Blood, dirt, and nomograms: A particular history of graphs

ISIS

Volumn 90, Issue 1, 1999, Pages 50-80

  Hankins, Thomas L ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002840457     PISSN: 00211753     EISSN: 15456994     Source Type: Journal    
DOI: 10.1086/384241     Document Type: Review

References (89)

1. Lawrence Joseph Henderson, Blood: A Study in General Physiology (New Haven, Conn.: Yale Univ. Press, 1928), pp. 3, 373; figure 41 faces p. 148.
2. E.g., Bruno Latour, "Drawing Things Together," in Representation in Scientific Practice, ed. Michael Lynch and Steve Woolgar (Cambridge, Mass.: MIT Press, 1988), pp. 19-68;
3. Lynch, "Discipline and the Material Form of Images: An Analysis of Scientific Visibility," Social Studies of Science, 1985, 15:37-66.
4. Here I am following the lead of Laura Tilling, "Early Experimental Graphs," British Journal for the History of Science, 1975, 8:193-213. There are numerous earlier examples of diagrams that we might want to call graphs, but they were either more like maps (Edmond Halley), or remained in manuscript (Christiaan Huygens), or were concerned with genealogy (Joseph Priestley), of were more like geometrical diagrams (Benjamin Thompson, Count Rumford). Also, they usually stood alone, while the graphs of Playfair, Watt, and Lambert were frequently mentioned by later creators of graphs.
5. A survey of these early examples is James Beniger and Dorothy L. Robyn, "Quantitative Graphics in Statistics: A Brief History," American Statistician, Feb. 1978, 32(1):1-11.
6. James Joseph Sylvester, "On an Application of the New Atomic Theory to the Graphical Representation of the Invariants and Covenants of Binary Quantics - With Three Appendices," American Journal of Mathematics, 1878, 1:64-128;
7. Sylvester, "Chemistry and Algebra," in Collected Mathematical Papers, 4 vols. (Cambridge: Cambridge Univ. Press, 1904-1912), Vol. 3, no. 14;
8. William Kingdon Clifford, "Remarks on the Chemico-Algebraic Theory," in Mathematical Papers, ed. Robert Tucker (London: Macmillan, 1882), no. 28;
9. Charles Sanders Peirce, Collected Papers, ed. Charles Hartshorne and Paul Weiss, 7 vols. (Cambridge, Mass.: Harvard Univ. Press, 1933), Vol. 4, par. 4.535. Peirce defines a graph more formally as "a superficial diagram [i.e., a diagram on a surface] composed of the sheet upon which it is written or drawn, of spots or their equivalents, of lines of connection, and (if need be) of enclosures. The type, which it is supposed more or less to resemble, is the structural formula of the chemist" (par. 4.418-419). This is close to the first definition given in the Oxford English Dictionary.
10. William Whewell, Philosophy of the Inductive Sciences, 2 vols., Vol. 2: Novum organon renovation (1840), 3rd ed. (London: J. W. Parker, 1858), pp. 202, 206-207.
11. We have retained the old meaning of the word "graph" in that branch of mathematics called "graph theory"; see Norman Biggs, E. Keith Lloyd, and Robin J. Wilson, Graph Theory, 1736-1936 (Oxford: Clarendon, 1976).
12. William Playfair, The Commercial and Political Atlas: Representing, by Copper-Plate Charts, the Progress of the Commerce, Revenues, Expenditure, and Debts of England, during the Whole of the Eighteenth Century (1785), 3rd ed. (London: Wallis, 1801).
13. For the French edition see Playfair, Tableaux d'arithmétique linéaire, du commerce, des finances, et de la dette nationale de l'Angleterre (Paris: Chez Barrois l'Aîné, 1789). William had worked as a draftsman for Watt and may have taken the idea for graphs from Watt's indicator diagram.
14. Thomas L. Hankins and Robert J. Silverman, Instruments and the Imagination (Princeton, N.J.: Princeton Univ. Press, 1995), Ch. 6.
15. Lambert included numerous graphs in his Pyrometrie; oder, Vom Maasse des Feuers und der Wärme mit acht Kupfertafeln (Berlin: Bey Haude & Spener, 1779).
16. He treated error graphically in "Zuverlässigkeit der Beobachtungen und Versuche," in Beyträge zum Gebrauch der Mathematik und derren Anwendungen, 3 vols. in 4 (Berlin: Verlage des Buchladens der Realschule, 1765-1772), Vol. 1, pp. 424-488.
17. C. A. Prieur, "Suite du rapport fait au nom de comité d'instruction publique, sur la nécessité et les moyens d'introduire dans tout la République les nouveaux poids et mesures précédemment décrétés," Journal des débats et des décrets (Germinal, an III [1795]), pp. 323-328, 342-344, 354-360, 379-381, on p. 360.
18. On the resistance to the metric system see Ken Alder, "A Revolution to Measure: The Political Economy of the Metric System in France," in The Values of Precision, ed. M. Norton Wise (Princeton, N.J.: Princeton Univ. Press, 1995), pp. 39-71;
19. John L. Heilbron, "The Politics of the Meter Stick," American Journal of Physics, 1989, 57:988-992;
20. Guillaume Bigourdan, Le système métrique des poids et mesures: Son établissment et sa propagation graduelle (Paris: Gauthier-Villars, 1901).
21. Louis-Ézéchiel Pouchet, Échelles graphiques des nouveaux poids, mesures et monnaies de France, comparées avec celles des pays les plus commerçants de l'Europe (Rouen, 1795).
22. The second edition had a subtitle: Augmentée d'un traité sur les changes et d'un arithmétique linéaire (Rouen, 1796).
23. The following year Pouchet published improved scales as Métrologie terrestre; ou, Tables des nouveaux poids, mesures et monnoies de France, with an appendix entitled "Arithmétique linéaire" (Rouen, 1797).
24. He later published the appendix separately as Arithmétique linéaire; ou, Nouvelle méthode abrégée de calculer, que l'on peut pratiquer sans savoir lire ni écrire (Rouen: Guedra, 1806). Pouchet's son, Félix-Archimède Pouchet (1800-1872), was the adversary of Louis Pasteur in the debate over spontaneous generation.
25. Frederick B. Artz, The Development of Technical Education in France, 1500-1850 (Cambridge, Mass.: Society for the History of Technology and MIT Press, 1966), p. 81.
26. Gaspard Monge, "Mémoire sur la théorie des déblais et des remblais," read 27 Jan. and 7 Feb. 1776, Histoire de l'Académie Royale des Sciences, 1781 [1784], pp. 34-38;
27. Mémoires de l'Académie Royale des Sciences, 1781 [1784], pp. 686-704.
28. See also René Taton, L'oeuvre scientifique de Gaspard Monge (Paris: Presses Univ. France, 1951), pp. 193-202.
29. On the problem of defilade see René Taton, L'oeuvre scientifique de Gaspard Monge ibid., p. 12;
30. Peter Jeffrey Booker, "Gaspard Monge and His Effect on Engineering Drawing and Technical Education," Transactions of the Newcomen Society, 1961-1962, 34:15-36, on p. 16.
31. Lazare N. M. Carnot, Géométrie de position (Paris: J. B. M. Duprat, an XI [1803]);
32. Jean-Victor Poncelet, Traité des propriétés projectives dis figures: Ouvrage utile à qui s'occupent des applications de la géométrie descriptive et d'opérations géométriques sur le terrain (Paris: Bachelier, 1822);
33. Michel Chasles, Traité de géométrie supérieure (Paris, 1852);
34. Chasles, Aperçu historique sur l'origine et le développement des méthodes en géométrie particulièrement de celles qui se rapportent à la géométrie moderne suivi d'un mémoire sur deux principes généraux de la science: La dualité et l'homographie (1837; Paris: Gauthier-Villars, 1889).
35. Chasles, Aperçu, pp. 196, 206, 408-416.
36. Antoine Picon, "Les ingénieurs et la mathématisation: L'exemple du génie civil et de la construction," Revue d'Histoire des Sciences, 1989, 42:155-172, esp. pp. 158-167. Mathematicians had long used graphical methods for solving equations.
37. In 1839 B.-E. Cousinery at the École des Ponts et Chaussées systematized these methods in Le calcul par le trait, ses éléments et ses applications à la mesure des lignes, des surfaces et des cubes, à l'interpolation graphique et à la détermination, sur l'épure, de l'épaisseur des murs de soutènement et des murs de culées des voutes (Paris: Carilia-Goeury & Dalmont, 1839).
38. In 1866 Karl Culmann at Zurich systematized methods of calculating forces in static structures such as vaults and bridge trestles: Culmann, Die graphische Statik (1866), 2nd ed. (Zurich: Mayer & Zeller, 1875);
39. French trans.: Traité de statique graphique, trans. from the 1875 German ed. by Georges Glasser, Jean Jacquier, and A. Valat (Paris: Libraire des Corps Nationaux des Ponts et Chaussées, des Mines et des Télégraphes, 1880). Courses in "graphical statics," including most of the graphical methods described in this essay, quickly entered the curriculum of engineering schools across Europe. D'Ocagne's point alignment charts became a separate specialty called "nomography."
40. In 1870 Antonio Favaro, the editor of Galileo's collected works, wrote Lezioni di statica grafica (Padua: Sacchetto, 1877) for his students at the University of Padua. The book begins with a course in projective geometry, followed by a course in graphical calculation. Favaro seems not to have gotten to graphical statics proper.
41. The expanded French edition contains much historical information: Favaro, Leçons de statique graphique, trans. Paul Terrier, 2 vols. (Paris: Gauthier-Villars, 1879-1885).
42. Charles Joseph Minard, Des tableaux graphiques et des cartes figuratives (Paris: Thunot, 1862).
43. See also Arthur H. Robinson, "The Thematic Maps of Charles Joseph Minard," Imago Mundi, 1967, 21:95-108;
44. Edward R. Tufte, The Visual Display of Quantitative Information (Cheshire, Conn.: Graphics, 1983), p. 40.
45. Cecil O. Smith, Jr., "The Longest Run: Public Engineers and Planning in France," American Historical Review, 1990, 95:657-692, on p. 669. In Great Britain and the United States, private rail companies competed for traffic.
46. For the law see "Établissement de grande lignes de chemins de fer," Annales des Ponts et Chaussées, 2nd Ser., 1842, 2:265-286.
47. Léon Lalanne, Méthodes graphiques pour l'expression des lois empiriques ou mathématiques à trois variables, avec des applications à l'art de l'ingénieur et à la résolution des équations numérique d'un degré quelconque (Paris: Imprimerie Nationale, 1878), pp. 8 (Coriolis tables, which were issued to the engineers on 18 Jan. 1836 and 24 Aug. 1837), 23 (mention of the 1851 and 1856 versions).
48. Lalanne's 1842 tables were sent to the railroad engineers by the Under-Secretary of State for Public Works in a circular dated 2 Sept. 1843: Ann. Ponts Chaussées, 2nd Ser., 1843, 3:676-683.
49. Alexandre Magnus d'Obenheim, Balistique (Strasbourg: P.-G. Levrault, 1814);
50. Obenheim, Mémoire contenant la théorie, la description et l'usage de la planchete du canonnier (Strasbourg: P.-G. Levrault, 1818);
51. Terquem, Mémorial de l'artillerie (1838).
52. See Maurice d'Ocagne, Le calcul simplifié: Graphical and Mechanical Methods for Simplifying Calculation, trans. J. Howlett and M. R. Williams (Cambridge, Mass.: MIT Press, 1986), p. 85.
53. Léon Lalanne, "Mémoire sur les tables graphiques et sur la géométrie anamorphique appliquée à diverses questions qui se rattachent à l'art de l'ingénieur," Ann. Ponts Chaussées. 2nd Ser., 1846, 11:1-69. Lalanne was also the first to draw a true isopleth, that is, lines indicating the distribution of average values, in this case the population density.
54. See Arthur H. Robinson, "The Genealogy of the Isopleth," Cartographic Journal, 1971, 8:49-53.
55. Marcellin Du Carla-Boniface, Expression des nivellements; ou, Méthode nouvelle pour marquer sur les cartes terrestres et marines les hauteurs et les configurations du terrain (Paris, 1782);
56. Alexander von Humboldt, "Sur les lignes isothermes," Annales de Chimie et de Physique, 1817, 5:102-112. Humboldt had been greatly impressed by Playfair's Atlas. In 1812 he wrote: "Cette méthode graphique est analogue à celle que M. Playfair a employée le premier et d'une manière très-ingénieuse, dans son atlas commercial et politique, et dans ses cartes statistiques de l'Europe . . . tout ce qui a rapport à l'étendue et à la quantité, est propre à être représenté par des figures géometriques. Les projections statistiques qui parlent aux sens sans fatiguer l'esprit, ont l'avantage de fixer l'attention sur un grand nombre de faits importans."
57. Humboldt, Atlas géographique et physique du royaume de la Nouvelle-Espagne (1812), ed. Hanno Beck and Wilhelm Bonacker (Stuttgart: F. A. Brockhaus, 1969).
58. Lalanne wrote an appendix ("Sur la représentation graphique des tableaux météorologiques et des lois naturelles en générale") to Ludwig Friedrich Kaemtz, Cours complet de météorologie, trans. Charles Frédéric Martins (Paris: Paulin, 1843), in which he converted all of Kaemtz's tables to graphical form.
59. Lalanne, "Mémoire sur les tables graphiques" (cit. n. 20), p. 13.
60. Maurice d'Ocagne, Traité de nomographie: Théorie des abaques, applications pratiques (Paris: Gauthier-Villars, 1899).
61. An especially good collection of early nomograms is in Rodolphe Soreau, Nomographie; ou, Traité des abaques, 2nd ed., 2 vols. (Paris: Chiron, 1921).
62. Lawrence Joseph Henderson, The Fitness of the Environment: An Inquiry into the Biological Significance of the Properties of Matter (New York: Macmillan, 1913).
63. Henderson, Blood (cit. n. 1), p. 114;
64. J. S. Haldane, The New Physiology (London: Charles Griffin, 1919), p. 76.
65. Henderson, Blood, pp. 153-173.
66. On Henderson see John Parascandola, "L. J. Henderson and the Mutual Dependence of Variables: From Physical Chemistry to Pareto," in Science at Harvard University: Historical Perspective, ed. Margaret W. Rossiter and Clark A. Elliott (Bethlehem, Pa.: Lehigh Univ. Press, 1992), pp. 167-190;
67. Parascandola, "Organismic and Holistic Concepts in the Thought of L. J. Henderson," Journal of the History of Biology, 1971, 4:63-113;
68. Parascandola, "Lawrence Joseph Henderson," in Dictionary of Scientific Biography, ed. Charles C. Gillispie, 18 vols. (New York: Scribners, 1970-1986), Vol. 6, pp. 260-262. I thank John Parascandola for providing me with information on Henderson.
69. D'Ocagne, Calcul simplifié, trans. Howlett and Williams (cit. n. 19), p. 106;
70. Lawrence Joseph Henderson, "Memories," pp. 257-258, unpublished MS, L. J. Henderson Papers, Harvard University Archives, Cambridge, Massachusetts. Henderson later called the diagram that he took to Wilson a "Cartesian nomogram" to distinguish it from the point alignment chart and his figure 41, which he called a "nomogram."
71. F. S. C. Northrop, Science and First Principles (New York: Macmillan, 1931), pp. 172, 175-176.
72. "The reactions of physiologists to this nomogram have been most amusing. Some have criticized it because it is true. It is but an unusual way of stating something that any well-trained physiologist knows, they say. Certainly, this is all to the good. One may add that the nomogram has the advantage of getting these ideas out of the imaginations of scientists onto paper in objective form, where we can know precisely what they are. Others have been unable to understand it." F. S. C. Northrop, Science and First Principles Ibid., p. 179.
73. Joseph Peuchet, Statistique élémentaire de la France (Paris, 1805), p. 33;
74. P. A. Dufau, Traité de statistique; ou, Théorie de l'étude des lois (Paris, 1840), p. 141;
75. Carl Knies, Die Statistik als selbständige Wissenschaft (Kassel, 1850), p. 114:
76. all quoted from H. Gray Funkhouser, "Historical Development of the Graphical Representation of Statistical Data," Osiris, 1st Ser., 1937, 3:269-404, on p. 295.
77. Étienne-Jules Marey, La méthode graphique dans les sciences expérimentales, 2nd ed. (Paris: Masson, 1885), p. iii.
78. D'Ocagne, Calcul simplifié, trans. Howlett and Williams (cit. n. 19), p. 12;
79. Zeno G. Swijtink, "Coup d'Oeil and Proprio Marte: Bodily Aspects of Reasoning in Johann Lambert's Graphical Representations," unpublished MS, 1996.
80. Marey, Méthode graphique (cit. n. 33), p. iii.
81. J. Willard Gibbs, "Graphical Methods in the Thermodynamics of Fluids," Transactions of the Connecticut Academy, Apr.-May 1873, 2:309-342,
82. rpt. in Gibbs, Collected Works, ed. W. R. Longley and R. G. Van Name (New York: Longmans, Green, 1931), pp. 1-32, on p. 1.
83. Stephen G. Brush, "The Reception of Mendeleev's Periodic Law in America and Britain," Isis, 1996, 87:595-628;
84. J. W. van Spronsen, The Periodic System of Chemical Elements: A History of the First Hundred Years (Amsterdam: Elsevier, 1969).
85. Sandy L. Zabell, "Arbuthnot, Heberden, and the Bills of Mortality," Technical Report no. 40, Department of Statistics, Univ. Chicago, 1976.
86. Boyle is quoted in Charles Webster, "The Discovery of Boyle's Law, and the Concept of the Elasticity of Air in the Seventeenth Century," Archive for History of Exact Sciences, 1965, 2:441-502, on p. 469.
87. Margaret C. Shields made an unsuccessful attempt to find any graph of Boyle's law in the eighteenth century; see Shields, "The Early History of Graphs in Physical Literature," American Physics Teacher, 1937, 5:68-71.
88. Lawrence Joseph Henderson, "Sociology 23 Lectures," in L. J. Henderson on the Social System, ed. Bernard Barber (Chicago: Univ. Chicago Press, 1970), pp. 139, 143-144;
89. Henderson, The Order of Nature: An Essay (Cambridge, Mass.: Harvard Univ. Press, 1917), p. 126.