to understand.”

The second comes from the side of geovisualization: Menno-Jan Kraak’s 2003 paper. It revisits the space-time cube as a visualization and explains how to read it, with vertical lines as stays and nearly horizontal lines as movements, and then names the limits of the hand-drawn era.

when the concept was introduced the options to create the graphics were limited to manual methods and the user could only experience the single view created by the draftsperson. An alternative view on the cube would mean to go through a laborious drawing exercise.

With hand drawing, the reader could see only the one viewpoint the draftsperson had chosen, and another angle meant redrawing. The problem of “height alone does not give the time” in Pred’s diagram can also be read as coming from this single viewpoint.

The third is criticism of the notation itself. According to the Wikipedia article “Time geography,” Bo Lenntorp (1999) wrote the following.

The notation system is a very useful tool, but it is a rather poor reflection of a rich world-view.

The notation is useful, he says, but a poor reflection of a rich world-view. In Feminism and Geography (1993), Gillian Rose criticized time geography: it overlaps with feminism in looking at the paths of everyday life, but it is also a form of masculinism in social science. Since then, Mei-Po Kwan (2002) and others have reexamined time geography.

What Pred’s 1984 diagram draws is one day of a male “merchant capitalist.” There are no paths for family, servants or women. Given that in 1981 he had drawn a family of four, reducing the figure to one line can be read as the result of choosing whose day to show. If Rose’s criticism is applied to this diagram, that is where the issue lies.

Uses

There are four things from this diagram that can be carried over into visualization work.

When time is assigned to one axis, staying and moving separate in the shape of the line. Vertical sections are stays and slanted sections are moves, and the length of a stay can be compared by the length of the line. This way of reading also works for activity logs and for delivery and patrol records.
In an oblique view, height gets mixed with depth. Pred writes the time at each bend and shows how to read the figure in the note for the reprinted version. Today, other options are a cube that can be rotated, or placing the map and a band of time side by side.
When drawing a “typical” case, show that it is a constructed image. Pred puts quotation marks around typical in the title.
Choosing whose line to draw is also choosing whose line not to draw. A single path is easy to read, but it leaves other people’s days out of the diagram.

The 1984 diagram is not one that invented a new notation. It borrowed Hägerstrand’s notation and made it concrete, with a map and clock times, for one day in one city.

References

Primary sources

Allan Pred, “Structuration, Biography Formation, and Knowledge: Observations on Port Growth during the Late Mercantile Period,” Environment and Planning D: Society and Space, 2(3), 1984, pp. 251–275. doi:10.1068/d020251 / Crossref (bibliographic record, abstract, references)
Allan Pred, Making Histories and Constructing Human Geographies: The Local Transformation of Practice, Power Relations, and Consciousness, Westview Press, 1990. Bibliographic record at archive.org
Allan Pred, “Biography Formation, Knowledge Acquisition, and the Growth and Transformation of Cities During the Late Mercantile Period: The Case of Boston, 1783-1812” (chapter 2 of the same book in its 2019 Routledge reissue, pp. 41–75). Crossref
Allan Pred, “The Choreography of Existence: Comments on Hägerstrand’s Time-Geography and Its Usefulness,” Economic Geography, 53(2), 1977, pp. 207–221. doi:10.2307/142726
Allan Pred, “Production, Family and Free-time Projects: A Time-Geographic Perspective on the Individual and Societal Change in Nineteenth-Century U.S. Cities,” Journal of Historical Geography, 7, 1981, pp. 3–36. doi:10.1016/0305-7488(81)90082-7
Torsten Hägerstrand, “What about people in regional science?,” Papers of the Regional Science Association, 24(1), 1970, pp. 7–21. doi:10.1111/j.1435-5597.1970.tb01464.x

Secondary sources

Jeremy Norman, “With ‘Time Geography’ Allan Pred Maps the Activity of Individuals and a Family During the Course of a Single Day,” HistoryofInformation.com. Article
Menno-Jan Kraak, “The Space-Time Cube Revisited from a Geovisualization Perspective,” Proceedings of the 21st International Cartographic Conference, 2003. PDF
Wikipedia, “Time geography” (source of the citations of Hägerstrand 1970, Lenntorp 1999 and Rose 1993). Article
Wikipedia, “Torsten Hägerstrand” (Pred’s English translation, the 1981 festschrift). Article
Wikipedia, “Allan Pred” (biography). Article

Switching Inks at the Imperial Average: The German Imperial Statistical Office's Wheat-Yield Map (1905)

Thu, 02 Oct 2025 00:00:00 +0900

The 1905 Vierteljahrshefte zur Statistik des Deutschen Reichs (Quarterly Journal of the Statistics of the German Reich) carries a map of wheat yields for the 1904 harvest. It was made by the Imperial Statistical Office (Kaiserliches Statistisches Amt). The map switches the color of its ink at the imperial average, and within each side, above and below the average, it tells the classes apart by pattern type and line density.

The figure is a single sheet with two maps, one above the other: winter wheat (Winter-Weizen) on top and spring wheat (Sommer-Weizen) below. Below, I read the printed text and legend as the primary source, and set the map beside a figure in the same style from the previous year and another figure showing the same year’s harvest.

Yield maps of winter wheat and spring wheat for the 1904 harvest

1905: A Plate for the Harvest Statistics

At the top of the figure, this is printed.

(Vierteljahrshefte zur Statistik des Deutschen Reichs, 1905. I.) Erntestatistik für das Jahr 1904. No. 1 u. 2.

It means: Part I of the 1905 Vierteljahrshefte, harvest statistics for the year 1904, plates No. 1 and No. 2. 1904 is the year of the harvest, and the publication is from 1905. The Office’s Statistisches Jahrbuch für das Deutsche Reich (Statistical Yearbook for the German Reich), 1905 edition, also gives Part I of the 1905 Vierteljahrshefte as the source of its 1904 harvest tables.

The harvest statistics rest on a resolution of the Bundesrat of 19 January 1899, and the results from 1900 onward appear in Part I of the following year’s Vierteljahrshefte. The Office was the Reich’s central statistical authority, established in 1872.

The title of the figure is “DEUTSCHES REICH. Schematische Karte bearbeitet im Kaiserlichen Statistischen Amt.” Schematische Karte means “schematic map”: instead of drawing the real boundaries of the administrative districts, it lays them out as rectangular blocks. Abbreviations such as Danzig and Posen appear in white inside the blocks. Whether the area of a block is proportional to the real area is not stated. The unit of aggregation is, as the subtitle “Nach preuss. und bayer. Regierungsbezirken, sächs. Kreishauptmannschaften pp.” says, Prussian and Bavarian Regierungsbezirke (governmental districts), Saxon Kreishauptmannschaften, and so on. No individual’s name appears on the figure.

My account of the 1904 figure is based on a scan of the single sheet bearing a holdings stamp of the Bibliothèque nationale de France (BnF). I could not verify the holdings record, so I do not show the image and present the contents of the legend in tables instead.

Switching Inks at the Imperial Average

The title of the legend is “Hectar-Ertrag in Tonnen 1904.” It shows the yield per hectare in tons. The scale runs from 0.61 to 3.40 in steps of 0.2 tons.

The legend is split in two by the line of the imperial average (Reichsdurchschnitt). The vertical label on the upper side reads “Unter Reichsdurchschnitt” (below the imperial average), and the one on the lower side reads “Ueber Reichsdurchschnitt” (at or above the imperial average). The winter wheat map states “Reichsdurchschnitt: 2,00” and prints the below-average classes in orange tones and the at-or-above-average classes in black.

The correspondence between data and appearance is as follows.

Data	Mapped to	Value in the winter wheat map
Position of the administrative district	Placement and abbreviation of the rectangular block	Real boundaries are not drawn
Yield per hectare	Classes in steps of 0.2 tons	14 classes, 0.61 to 3.40
Above or below the imperial average	Switch of ink color	Average 2.00. Below is orange, at or above is black
Rank within the same side	Pattern type, and line weight and density	Dots, diagonal lines, horizontal lines, wavy lines, grids, blocks
Classes that appear on the map	“*” mark to the left of the legend	10 of the 14 classes
Smallest and largest districts	District names and values above and below the legend	Hamburg 1.08 / Danzig 2.96

Reading the winter wheat legend from the top gives the following.

Class (t/ha)	Color	Pattern	Appears on the map
0.61–0.80	Pale orange	Dots	—
0.81–1.00	Pale orange	Fine diagonal lines	—
1.01–1.20	Pale orange	Fine horizontal lines	*
1.21–1.40	Pale orange	Fine wavy lines	*
1.41–1.60	Deep orange	Heavier horizontal lines	*
1.61–1.80	Deep orange	Heavier diagonal lines	*
1.81–2.00	Deep orange	Heavier wavy lines	*
(Imperial average 2.00)
2.01–2.20	Black	Horizontal lines	*
2.21–2.40	Black	Thick diagonal lines	*
2.41–2.60	Black	Coarse diagonal grid	*
2.61–2.80	Black	Fine diagonal grid	*
2.81–3.00	Black	Thick horizontal band	*
3.01–3.20	Black	Blocks separated by white lines	—
3.21–3.40	Black	Larger black blocks	—

There are two layers, “below the average” and “at or above the average,” with no middle layer.

In the spring wheat map the average is “1,93”. The below-average classes are printed in red tones, and the at-or-above-average classes in a dark color close to black. In the scan the dark color looks like a dark brown, redder than black. The scale is the same as for winter wheat, but only the class 1.81–2.00 is split at the average, into 1.81–1.83 and 1.84–2.00. This can be read as a design in which the average of that year and that crop is inserted as a boundary into a fixed ruler with 0.2-ton steps.

Dividing Patterns Above and Below the Average

Color is responsible for whether a value is above or below the average. The rank within the same side is the job of pattern type and line density.

The below-average side has four pale orange classes and three deep orange classes, and it reuses the same kinds of pattern: diagonal lines, horizontal lines, wavy lines. Pattern type in itself has no order of large and small. It can be read that the order is conveyed mainly by the depth of color and by being above or below the average, and that the pattern takes on distinguishing the classes within the same depth. The at-or-above-average side is arranged in order of increasing black area, from lines to grids and from grids to blocks. Here the blackness of the pattern itself can be read as expressing the order of quantity.

The legend also carries a summary of the distribution. To the right of the “*” mark on the left there is an explanation in vertical text.

In dieser Karte vorkommende Stufen.

It means: the classes that occur in this map. Above and below the legend are written the names and values of the smallest and largest districts.

Figure	Classes in legend	Classes on the map	Smallest	Largest
Winter wheat (No. 1)	14	10	Hamburg 1.08	Danzig 2.96
Spring wheat (No. 2)	15 + “not cultivated”	11	Oberpfalz 0.95	Schaumburg-Lippe 2.80

0.61 and 3.40 are the two ends of the scale, not the actual minimum and maximum. The spring wheat legend also has a white box marked “0”, “nicht angebaut” (not cultivated). The smallest value agrees with the yearbook’s table: on p. 27 of the 1905 edition, the 1904 wheat yield of Hamburg is 10.8 dz/ha, that is, 1.08 t/ha.

Legend of the previous year’s winter wheat map: above the line of the imperial average, 1.93, are seven gray-black patterns, and below it eight crimson patterns

Source: Kaiserliches Statistisches Amt, Statistisches Jahrbuch für das Deutsche Reich, 1904 edition, plate No. 1, legend / Mannheim University Library, “Statistische Jahrbücher” (Public Domain Mark 1.0)

This is the legend of a figure in the same style that depicts the harvest of the previous year, 1903. The structure is the same: vertical labels above and below, the “*” on the left, and the smallest and largest districts above and below. The way color is used is different.

Placing It Beside the Previous Year’s Map

This style is not a one-off. The preface of the 1904 yearbook describes the plates at the back of the volume as follows.

Die graphischen Beilagen zeigen in 8 schematischen Karten für die einzelnen Verwaltungsbezirke den Ernteertrag im Jahre 1903 für Winter- und Sommerweizen, Winter- und Sommerroggen, Gerste, Hafer, Kartoffeln und Klee (Heu).

It means: eight schematic maps show the 1903 harvest for each administrative district. The crops are winter and spring wheat, winter and spring rye, barley, oats, potatoes, and clover (hay).

The administrative districts of the German Reich, laid out as rectangular blocks, colored in with gray-black and crimson patterns

Source: Kaiserliches Statistisches Amt, Statistisches Jahrbuch für das Deutsche Reich, 1904 edition, plate No. 1 “Winter-Weizen” / Mannheim University Library, “Statistische Jahrbücher” (Public Domain Mark 1.0). The original is in landscape orientation and has been rotated by 90 degrees.

Compare the winter wheat maps of 1903 and 1904.

	1903 harvest (yearbook 1904)	1904 harvest (Vierteljahrshefte 1905, I)
Below average	Gray-to-black patterns	Orange patterns
At or above average	Crimson patterns	Black patterns
Imperial average	1.93 (class split into 1.81–1.93 / 1.94–2.00)	2.00
Smallest / largest	Birkenfeld 1.16 / Anhalt 2.90	Hamburg 1.08 / Danzig 2.96

In the eight maps of 1903, the below-average classes are printed in gray to black, and the at-or-above-average classes in one color per crop: crimson for winter wheat, salmon for spring wheat, blue for potatoes, green for clover. In the 1903 edition, “color = at or above the average”, and in the 1904 edition, “black = at or above the average”, so the role of color can be read as reversed from year to year.

I have not found any source that explains the use of patterns by printing constraints. The same Office printed the previous year’s eight maps in a different color for each crop, and plate No. 1 at the back of the 1905 yearbook is also multicolor.

A figure showing the yields of five crops by the width and height of rectangles for each region, colored in yellow, orange, and pink by crop

Source: Kaiserliches Statistisches Amt, Statistisches Jahrbuch für das Deutsche Reich, 1905 edition, plate No. 1 / Mannheim University Library, “Statistische Jahrbücher” (Public Domain Mark 1.0)

This figure depicts the same 1904 harvest. Its encoding is written in the subtitle.

(Erntefläche = Grundlinie; Hektarertrag = Höhe; Erntemenge = Rechteck aus Grundlinie × Höhe.)

It means: harvested area corresponds to the width, yield per hectare to the height, and harvest quantity to the area of width times height. The same Office shows the same year’s yields by “above or below the average, and class” in the map, and by “width times height” in this figure. One can read in it the idea of drawing separately the yield as a rate and the harvest as a total.

Through Third-Party Frameworks

I could not find any third-party text that discusses this figure itself. I use three sources that place the method in context.

The first is the number of classes. The English Wikipedia article “Choropleth map,” citing Monmonier (1977), Brewer (1994) and others, says the following.

for shades of gray, tests have shown that when value alone is used (e.g., light to dark, whether gray or any single hue), it is difficult to practically use more than seven classes. … If differences in hue and/or saturation are incorporated, that limit increases significantly to as many as 10-12 classes.

In short: with lightness alone it is hard to go beyond seven classes, and adding hue or saturation raises that to 10–12. The same article calls a color scheme that splits two series around a center such as the average “divergent”. The 14 to 15 classes of the 1904 figure exceed this guideline, and the construction that splits color at the average can be read as the same idea as today’s divergent color schemes. The article also says that the oldest choropleth map is Dupin’s map of 1826, and that color came into wide use after 1850. The 1904 figure is not an early example of the choropleth.

The second is how patterns work. Axis Maps’ “Cartography Guide: Visual Variables,” based on the visual variables of Jacques Bertin, says the following.

Shape is the only one of Bertin’s variables that he thought is never selective, along with orientation when used for area representation (e.g., polygons symbolized by differently angled stripe patterns).

That is, when stripe patterns of different angles are used on areas, orientation, like shape, cannot be picked out at a glance. The same guide also says that size and value have an order that can be seen at a glance, and hue does not. The differences between diagonal and horizontal lines and between straight and wavy lines in the 1904 figure have no order, and the patterns can be read as serving to tell classes apart by checking against the legend.

The third is Germany of the same period. The English Wikipedia article “Cartogram” gives as the oldest known continuous cartograms a pair of maps by Hermann Haack and Hugo Weichel. They depict the results of the 1898 Reichstag election, in preparation for the 1903 election. The schematic map of the Statistical Office is not described as making area proportional to quantity. Even so, it can be read that, in Germany around the same time, attempts to show statistics by simplifying geographic form were happening side by side.

How to Use This

What we can take away is a design that assigns separate jobs to color and pattern.

Split above and below a baseline by color. Use two color families, and write the baseline value into the legend.
Insert the baseline into a fixed ruler. Keep the class widths common across figures, and when the baseline falls in the middle of a class, split that class, as in the spring wheat map.
Use pattern for telling classes apart. Give the order of quantity to depth or to the black area, and use the pattern as a clue for checking against the legend.
Write a summary of the distribution in the legend. Mark the classes that actually occur, and add the names and values of the smallest and largest districts.
In a series, fix the roles of the colors. When the roles are reversed, as between 1903 and 1904, readers have to check the legend every time.

If we were making this today, we could consider reducing the number of classes in line with the guideline above (for the basics, see the article on the choropleth map). Even so, the 1905 legend, which separates the roles of color and pattern, can be read as a model for designing a legend.

References

Primary sources

This figure: Kaiserliches Statistisches Amt, „Schematische Karte" No. 1 Winter-Weizen / No. 2 Sommer-Weizen, Vierteljahrshefte zur Statistik des Deutschen Reichs, 1905, I. (Erntestatistik für das Jahr 1904). Confirmed from a single-sheet scan bearing a BnF holdings stamp. Holdings record not verified
Statistisches Jahrbuch für das Deutsche Reich, 1904, preface p. III: PDF
Same, 1904 edition, plate “Erntestatistik für das Jahr 1903” No. 1 Winter-Weizen: PDF, No. 2 Sommer-Weizen: PDF, No. 7 Kartoffeln: PDF, No. 8 Klee (Heu): PDF
Statistisches Jahrbuch für das Deutsche Reich, 1905, preface p. III: PDF
Same, 1905 edition, list of sources p. XII: PDF, p. XIV (where the harvest statistics are published): PDF
Same, 1905 edition, p. 26 (harvest table for 1904): PDF, p. 27 (yield per hectare): PDF
Same, 1905 edition, plate No. 1 “Erntefläche, Hektarertrag und Erntemenge i.J. 1904”: PDF
Mannheim University Library, “Statistische Jahrbücher” (Public Domain Mark 1.0): Digital edition / Terms of use
Bibliographic record of Vierteljahrshefte zur Statistik des Deutschen Reichs: Internet Archive

Secondary sources

Wikipedia, “Choropleth map”: en.wikipedia.org
Axis Maps, “Cartography Guide: Visual Variables”: axismaps.com
Wikipedia, “Cartogram”: en.wikipedia.org
Wikipedia (German), “Kaiserliches Statistisches Amt”: de.wikipedia.org

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