1 I have searched the following journals for experimental graphs: Acta eruditorum; Annals if philosophy; Edinburgh journal of science; Edinburgh philosophical journal; Mémoires de l'Académie des Sciences, Paris; Mémoires de l'Académie Royale des Sciences et Belles-Lettres, Berlin; Mémoires présentés bar divers savans à l'Académie Royale des Sciences, Paris; William Nicholson's Journal of natural Philosophy, &c; Novi commentarii Academiœ Scientiarum Imperialis Petropolitarœ; Observations sur la physique (later Journal de physique); Philosophical transactions of the Royal Society; Transactions of the Royal Society of Edinburgh. With the exception of the Berlin Mémoires, no experimental graphs used for analysis of results are to be found in any of these journals for the eighteenth century. M. C. Shields, who examined a large number of periodicals, lists the graphs he found, both in the eighteenth and early nineteenth centuries; however, the majority of these are either not experimental or are not accompanied by any comment or analysis. See his paper, ‘The early history of graphs in physical literature’, The American physics teacher, v (1937), 68–71.
2 See, for example, Royston, E., ‘A note on the history of the graphical representation of data’, Biometrika, xliii (1956), 241–7;
also reprinted in Pearson, E. S. and Kendall, M. G., Studies in the history of statistics and probability theory (London, 1970), p. 173. There the use of graphs in statistics and economics is discussed.
3Taylor, Brook, ‘Concerning the ascent of water between two glass planes’, Philosophical transactions (1712), p. 538,
and Francis Hauksbee (the elder), ‘Account of the experiment on the ascent of water between two glass planes in an hyperbolick figure’, Taylor, Brook, pp. 539–40. Hauksbee's original graphs (Royal Society, Classified papers, 1660–1740, xviii. fo. 132) are somewhat more accurate than the printed versions; however, they are crudely drawn and clearly hampered by a lack of squared paper.
4Middleton, W. E. Knowles, The history of the barometer (Baltimore, 1964), pp. 287 ff.,
and Invention of the meteorological instruments (Baltimore, 1969), pp. 245 fF.
Hoff, Hebel E. and Geddes, L. A., ‘Graphic recording before Carl Ludwig: an historical summary’, Archives internationales d'histoire des sciences, xiie année (1959), 1–25;
‘The anemograph of Ons-en-Bray’, Journal of the history of medicine and allied sciences, xii (1957), 424–8;
and ‘The beginnings of graphic recording’, Isis, liii (1962), 287–310.
5Middleton, , 1969, op cit. (4), p. 245.
6 See Hoff, and Geddes, , 1962, op cit. (4), p. 303, where the devices invented by Wren and Hooke are discussed.
7Cruquius, , ‘Observations accuratæ captæ … circa mediam barometri altitudinem, mediam thermometri elevationem, turn et hydrometri varietatem mediam, etc.’, Philosophical transactions (1724), pp. 4–7.
8 Meteorological graphs appear in the Novi commentarii Academiœ Scientiarum Imperialis Petrpolitanœ and in the Nouveaux mémoires de l'Académie des Sciences et Belles-lettres, Berlin, in the 1770s.
9 See Hoff, and Geddes, , 1962, op. cit. (4), pp. 287–310.
10Ons-en-Bray, , ‘Anémomètre qui marque de lui-même sur le papier, non seulement les vents qu'il a fait pendant les 24 heures, et à quelle heure chacun a commencé et fini, mais aussi leur différentes vitesses et forces relatives’, Mémoires de l'Académie Royale des Sciences … 1734 (Paris, 1736), pp. 123–34.
A translation, from which I quote, is in Hoff, and Geddes, , 1957, op. cit. (4), p. 424.
11Beaufoy, Mark, ‘Description of an instrument to measure and register the rise and fall of the tide throughout the whole flow and ebb’, Annals of philosophy, vi (1815), 273–81.
12Keith, Alexander, ‘Description of a thermometer, which marks the greatest degree of heat and cold from one time of observation to another, and may also register its own height at every instant’, William Nicholson's Journal of natural philosophy, chemistry, and the arts, iii (1800), 266–8; see p. 268.
13Christie, S. H., ‘On the diurnal deviations of the horizontal needle when under the influence of magnets’, Philosophical transactions (1823), pp. 342–92.
14 See Dickinson, H. W. and Jenkins, R., James Watt and the steam engine (Oxford, 1927), pp. 228–33.
15 See Robison, John, The articles ‘Steam’ and ‘Steam-engines’ written for the Encyclopœdia Britannica … with notes and additions by James Watt, ed. Brewster, D. (Edinburgh, 1818), pp. 29 and 170.
I quote from Watt's annotations to the article. See also Farey, John, A treatise on the steam engine (London, 1827;
reprinted by David, and Charles, , London, 1971), i. 394–405.
Shields, M. C., in ‘James Watt and graphs’, The American physics teacher, vi (1938), 162, also discusses Watt's use of graphs and speculates on a possible connexion between Watt's work and William Playfair's work; see below. Playfair served as a draughtsman in Watt's workshop in 1780.
16Robison, , op. cit. (15), p. 160, ‘Letter from Mr Southern to Mr Watt’. The experiments were done in 1796, at Watt's request, by John Southern and William Creighton.
17 A later French edition, Tableaux d'arithmétique linéaire, du commerce, des finances, et de la dette nationale de l'Angleterre (Paris, 1789), contains many of the same graphs but they are here even more attractively produced.
18 Biographies of Lambert in English are in P.W., ‘Life of John Henry Lambert’, Philosophical magazine, xviii (1804), 333,
and Jacque, J., ‘Ecomium of Mr. Lambert’, prefaced to Lambert, 's The system of the World (London, 1800).
Details of Lambert's work, both published and unpublished, may be found in Steck, M., Bibliographia Lambertiana (Hildesheim, 1970).
19 See, for example, Griffing, H., ‘J. H. Lambert, a study in the development of the critical philosophy’, Philosophical review, ii (1893), 54–62,
and Vleeschauwer, H-J, L'ésolution de la pensée Kantienne (Paris, 1939).
20 I discuss Lambert's general methodology and its relationship to his theory of errors in Chapter V of my thesis, ‘The interpretation of observational errors in the eighteenth and early nineteenth centuries’ (London University Ph.D. thesis, 1973). His work on graphs is discussed on pp. 233–40.
21 The paper appears in Beyträge zum Gebrauche der Mathematik und deren Anwendung (Berlin, 1765), i. 424–88. See pp. 476 ff. and the plate ‘Mathes. Applicat. Tab. V.’.
22Mémoires de l'Académie Royale des Sciences et Belles-lettres … 1769 (Berlin, 1771), pp. 68–127 and Plate I facing p. 126.
23Pyrometrie (Berlin, 1779), p. 190 and Plate.
24 See Chapter V of my Ph.D. thesis, op. cit. (20), and articles by Sheynin, O., ‘J. H. Lambert's work on probability’, Archive for history of exact sciences, viii (1971), 244–56,
and ‘The origin of the theory of errors’, Nature, ccii (1966), 1003–4.
25 Op. cit. (21), i. 430–1.
26Photometria (Augustæ Vindelicorum, 1760), pp. 129–30.
27 Op. cit. (21), i. 476–7.
28 ‘Mémoire sur la force avec laquelle les corps solides adhèrent aux fluides, où l'on détermine les loix auxquelles cette force est soumise, tant suivant la nature du fluide que suivant celle du solide’, Nouveaux mémoires de l'Académie Royale des Sciences et Belles-lettres … 1776 (Berlin, 1777), pp. 149–59 and Tab. II facing p. 159.
29Herschel, William, ‘Experiments on the solar, and on the terrestrial rays that occasion heat; with a comparative view of the laws to which light and heat, or rather the rays which occasion them, are subject, in order to determine whether they are the same, or different’, Philosophical transactions (1800), pp. 437–538; plate facing p. 538.
30Robison, John, ‘Strength of materials’, in Encyclopœdia Britannica (6th edn., Edinburgh, 1823), xix. 779, and Plate DXII, fig. 26; first published in the third edition of 1797.
31Dalton, John, A new system of chemical philosophy (2 vols., Manchester, 1808–1827), i. Plate 8
32 See, for example, Gauss, C. F. and Weber, Wilhelm (eds.), Resultate aus den Beobachtungen des magnetischen Vereins (1836–41) (Göttingen, 1837–1842),
and Gauss, , Atlas des Erdmagnetismus von Gauss und Weber (Leipzig, 1840).
33Lubbock, J. W., ‘Note on the tides’, Philosophical transactions (1833), pp. 19–22; plate facing p. 19.
34Forbes, J. D., ‘On the horary oscillations of the barometer near Edinburgh’, Transactions of the Royal Society of Edinburgh, xii (1834), 153–90 and Plate VII, facing p. 180. Read 4 April 1831.
35Forbes, J. D., ‘Further experiments and remarks on the measurement of heights by the boiling point of water’, Transactions of the Royal Society of Edinburgh, xxi (1857), 235–43 and Plate III, facing p. 236. Read 4 December 1854.
36Forbes, J. D., ‘Account of some experiments on the temperature of the earth at different depths and in different soils near Edinburgh’, Transactions of the Royal Society of Edinburgh, xvi (1849), 189–236; see p. 189.
37Whewell, William, ‘Novum organon renovatum’, which forms part of the Philosophy of the inductive sciences, first published 1840; I quote from the third edition (London, 1858), ii. 202.
38Whewell, William, ii. 206–7.
39Herschel, J. F. W., ‘On the investigation of the orbits of revolving double stars …’, Memoirs of the Royal Astronomical Society, v (1833), 171–22 and Plates I and II. Read 13 January 1832.