An examination of the original diagrams by Charles-Joseph Minard, and related materials by Léon Lalanne and Émile Cheysson in the ENPC Archives

NOTE: In the interest of consistency, throughout this essay I identify Minard's diagrams using the number (preceded by #) and English name assigned by Sandra Rendgen in The Minard System: The Complete Statistical Graphics of Charles-Joseph Minard [1], along with their French titles.

The Man and the School

I wanted to visit and touch a Minard. I have seen his work reproduced in many books. I have copied digital images of Mindard's drawings from library websites and used them in presentations. I have assigned graduate students to study Minard and do presentations about his work for my information design history seminar. I have studied writing about Minard by Marey [2], Funkhouser [3], Robinson [4], Tufte [5]–[7], Friendly [8] and others [9]–[13]. Recently I have read and re-read The Minard System [1], the first comprehensive collection of all his drawings. Though I knew where the drawings were archived, I had never bothered to see the original prints.

Many of us in the data visualization community think of Charles-Joseph Minard today as a great information designer, an important figure in the development of data visualization. His representation of Napoleon's losses during the invasion of Russia, #60 Hannibal's March over the Alps and Napoleon's Russian Campaign (Carte figurative des pertes successives en hommes de l'Armée Française dans la campagne de Russie 1812–1813), has become his ticket to design immortality. Everyone who sees the diagram is fascinated and impressed. I can support a conversation about Minard with anyone today by simply googling "Minard", bringing up an image of this diagram on my phone, and letting it speak for itself.

Napoleon's Russian Campaign tells the story in brown and black of a 422,000-strong invading army's movement, losses, retreat across freezing rivers during plunging temperatures, and the return of 10,000 survivors. Minard's son-in-law wrote in his obituary that the diagram "inspires bitter reflections on the cost to humanity of the madness of conquerors and the merciless thirst of military glory" (inspire d'amères réflexions sur ce que coûtent à l'humanité les folies des conquérants et la soif impitoyable de la gloire militaire). [14] Étienne-Jules Marey, who was the first to reproduce it in his book on graphic methods of scientific visualization, remarked that the diagram's "brutal eloquence … seems to defy the pen of the historian" (brutale éloquence qui … semble défier la plume de l'historien). [2]

The man who drew this diagram was neither a designer nor a historian. Charles-Joseph Minard was a civil engineer. His life's work was building the infrastructure that supported industrialization and global trade in France. During the first half of the 19th century, he observed, documented, and planned for the shift of transporting goods from roads to canals to railroads. He witnessed the growth of dependence on fossil fuel and the shifting sources of the raw material for the textile economy.

Born in 1781, he grew up in the provincial city of Dijon. During the years between the French Revolution and the rise of Napoleon, he was selected to be educated at the elite schools in Paris. Those schools, Polytechnique and Ponts et Chaussées (bridges and roads), prepared him to become a caretaker for the infrastructure of France. He served in various governmental roles as engineer and supervisor of canals and ports. In his middle age, he became an inspector general, and moved from the field to the classroom to train the next generation of bridge and road engineers. During his career, he developed a technique for encoding data in drawings that he called tableaux and cartes figuratives (figurative tables and maps). He visualized the flow of goods and passengers with this technique in a few articles and presentations. The name he chose suggests something inexact. He saw his drawing as less precise than rows and columns of numbers and only secondarily representations of geographic position. They were primarily representations of data that spoke to the eye, and by speaking to the eye were quicker and easier to understand than their underlying numbers.

In 1851 he retired at the age of 70. His obituary makes the point that his retirement was required by a recent government regulation. For two more decades, no longer responsible for inspecting or teaching, M. Minard, Inspector General of Bridges and Roads in Retirement, produced fifty figurative tables and maps.

In Minard's time, École des Ponts et Chaussées was located on Rue des Saints-Pères in the heart of Paris, adjacent to the School of Fine Arts and other elite institutions. The printers and geography publishers who turned his drawings into hand-colored lithographic prints were located a few blocks away.

Today the École nationale des Ponts et Chaussées is the École des Ponts ParisTech. The school, its library and archives are one of several engineering and architecture schools in Cité Descartes, a university complex located in the Marne valley to the east of Paris. In February 2020, my wife and I arrived at this very 20th century steel-and-glass campus where we were welcomed by Charles Riondet, one of the archivists. He placed the two surviving collections of Minard's work, a bound portfolio, and a box, on a cart. He brought us to a room where we spend the day unfolding and refolding, admiring and contemplating Minard's diagrams.

Whomever had prepared Minard's work for deposit in the library had collected and mounted or bound together 54 diagrams. Riondet explained the portfolio and some other isolated maps were a gift to the library from Minard's widow a few years after his death, so the editor was likely Minard himself. My first question was whether we were looking at lithographs or original drawings. The short answer was hand-colored lithographs. The one exception was #5 Commercial Traffic on the Canal du Centre in 1844 (Tableaux figuratifs de la mouvement commercial du Canal du Centre en 1844), a drawing Minard prepared to illustrate an article in the 1840s. This drawing was bound at the upper half of the portfolio's very first page.

In this one case, he seems to have preserved the original ink drawing. I thought I could see ink brush strokes fading off the edge of the page. There are other copies of the drawing in booklet form in Bibliothèque nationale de France collection and in a torn state in the New York Public Library digital collection. Both of these copies have "Autog. Regnier et Dourdet…" in the lower right corner. That printer signature is missing from the copy in the portfolio.

The Box

The first collection we examined, Cartes figuratives (1853–1863), was a box containing thirteen diagrams mounted on canvas and folded in eight sections. This selection consists entirely of diagrams that use the width of lines drawn over geographic outlines. The selection included several series. Two illustrate the flow of good on the French rivers and canals. Six others illustrate and compare the annual flow of good in France by water and by railway. Three show the sources of raw cotton being imported into Europe in the years before, during and after the American Civil War. One shows the flow of coal imported into France from various parts of Europe. Another shows the flow of wine from France to destinations around the world.

The title of each folded map is printed on the outside along with the printer's label (Andriveau-Doujon, Géographe Éditeur, rue du Bac, 21). This label secures a hand-written paper tab identifying the year and topic of the diagram. The box itself contains no list of contents or note of explanation. The selection includes diagrams from 1852 to 1864. The printer's label changes in the late 1850s, when "J. Andriveau-Goujon, Géographe Éditeur," becomes "E. Andriveau-Goujon". This suggests that the box was probably added to over time.

I use the phrase "geographic outlines" to describe these diagrams for the same reason I believe Minard used "figurative maps". Minard's technique favored the size and position of lines over the accurate geography. The lines encoded the data while geographic contours represented context. The geographer Arthur H. Robinson has an eloquent way of describing this feature of Minard's work. Robinson notes that while "the flow lines were strictly proportional to the numbers", Minard would "strongly resist the tendency of the tyranny of precise geographical position to detract from the essential communication of his chosen theme." [4] To put it another way, Minard distorted geography when it allowed him to better tell the data's story. His diagrams frequently include altered coastlines and changes to the relative size of countries, oceans and continents, always to accommodate the data. In the Cotton diagrams, for example, he flattened the North American coastline and extended the length of England's coast to accommodate the export and import quantities he needed to represent.

The Portfolio

The second collection we examined was a large-format bound portfolio, titled Tableaux Graphiques et Cartes Figuratives. The portfolio's leather cover is embossed with this title along with "de M. Minard". While the box set is a selection, the portfolio's two leather-bound boards enclose what someone considered to be complete set consisting of the fifty-four prints. Rendgen has now identified and reproduced sixty-one diagrams [1], seven of which are omitted from this portfolio. The format of most prints fit within the boards, either attached to a single board, or across two pages in an open spread. A few are wider or higher than the boards, folded on their edges to fit. On two pages, small prints are combined to fill a page.

All the mounted prints in the quarto box set are also found in the portfolio book. In the mounted box copies, the canvas shows through as brown lines on the folds. These lines, of course, are absent in the original lithographs, which also has a wider white margin outside the drawing box. More significantly, the canvas mounting has slightly darkened the color of the paper.

The portfolio copies are glued only to narrow paper strips in the center. When placed alongside the mounted prints from the box, the folio copy is noticeably brighter.

A part of Minard's style was a note, carefully lettered and boxed, explaining the content of the diagram and source of the data represented. These notes were a part of the lithograph. I was looking for anything that had been added or written directly on the print. I found an example in the note on #14 English Coal Exported in 1850, explaining the quantities of coal exports from England to destinations in France and other parts of the world for one year. The legend gives comparative export totals for 1850, 1851 and 1852, then adds that the totals for 1853 are not yet published. Someone, perhaps Minard, has written on the lithograph in ink (ajourd'hui …..Mars 1854) [today….March 1854] to indicate when this note was added. I found two other copies of the same diagram, one in the Lalanne portfolio described below and the other in the Bibliothèque nationale de France collection, neither of which had this additional note.

This note on the English coal export diagram is an indication of Minard's interest in producing visualizations of similar data from different years. The portfolio's hand-lettered table of contents illustrates this. We find diagrams organized chronologically for data on Voyageurs (railway passengers), Houille (coal), Voies d'eau et de fer (waterways and railways), and Ports de Mer (seaports). The binding of the portfolio seems to have been started while these series were still in progress Already in the numbering sequence, duplicate and triplicate page numbers are used to account for diagrams that have been added to the original bound collection (a second page 1, a second and third page 7 and 15). The third in the Ports de Mer series is listed in the table with an incomplete date (Ports de Mer 185 ) and no page number. Whatever his intention was for this diagram, it was not produced. When Minard did produce a third seaport diagram, #34 Great Ports of the Globe, 1861 (Carte figurative et approximative des Grands Ports du Globe 1861), it was deposited it at the Imperial Library but not included in the portfolio.

The table of contents itself appears to have been created in several stages. The lettering and numbering are systematic, and the series are ordered sequentially through the second of the cotton diagrams (page 25). Then two more page numbers and ten more drawings are added out of sequence, glued into the binding between existing pages. On the table's second page, the lettering changes from All Caps to a calligraphic flourish and eight more drawings are added to existing page numbers. The last three drawings, which date from the last years of Minard's life, are written in a lighter calligraphic style and bound into the end of the portfolio with three sequential page numbers.

#10 Transport of Mineral Fuels in France, 1845 (Carte Figurative des principaux mouvements des combustibles minéraux en France en1845) [15], listed as Houille 1845 in the portfolio's table, is the first in the coal series. Its printing format is longer than the folio boards. Because of its length, the lower part of the unmounted print has been folded to fit and the bottom is now cracked and torn. Minard seems to have corrected this size issue in the prints that follow in the series. All the others conform to a size that fits neatly into the two-page portfolio spread.

It is the brightness of the folio prints and the strength of the colors that comes across more strongly in the originals than in any reproduction. Minard used two colors to distinguish water and railway traffic in the Voies d'eau et de fer (waterways and railways) series, five to represent the sources of raw cotton in that series, and seven to represent the sources of coal providing fuel to parts of France. Later examples from these series become increasingly bright and saturated. I felt an emotional thrill as I viewed the brilliance of colors from page to page. Moving pages back and forth to overlap sections through the series of six Coal diagrams, I could clearly see how Minard evolved his use of color, how he added it in legends and how he may have instructed the lithographer to adjust the tones.

Lalanne and the Legacy

During a second visit, Riondet gave me the chance to examine an additional table-full of materials from the ENPC archives: a portfolio of diagrams that were selected by Léon Lalanne [16] and the Atlas de Statistique Graphique series edited by Émile Cheysson. As he suggested, an appreciation of Minard's work benefits from an appreciation of the work by these men. Both Lalanne and Cheysson were well known and well respected in engineering and statistics circles, during and after Minard's career.

Lalanne was an important engineer, responsible for the building and management of railroads. He was a leading theorist and creative mathematician whose writing described visual computing techniques for calculating numerical results.. Minard and Lalanne were colleagues from different generations. As Minard was approaching retirement, Lalanne, in his late 30s, was a rising star developing his own visualization practices and techniques. The two men were part of the same social and intellectual team at Ponts et Chaussées and had a common interest: the relationship between cities, transportation networks and the flow of goods. They both spent their lives engaged in planning, building and supervising these networks. Lalanne developed theoretical models of the relationship between population density and transportation networks [17] that would propel his election to the French Academy of Sciences. The publishing of books and election to the Academy were both levels of recognition that eluded Minard. In 1851, the year that Minard retired and began his period of diagram production, Lalanne had just published Abacus or universal counter giving a view of the results of all arithmetic, geometry, practical mechanics, etc. [18], a book that described how to use drawing on grid lines to calculate complex mathematical relationships.

In the field of cartography, Lalanne pioneered the use of isopleth lines to represent height and depth. While Minard avoided the "tyranny of precise geographical position", Lalanne clearly embraced and advanced it. His goals for map making were anything but "approximative" to use a term Minard applied to his own maps. Despite these differences, Lalanne collected Minard's work. Six of the twenty-four items in Lalanne's portfolio are by Minard, five of which date from before Minard's retirement. One of these is a clean unfolded copy of Figurative map of the main movements of mineral fuels in France in 1845, the same lithograph badly cracked and folded in Minard's portfolio. This was the first in the series visualizing the movement of coal from mines outside and inside France to major ports and inland destinations. Lalanne's copy is printed on two sheets that were never joined in the middle.

Another item in the portfolio is a copy of #4 Circulation of Passengers between Dijon and Mulhouse, March 1841, (Carte de la circulation des voyageurs Par Services Réguliers de Voitures Publiques sur les routes de la contrée ou sera placé le chemin de Fer de Dijon à Mulhouse) [19], Minard's earliest passenger flow diagram. Its full title, "Passenger traffic map By Regular Services of Public Cars on the country roads where the railway will be placed from Dijon to Mulhouse" indicates it was a strategic visualization of data to assist the planning process, picturing the current movement of passengers between these cities before the railway was built. Writing in 1861, Minard describes the diagram as a major breakthrough in the development of what would become his graphic system:

In March 1845, during the [planning] discussion of the railway from Dijon to Mulhouse, I published my first figurative map…. Passengers traveling on the roads in the region, between two cities, were represented by tinted areas that follow the contours of the roads and have widths proportional to the number of passengers passing through them in public coaches. Mr. Frémy, then an auditor with the State Council and now a State Councilor and Governor of Real Estate Credit, carefully took note of the situation on the spot. [RJ Andrews translation] [20]

In Minard's diagram the tinted areas are proportional to the quantity of passengers, but there are no numbers to represent the quantities. On the copy in Lalanne's portfolio, someone has written summary numbers in red ink below many station names.

There is no indication of who wrote these numbers, and they are not found in any other copy. Perhaps this was Lalanne's critique of his colleague's experiment. In #9 Circulation of Goods in Belgium 1834 and 1844 (Mouvement des marchandises en Belgique sur les chemins de fer en 1844 et sur les voies navigables en 1834 et en 1844) [20], another diagram Lalanne collected, Minard has add numbers inside the tinted lines.

This use of numbers either inside or adjacent to the lines to clarify their quantitative meaning became a feature of Minard's technique from this point forward. In the later statistical graphics I had before me, all created after Minard's death, the combination of line width and numbers to visualize the flow of passengers on the French railways had become the standard format. Lalanne's portfolio includes two examples of these diagrams for 1872 and 1874, produced by the French railroad's central bureau of statistics. These can be placed side by side with any of the 10 diagrams Minard produced between 1852 and 1863 to reveal the similarity and differences.

Minard's diagrams compared the flow of goods on French waterways and railways shows how the official bureaus adapted his technique. The draftsmen of the central bureau of statistics paid far more attention to representing the coastal outlines. Minard's diagrams use different colors to compare the volume of goods on the railroads and the river-canal networks. The bureau diagram reports the numbers but does not compare that year's rail traffic to previous years or to other transport methods.

Émile Cheysson employed this technique in the Album de Statistique Graphique (Album of Graphic Statistics) series. Cheysson led the Direction des Cartes, Plans et Archives et de la Statistique Graphique, a unit within the Ministry of Public Works. I had before me, piled high on the table, fourteen volumes of the albums produced between 1878 and 1900. The first two volumes contained the largest diagrams. They were printed on sheets about nine times as big as the book itself, carefully creased and folded to be opened either up or down from the book.

This first album consists of maps of France visualizing the flow of goods and travelers on the networks of waterways, roads and railroads. Each data set is treated separately. Carte Figurative des recettes brutes Kilométriques des chemins de fer Français pour 1876 (Gross revenue per kilometer of the French railways) and Carte Figurative du tonnage des Rivières, Canaux et Ports de la France en 1876 (Tonnage on French rivers, canals and ports) are found in this collection. These employ a style I had already seen in the earlier examples Lalanne had collected. It is the style Cheysson went on to employ for over twenty years.

These and other diagrams in the series use line widths and numbers to represent quantities that flow between geographical points positioned on the map. The numbers represented by the width of the lines are placed over or within each line. Color is used to differentiate categories of lines when more than one category of data is represented. There are other types of diagrams in vast collection. Cheysson employed a number of inventive glyphs to encode quantities per department across maps of France, but the primary program of the albums was to repeat the same visualizations of national infrastructure — waterways, roads and railways — year after year. These maps based on Minard's "figurative map" technique dominate the collection. Minard's system had become the annual report of the French Ministry of Public Works.

A Thought Experiment

As I looked at all the graphics produced by Cheysson's team, along with the various maps, diagrams, timelines and stock market charts in Lalanne's portfolio, I continued to puzzle over a question that has bothered me since I first learned that Minard had created many kinds of diagrams on many themes. Why had his diagrams never been published in book form during his lifetime or in the years after his death? While it is certainly ingenious and impactful, his diagram of Napoleon's invasion of Russia is hardly representative of his body of work. Why is he remembered today for that single diagram?

I began a thought experiment: What if Minard had not created the diagram of Napoleon's invasion of Russia at the end of his career? If the last diagram he made had been the Figurative map of the movements and origins of Cereals imported in France in 1867, along with the ones that preceded it, how would he be remembered today?

His contemporaries recognized him as someone who popularized data visualization. They recognized his communication skills. But perhaps the sets of statistics he chose to visualize had no interest to the statisticians of the Third Republic. In 1890, mid-way through the Atlas de Statistique Graphique series, Cheysson wrote about how data visualization (aka statistical graphics) should be part of national policy [21]. In the opening paragraph of his essay he credits both Minard and Lalanne as the pioneers of his field.

The team at École des ponts et chaussées can rightly claim a significant role in the use and popularization of statistical graphics. M. Minard was one of the first to apply it, and his fine works demonstrated its fruitfulness and flexibility; Mr. Lalanne, a member of the Institute, for his part, raised the scientific scope and made remarkable progress in the area of line calculation. (author's translation)

Cheysson recognized the "fruitfulness and flexibility" (la fécondité et la souplesse) of Minard's work, but neither he nor anyone associated with the relevant institutions — the school and the ministries — made any effort to reprint them. The data that Minard had visualized was old news in the 1870s and onwards. Perhaps those who saw his work when he was producing several diagrams per year — who received them in the mail or heard about them at meetings — viewed him as a one-man data visualization research institute. Contemporaries such as Lalanne and Cheysson were looking for technique and methodology. They both saw something in his work they could use. Yet his achievement remained obscure enough that when the Irish engineer Henry Riall Sankey published his visualization of the loss of power in steam engines in 1898 [22], the resemblance to Minard's technique went unnoticed.

Sankey's work, rather than Minard's, became the template for representations of industrial ecology and energy metabolism. Today our data visualization libraries contain routines for Sankey, and not Minard diagrams [23].

There is the sentence in his obituary that suggests his work was distributed throughout the French government:

Thanks in effect to diverse ministers of public works, just as to M. de Franqueville, general director of bridges and roads and railways, M. Minard had always received from the administration powerful encouragement for his eminently useful maps. [Dawn Finley translation] [7]

What did these people think? By his own account, Minard felt he had a large audience. In an essay he also titled Des tableaux graphiques et des cartes figuratives [24], Minard describes how he developed his technique, how it was presented and adapted in the engineering community, with and without acknowledging his inventive role. He describes how his later work was encouraged and accepted by leaders in the administration, including Emperor Napoleon III.

I was able to publish a total of nearly ten thousand copies, graphic tables and maps on various subjects such as passenger traffic on roads and railways; freight traffic in general, and in particular coal, cereals and wine, by water and by rail tonnages of sea ports in France, Europe and world-wide, the consumption of meat in Paris, goods transiting through France and recently the import of raw cotton into Europe, etc., etc. [RJ Andrews translation]

The ENPC library has a number of individual Minard diagrams which were donated by officials in the ministries, another indication of how they were distributed. Finally, a reference in Minard's obituary has led several researchers to Portrait de Eugène Rouher, the formal painting of an important minister posing with a Minard diagram beside him [25], [13]. Clearly, neither Minard, nor the son-in-law who wrote his obituary, were fabricating the audience he had. But if M. Rouher's portrait is one of many, it appears to be the only surviving example.

If he hadn't applied the technique perfected by representing passengers, freight and coal to represent the deaths of half a million soldiers as the result of an Emperor's whim, we would be hard pressed to find references to him at all. None of his charts would have motivated Marey to reproduce his work, or inspired Tufte to reprint one charts as "the best statistical graphic ever drawn". Unless it effects our business, we don't get too emotional about the tonnage of goods shipped by rail or by water around France, or the shipments of cotton, coal or meat in any one year. If we were seeking examples of how to visualize the flow of quantities through a network, and represent how those quantities are distributed in space, we would have to stumble across individual lithographs he deposited at the Imperial Library (now the BnF) or come across the portfolio left at his school. We might never learn to appreciate his visual insight, his creative use of space and color and line.

At the end of the thought experiment, I came to the conclusion that without that creatively fruitful thought and the flexibility of research hypothesis, we might not understand how effective Minard's system could be.

I imagined him thinking: I will visualize the flow of an invading army across a landscape by applying a technique used to visualize the flow of passengers on a railroad.

And then: I will use color to distinguish the invasion and the retreat.

And then: I will visualize a correlation between loss of troops and temperature by aligning this flow of data across physical space with a graphic table of temperature readings over time.

And when it was done: I will have this printed and distributed to the list, and deposit a copy in the Emperor's Library.

And he wrote "pour la Bibliothèque Imperiale" in ink on the upper corner of one copy.

There may have been thousands of his diagrams printed and distributed during his lifetime, but their survival rate has proven to be similar to the soldiers in Napoleon's Grand Army. Only a few copies of each diagram remain in the collections of École des Ponts ParisTech and the Bibliothèque nationale de France. Yet these few survivors give us a portrait of a man — civil engineer, information designer, educator — whose communication skills transformed the relationships between complex sets of numbers into images that speak directly to our eyes. Minard's "fruitfulness and flexibility" — the precision and boldness of his imagination — should be an inspiration to anyone struggling with data visualization today.

Plancoët, March 2020

Acknowledgements

The author wishes to thank Charles Riondet and the staff of the ENPC library archives for their assistance in identifying the documents related to Minard's work. Thanks are also due to Charles Riondet and Sandra Rendgen for reviewing and commenting on an early version of this essay.

Bibliography

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[19] C.-J. Minard, "Carte de la circulation des voyageurs Par Services Réguliers de Voitures Publiques sur les routes de la contrée oú sera placé le chemin de Fer de Dijon à Mulhouse," 1845.

[20] C.-J. Minard, "Mouvement des marchandises en Belgique sur les chemins de fer en 1844 et sur les voies navigables en 1834 et en 1844.," 1847.

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[22] H. R. Sankey, "Introductory note on the thermal efficiency of steam-engines," Minutes of Proceedings of the Institution of Civil Engineers, vol. 134, pp. 278–283, 1898.

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[24] C.-J. Minard, Des tableaux graphiques et des cartes figuratives. Paris: impr. de Thunot, 1862.

[25] G. Palsky, Des chiffres et des cartes: naissance et développement de la cartographie quantitative française au XIXe siècle. Paris: Comité des Travaux Historiques et Scientifiques, 1996.