Work and Waste: Political Economy and Natural Philosophy in Nineteenth Century Britain (II)

Landes David , The unbound prometheus: Technological change and industrial development in Western Europe from 1750 to the present (Cambridge, 1969), 117–23.

The preceding paragraphs summarize key points from Berg Maxine , The machinery question and the making of political economy: 1815–1848 (Cambridge, 1980), 43–110, without, however, doing justice to the subtlety of her analysis. On one point I have reservations. It goes too far to say that Ricardo envisaged “a progressive continuously transforming economy … in stark contrast to the assumptions of a static self-regulating economy then underlying government policy”, because his analysis of the role of machinery occurs largely within the context of labour productivity and the distribution of labour in a world market, which looks toward an ultimate distributive balance. See the chapter “On foreign trade” in Ricardo David , Principles of political economy and taxation (London, 1817), 128–49, esp. p. 136n. He there treats “improvements in arts and machinery” as “disturbing causes”, which, like taxes and duties, “interfere with the equilibrium” (pp. 141–2). They are the “accidental and temporary” causes which for a time can raise the market price above the natural price (pp. 88–92). But for that reason they cannot be continuously transforming causes, except as a succession of accidents which cannot be accounted for within the system of natural law. His language is almost entirely that of the traditional balancing model. That Ricardo's optimism nevertheless rested on such “accidental and temporary causes” dramatizes the increasing inadequacy of balancing models of the economy, which is Berg's main point about the machinery question.

Whewell William to Jones Richard , 9 September 1828, Whewell to H. J. Rose, 10 January 1830 (quotation), and Whewell to J. C. Hare, 30 October 1838, in Todhunter I. , William Whewell, D. D.: Master of Trinity College, Cambridge (2 vols, London, 1876), ii, 92–94, 105–6. Whewell William , “Mathematical exposition of some doctrines of political economy” (1829) and “Mathematical exposition of some of the leading doctrines in Mr. Ricardo's ‘Principles of Economy’” (1831), Transactions of the Cambridge Philosophical Society, iii (1830), 191–230 and iv (1833), 155–98; both in Mathematical exposition of some doctrines of political economy (Farnborough, 1968), paginated separately; see esp. (1829) pp. 18–29, (1831) pp. 22–23. I have benefited from a preprint of Margaret Schabas, “William Whewell's mathematical exposition of economic theory”.

Whewell , “Mathematical exposition” (ref. 3, 1829), 4; “Mathematical exposition” (ref. 3, 1831), 5–8, 12. For Whewell's critique of Ricardo's premature deductive method see Hollander Samuel , “William Whewell and John Stuart Mill on the methodology of political economy”, Studies in history and philosophy of science, xiv (1983), 127–68, esp. pp. 141–54, and DeMarchi N. B. Sturges R. P. , “Malthus and Ricardo's inductivist critics: Four letters to William Whewell”, Economica, xl (1973), 379–93. These informative papers want Whewell's dynamical viewpoint and its role in his moral-political position.

Whewell , “Mathematical exposition” (ref. 3, 1831), 13. Repeated in Whewell William , “Mathematical exposition of some doctrines of political economy — Second memoir” (1850), Transactions of the Cambridge Philosophical Society, ix (1856), 128–49, in Mathematical exposition, 22. Whewell would later express strong reservations about Laplace's entire approach when G. B. Airy touted it as giving the right direction to the move from equilibrium theories to dynamics. Whewell to Airy, 18 January, 22 February, and 2 March 1843, in Todhunter , Whewell (ref. 3), ii, 306–12.

Whewell William to Jones Richard , 23 July 1831, in Todhunter , Whewell (ref. 3), ii, 124–6. Whewell , “Mathematical exposition” (ref. 3, 1831), 12.

Whewell , “Mathematical exposition” (ref. 3, 1831), 12, my emphasis. One can hardly avoid thinking of Charles Darwin's similar moves from perfect adaptation to evolution. Indeed, according to Dov Ospovat's account, “Darwin after Malthus”, Journal of the history of biology, xii (1979), 211–30, which stresses Darwin's gradual movement away from the balancing model of perfect adaptation, it was precisely the idea of variable circumstances driving variation that constituted, in the early 'forties, one of Darwin's primary insights into the origin of new species, before he developed a non-equilibrium evolutionary model. The significance of Malthus and of political economy for Darwin has been widely discussed. See the succinct commentary by Antonello La Vergata, “Images of Darwin: A historiographic overview”, in Kohn David (ed.), The Darwinian heritage (Princeton, 1985), 901–72, pp. 953–8.

Whewell William to Jones Richard , 9 September 1828 (quotation) and 23 August 1832 (where Whewell reports landholding and farming arrangements in France), Todhunter , Whewell (ref. 3), ii, 93, 143–6. Whewell's interaction with Jones on inductivist methodology is discussed in Hollander , “William Whewell and John Stuart Mill” (ref. 4), passim, and in DeMarchi Sturges , “Malthus and Ricardo's inductivist critics” (ref. 4).

Jones Richard , An essay on the distribution of wealth and on the sources of taxation — Part I. Rent (Cambridge, 1831), 138; quoted in William Whewell, Six lectures on political economy (Cambridge, 1860), 93. Whewell summarizes Jones's views in “Lecture VI: Transitions of forms of rents”, pp. 83–102. See also his “Prefatory notice” to Jones Richard , Literary remains, consisting of lectures and tracts on political economy, ed. by Whewell William (London, 1859), pp. ix–xl, where Whewell attacks the ‘tendency’ theory and associated deductive methodology of Ricardo and company.

Whewell William to Jones Richard , 19 February 1832, in Todhunter , Whewell (ref. 3), ii, 140–1.

Whewell William , The Bridgewater treatises on the power wisdom and goodness of God as manifested in the Creation. Treatise III: Astronomy and general physics considered with reference to natural theology (1833), 4th edn (London, 1834), 75, 164.

Whewell , Bridgewater treatise (ref. 11), 200–3.

de Laplace P.-S. , The system of the world , trans. by Pond J. (2 vols, London, 1809), ii, 145–50, 363–6. Whewell , Bridgewater treatise (ref. 11), 184.

Whewell , Bridgewater treatise (ref. 11), 206–7. Whewell here took advantage of a glaring inconsistency in Laplace's scheme. Laplace made extensive use of the dissipative effects of friction in the solar atmosphere to establish the periodic motions of the planets and the elliptic paths of comets; but he then treated these motions as eternally stable (the primary burden of his work and essential to his conception of a natural system as a balance) as if the dissipative effects had disappeared from nature: “We may be … certain that these [heavenly] bodies experience no sensible resistance from the fluids through which they pass, as light, the tails of comets, or the zodiacal light” (System of the world (ref. 13), ii, 235). On the other hand, he was aware both of the logical problem and of the ongoing effects of friction and other resistances. In the Essay on probabilities, immediately after summarizing his accomplishment in proving the eternal succession of states, he thoroughly compromised its force with a qualifier: “The actions of the ocean, of the atmosphere, and of meteors, of earthquakes, and the eruptions of volcanoes, ceaselessly agitate the surface of the earth and ought to produce in the long run great changes …. Moreover, if the entire earth has been primitively fluid, as everything appears to indicate, one conceives that in passing from that state to the one which it has now, its surface ought to have met with prodigious changes. The firmament itself, in spite of the order of its movements, is not inalterable. The resistance of light and of other ethereal fluids, and attraction of the stars ought, after a very large number of centuries, to considerably alter the planetary movements”, Essai philosophique sur les probabilités, 4th edn (1819), reprinted as the Introduction to Théorie analytique des probabilités, 3rd edn (Paris, 1820), p. cxi. For Laplace, the contradictions were only apparent, since he believed in conservation of vis viva, but that principle could play no role in his inductive argument from observations.

Whewell , Bridgewater treatise (ref. 11), 373–4.

Whewell , Bridgewater treatise (ref. 11), 245–9. Cf. Laplace on friction, System of the world (ref. 13), ii, 146, 156–7, 189, 235.

Whewell , Bridgewater treatise (ref. 11), 250.

Whewell William , “Mathematical exposition” (ref. 5, 1850), 19, 22. William Whewell to G. B. Airy, 2 March 1843, in Todhunter , Whewell (ref. 3), ii, 310. In his Bridgewater treatise Whewell treated water and air, like the interplanetary medium, as exhibiting no effects of friction, but with the qualification that “even their motions are interrupted, alternate, variable, and on the whole slight deviations from the condition of equilibrium” (p. 247).

Chalmers Thomas , On political economy, in connexion with the moral state and moral prospects of society (Glasgow, 1832), pp. iv, and generally 420–49. The discussion below would benefit greatly from the richly detailed analysis by Hilton Boyd , The age of atonement: The influences of evangelicalism on social and economic thought, 1795–1865 (Oxford, 1988), which I acquired only in final editing.

Chalmers , Political economy (ref. 19), 274; also 25.

Chalmers Thomas , The Bridgewater treatises on the power wisdom and goodness of God as manifested in the creation. Treatise I: The adaptation of external nature to the moral and intellectual constitution of man , 2nd edn (2 vols, London, 1833), ii, 50, 274–9 (moral dynamics). Chalmers , Political economy (ref. 19), p. vi.

Chalmers , Bridgewater treatise, ii, 560 (quotation), 301–9 (taxes), 329–31 (tithes), 346–51 (productive and unproductive labour), 86–90, 102–5, 555 (stationary state).

Chalmers , Bridgewater treatise (ref. 21), ii, 45–51, p. 46; idem. Political economy (ref. 19), 71. Chalmers's perspective on natural law sometimes seems incoherent, because he assumes the inviolable rule of “natural jurisprudence” also with respect to the deepest affections of the mind, such as the right of property (Bridgewater treatise, ii, 2, 14). He would no doubt respond that although both the physical and moral nature of man are fixed in themselves, the moral can dominate over the physical.

Hume David , Dialogues concerning natural religion (1779), ed. by Aiken H. D. (New York, 1948), 20; 34.6. Chalmers Thomas , “On the non-eternity of the present order of things”, in The works of Thomas Chalmers (25 vols, Glasgow, 1836–42), i, 161–87, p. 167. Chalmers , Bridgewater treatise (ref. 21), i, 38–41. See Smith Crosbie , “From design to dissolution: Thomas Chalmers' debt to John Robison”, The British journal for the history of science, xii (1979), 59–70, and Rice D. F. , “Natural theology and the Scottish philosophy in the thought of Thomas Chalmers”, Scottish journal of theology, xxiv (1971), 23–46.

Chalmers Thomas , “On the consistency between the efficacy of prayer — And the uniformity of nature”, in Works (ref. 24), vii, 234–62, p. 234.

Chalmers Thomas , “The transitory nature of visible things”, Works (ref. 24), vii, 263–5.

Mill J. S. to Nichol J. P. , 30 August 1834, in Mineka F. E. (ed.), The earlier letters of John Stuart Mill, 1812–1848 , in Collected Works of John Stuart Mill (29 vols, Toronto, 1963–88), xii, 231. See also the letters of 16 and 17 January 1833, 10 July 1833, and 15 April 1834.

Schaffer Simon , “The nebular hypothesis and the science of progress”, in Moore J. R. (ed.), The humanity of evolution (Cambridge University Press, forthcoming). The place of the nebular hypothesis in Comte's writings has been discussed by S. S. Schweber (“Auguste Comte and the nebular hypothesis” (unpublished), who stresses the fact that the nebular hypothesis was regularly connected in Britain with evolutionary conceptions of geology and biology. See also Brush S. G. , “The nebular hypothesis and the evolutionary world view”, History of science, xxv (1987), 246–78.

Mill J. S. to Nichol J. P. , 30 August 1834 and 21 December 1837, Earlier letters (ref. 27), xii, 231, 363. Auguste Comte, Cours de philosophie positive (6 vols in 2, Hermann, Paris, 1975), i, ed. by Seres M. Dagognet F. Sinaceur A. , Philosophie première , leçon 26, 423; leçon 27, 432–9. N[ichol] J. P. , “State of discovery and speculation concerning the nebulae”, London and Westminster review , iii and xxv (1836), 390–409, esp. pp. 402–6; idem. Views of the architecture of the heavens, in a series of letters to a lady (1838), 3rd edn (Edinburgh, 1839), 193–6.

Nichol , “State of discovery and speculation” (ref. 29), 406–9, 405n.

I shall omit discussion here of the extended political-intellectual polemic between Whewell and Mill on induction and ethics. For concise statements see Whewell William , Of induction, with especial reference to Mr. J. Stuart Mill's System of Logic (London, 1849) and Mill J. S. , “Whewell's moral philosophy”, Westminster and foreign quarterly review (1852), in Collected works (ref. 27), x, 169–91. Some of the issues are discussed in Hollander, “William Whewell and John Stuart Mill” (ref. 4), but with too much attention to finding ultimate agreement and with the peculiar claim that Whewell abandoned his nativist theory of induction in favour of Mill's views (pp. 133, 161–3).

Mill J. S. to Nichol J. P. , 14 October 1834, Earlier letters (ref. 27), xii, 237. Nichol , “State of discovery” (ref. 29), 407. Mill J. S. , A system of logic ratiocinative and inductive , in Robson J. M. (ed.), Collected works (ref. 27), vii, 105. Comte , Cours de philosophie positive (ref. 29), ii, ed. by Enthoven Jean-Paul , Physique sociale, leçons 50–51, pp. 176–234.

Mill J. S. to Nichol J. P. , 14 October 1834 and 30 September 1848, Earlier letters (ref. 27), xii, 237, 739.

Mill J. S. , Principles of political economy with some of their applications to social philosophy , in Collected works (ref. 27), ii, 199–214 (socialism); 252–336 (peasants); iii, 752–7 (stationary state); 758–96, 1006–14 (“On the possible futurity of the labouring classes”). For extended analysis see Hollander Samuel , The economics of John Stuart Mill (2 vols, Oxford, 1985); socialism and cooperatives in ii, 770–824.

Mill , Logic (ref. 32), viii, 912.

Ibid., viii, 918 (inner quotation from Comte, Philosophie positive, 1st edn, iv, 325), 934 (added to 1862 edition), 913, 928. On “orbits” and “circles” compare Logic (ref. 32), viii, 790 with Mill's 1834 review, “On Miss [Harriet] Martineau's summary of political economy”, Monthly repository, viii (1834), 318–22; Essays on economics and society, 1824–1879, in Collected works (ref. 27), iv, 223–8, p. 226. The historical views of Kant, Herder, and Hegel did not qualify as properly scientific in Mill's terms, or in those of British scientific culture generally, because they did not provide a sufficient induction, only speculation.

Mill J. S. , Autobiography (1873), in Autobiography and literary essays, Collected works (ref. 27), i, 168–9. Hollander , Economics of J. S. Mill (ref. 34), i, 83–104. I thank Nancy Cartwright for helpful discussions of Mill's concept of causation and composition.

Mill , Logic (ref. 32), vii, 507–8 (where Mill gives his only footnote to Nichol, which he removed in the 2nd edn, 1846, after Herschel and others denounced the nebular hypothesis as vacuous speculation), 514; viii, 913. See Schaffer , “Science of progress” (ref. 28), and Schweber , “Auguste Comte” (ref. 28). Mill omits to mention Comte's dedication of his Philosophie positive to Joseph Fourier, whose theory of the conduction of heat provided strong opposition to Laplacian mathematical physics and whose theory of a cooling Earth provided powerful support for progressionist, anti-Lyellian geological theories, as discussed below.

Mill , Logic (ref. 32), vii, 326, 336–7, 344, 509–14. Cf. the more conventional views on action–reaction of J. F. W. Herschel in his review of Whewell's History and Philosophy, “Whewell on the inductive sciences”, Quarterly review, lxviii (1841), 177–238, reprinted in Herschel J. F. W. , Essays from the Edinburgh and Quarterly reviews, with addresses and other pieces (London, 1857), 142–256, esp. 206–14 (weakly discussed by Mill, vii, 344); and of William Whewell, “Discussion of the question: — Are cause and effect successive or simultaneous?” (response to Herschel, Transactions of the Cambridge Philosophical Society, vii (1842), reprinted in The philosophy of the inductive sciences, 2nd edn (2 vols, London, 1847), ii, 634–46. Comte closely follows Lagrange's presentation; Comte, Philosophie positive (ref. 38), i, leçon 15, p. 235; leçon 16, pp. 251–2; leçon 17, pp. 277–80.

Mill , Logic (ref. 32), vii, 315–22, 464–83, 513–14 (quotation).

Mill , Logic (ref. 32), vii, 347; viii, 899, 913. J. S. Mill to John Sterling, 24 May 1832, Earlier letters (ref. 27), xii, 101.

Mill , Logic (ref. 32), viii, 926–7. See also Political economy (ref. 34), ii, 107–15 on the productiveness of labour in relation to intellectual and moral education.

Mill , Logic (ref. 32), viii, 921–2, 926–7.

This distinction, which Timothy Lenoir pointed out to me, is important retrospectively in categorizing theories of evolution, even though Comte and Nichol, for example, used the terms interchangeably in reference to the nebular hypothesis.

Hollander , Economics of J. S. Mill (ref. 34), i, 165. I thank Margaret Schabas for a preprint of her paper, “John Stuart Mill on mathematical economics”, which describes Mill's ambivalence to attempts to mathematize economics but argues that he nevertheless espoused views close to those of William Stanley Jevons in 1871.

Mill , Logic (ref. 32), viii, 901, 904. In the latter, Mill is quoting himself from 1834, “Miss Martineau's summary of political economy”, 319; Collected works (ref. 27), iv, 225–6, where he also charged political economists with “revolv[ing] in their eternal circle of landlords, capitalists, and labourers”. See also Political economy (ref. 34), iii, 705. I have not taken up Mill's distinction between laws of production, which like physical laws are everywhere and always the same and depend on permanent causes, and laws of distribution, which are variable and depend on circumstances. Under constant cultural conditions the two causal factors explain the statics of political economy, while under changing conditions they should explain dynamics. Mill devotes his short Book IV to the latter subject, Political economy, iii, 705–96; definitions in ii, 199–200; iii, 705; discussion in Hollander, Economics of J. S. Mill (ref. 34), i, 188–91, 216–23, and passim.

Schaffer Simon , “Charles Babbage and the religion of the computer”, unpublished. Babbage Charles , The ninth Bridgewater treatise, a fragment (1837), 2nd edn (London, 1838), 48–49.

Mill , Political economy (ref. 34), ii, 100–7, on p. 106; iii, 706. Babbage Charles , On the economy of machinery and manufactures (1832), 4th edn (London, 1835; reprinted New York, 1971), 156. The book saw three editions in its first year. It was considerably revised in the second edition, with new chapters on money, profit sharing, and the effect of machinery on labour.

Babbage , Machinery and manufactures (ref. 48), 169–202, p. 175.

Babbage , Machinery and manufactures (ref. 48), 191–5. Schaffer, “Babbage and the religion of the computer” gives a rich interpretation of Babbage's calculating engines in relation to political economy and religion. See also, on the context of Babbage's study of economy, Hyman Anthony , Charles Babbage: Pioneer of the computer (Oxford, 1982), 43–44, 103–22; and on the mathematical and mechanical design of the engines, Dubbey J. M. , The mathematical work of Charles Babbage (Cambridge, 1978), 173–219.

Babbage , Machinery and manufactures (ref. 48), 195–202. Dubbey , Mathematical work (ref. 50), 199. Hyman , Babbage (ref. 50), 166–8.

Babbage , Machinery and manufactures (ref. 48), 16–18. The general term ‘engine’ as I define it here does not appear in Babbage's formal classification of machines but encompasses his metaphorical usage with respect to the calculating engine and manufacturing engines (pp. 230, 283) as well as his literal usage with respect to “engines for producing power, such as wind-mills, water-mills, and steam-engines” (p. 198).

Babbage , Machinery and manufactures (ref. 48), 4, 254, 270, 339 (capital); 21, 231 (flywheel); 128, 310 (money); 27, 202 (governor).

Babbage , Machinery and manufactures (ref. 48), 16, 186, 201, 211–17.

Babbage , Machinery and manufactures (ref. 48), 49–50.

Babbage , Machinery and manufactures (ref. 48), 35, 64, 159, 215, 245, 277. Quotation from Charles Babbage, History of the invention of the calculating engines, 10, Buxton papers, Museum for the History of Science, Oxford; in Hyman, Babbage (ref. 50), 49.

Babbage , Machinery and manufactures (ref. 48), 5, 216, 227–9, 253.

Babbage , Machinery and manufactures (ref. 48), 285, 386–8.

[ Babbage Charles Herschel J. F. W. ], “Preface”, Memoirs of the Analytical Society, 1813 (Cambridge, 1813), p. xxi; photoreproduction in Schweber S. S. (ed.), Aspects of the life and thought of Sir John Frederick Herschel, i (New York, 1981).

Schaffer , “Babbage and the religion of the computer”. Babbage , Bridgewater treatise (ref. 47), 33–49.

Babbage , Machinery and manufactures (ref. 48), 160–3.

Gordon Lewis , “On dynamometrical apparatus; or, the measurement of the mechanical effect of moving powers”, Proceedings of the Philosophical Society of Glasgow, i (1841–44), 41–42. On the Regius chairs see Smith Crosbie Wise M. Norton , Energy and Empire: A biographical study of Lord Kelvin (Cambridge, 1989), ch. 2.

Poisson S. D. , Traité de mécanique (2 vols, Paris, 1833), ii, 747, 751. On French engineering mechanics see Grattan-Guinness Ivor , “Work for the workers: Advances in engineering mechanics and instruction in France, 1800–1830”, Annals of science, xli (1984), 1–33.

Whewell William , The mechanics of engineering (Cambridge, 1841), pp. iii–vi, where “fundamental ideas” are implicit.

Whewell , Mechanics of engineering (ref. 64), 145, vii.

Whewell , Mechanics of engineering (ref. 64), 148–9.

Although no general treatment of concepts of work has been published, I have found particularly suggestive: Sewell William H. Jr , Work and revolution in France: The language of labor from the old regime to 1848 (Cambridge, 1980), and Reddy William M. , The rise of market culture: The textile trade and French society, 1750–1900 (Cambridge, 1984).

Whewell , Six lectures on political economy (ref. 9), 5–19.

Whewell , Mechanics of engineering (ref. 64), 155–8.

Babbage , Machinery and manufactures (ref. 48), 217–18.

Babbage , Machinery and manufactures (ref. 48), 235–6.

Whewell , Mechanics of engineering (ref. 64), 159.

Whewell , Mechanics of engineering (ref. 64), 216.

Whewell , Mechanics of engineering (ref. 64), 173.

Whewell , Bridgewater treatise (ref. 11), 95.

Whewell , Mechanics of engineering (ref. 64), 173.

Whewell , Bridgewater treatise (ref. 11), 376. Schaffer , “Babbage and the religion of the computer” gives another example of the amoral character of “trains” of mechanism for Whewell, from his Of a liberal education in general, and with particular reference to the leading studies of the University of Cambridge (London, 1845), 40–41, where analytic mathematics, as opposed to geometry, carries one along “as in a railroad carriage, entering it at one station, and coming out of it at another, without having any choice in our progress in the intermediate space”.

Laplace , Essay (ref. 14), pp. cxi–cxii.

Herschel J. F. W. , A treatise on astronomy (London, 1833), 308–9. Thomson James Sr , “Introductory lecture at Glasgow College, 6 November 1832”, Queens University Library, Belfast.

Schaffer , “The nebular hypothesis and the science of progress” (ref. 28). Nichol J. P. , Views of the architecture of the heavens, in a series of letters to a lady, 3rd edn (Edinburgh, 1839), p. ix. This is the second volume, and centrepiece, published first (1838).

Nichol J. P. , The phenomena and order of the solar system (Edinburgh, 1838), 205–6; Architecture (ref. 80), 154, also 189.

Nichol , Phenomena and order (ref. 81), 174–5, 195, 204; Architecture (ref. 80), 156.

Nichol , Phenomena and order (ref. 81), 145–6, 172–4, 190. Given this scheme it is not surprising that when in 1844 Robert Chambers published anonymously his speculations on the evolution of species, the infamous Vestiges of creation, drawing on Nichol's nebular hypothesis, it was widely regarded as another in Nichol's series.

Nichol , Architecture (ref. 80), 174, 187–8, 198. Cf. Laplace on constant forces and chaos, Part One of this paper, at ref. 49.

Nichol , Architecture (ref. 80), 198, 209–10.

Nichol , Phenomena and order (ref. 81), 186, 191–4.

Thompson S. P. , The life of William Thomson, Baron Kelvin of Largs (2 vols, London, 1910), i, 9–14. Fourier Joseph , The analytical theory of heat (Paris, 1822); idem, “Extrait d'un mémoire sur le refroidissement séculaire du globe terrestre”, Annales de chimie et de physique, xiii (1820), 418–38; idem, “Remarques générales sur les températures du globe terrestre et des especes planétaires”, Annales de chimie et de physique, xxvii (1824), 136–67.

For the Cambridge geological style, especially ‘physical geology’ and ‘dynamical geology’ discussed below, see Smith Crosbie , “William Hopkins and the shaping of dynamical geology; 1830–1860”, The British journal for the history of science, xxii (1989), 27–52; idem, “Geologists and mathematicians: The rise of physical geology”, in Harman P. M. (ed.), Wranglers and physicists: Studies on Cambridge mathematical physics in the nineteenth century (Manchester, 1985), 49–83.

Hopkins William , “Researches in physical geology”. Transactions of the Cambridge Philosophical Society, vi (1835), 184; idem, “An abstract of a memoir on physical geology, with a further exposition of certain points connected with the subject”, Philosophical magazine, viii (1836), 227–36; 272–81; 357–66. The two magnificent new books on British geology by Rudwick Martin J. S. , The great Devonian controversy: The shaping of scientific knowledge among gentlemanly specialists (Chicago, 1985), and Secord James A. , Controversy in Victorian geology: The Cambrian-Silurian dispute (Princeton, 1986), leave me uncertain about the relation of physical or dynamical geology (related to natural philosophy and mathematics) to stratigraphic geology (related to natural history). Both of these works downplay the theoretical concerns of professional geologists with causal dynamics and demonstrate their predominant concern with the practices of rock-hammering and of establishing empirically the order of the British rocks. Nevertheless, Rudwick especially shows that a major transition took place in the 1830s which subtly changed the former ordering of strata according to what type of rock was above what other type, which was only implicitly a temporal ordering, to a definite ordering in time judged by fossil remains (pp. 448–50). This transition seems to mirror in the realm of natural history the transition I have been largely concerned with in natural philosophy and political economy. Rudwick himself notes that the same person often carried on these different activities in parallel (p. 45). I suspect that a thorough study of the differences of natural history from natural philosophy in the 1830s — Intellectually, professionally, and socially — Would reveal interestingly different conceptions of temporality in the two areas, not simply as a reflection of data versus theory but of different conceptions of explanation, which is another of Rudwick's points. Analogous differences would likely appear, for example, between statisticians and political economists. If so, I should be using a more encompassing term than ‘dynamics’ in relation to temporality in nature.

Whewell William , “Principles of geology … by Charles Lyell … Vol. I”, The British critic, quarterly theological review, and ecclesiastical record, ix (1831), 180–206, p. 195; idem, “Principles of geology … by Charles Lyell… Vol. II”, The quarterly review, xlvii (1832), 103–32, p. 107n.

Whewell , “Principles, Vol. I” (ref. 90), 202–3.

Whewell , “Principles, Vol. I” (ref. 90), 203–4; “Principles, Vol. II” (ref. 90), 125–6.

Whewell , “Principles, Vol. II” (ref. 90), 112–13.

Whewell William , “Report on the recent progress and present condition of the mathematical theories of electricity, magnetism, and heat”, Report of the British Association for the Advancement of Science meeting at Dublin in 1835 (London, 1836), 1–34, p. 27. For extended discussion of the character of Fourier's theory and its reception in Britain see Smith Wise , Energy and empire (ref. 62), ch. 6.

Daston Lorraine J. , “The physicalist tradition in early nineteenth century French geometry”, Studies in the history and philosophy of science, xvii (1986), 269–95. Grattan-Guinness, “Work for the workers” (ref. 63).

Whewell William , An elementary treatise on mechanics: Designed for the use of students in the university , 5th edn (Cambridge, 1836), pp. vi, 138–61 (laws of motion). Whewell's complaints appear already in “On the principles of dynamics, particularly as stated by French writers”, The Edinburgh journal of science, viii (1828), 27–38, and achieved mature elaboration in his “On the nature of the truth of the laws of motion”, Transactions of the Cambridge Philosophical Society, v (1835), 149–72. For extended discussion see Fisch Menachem , “Necessary and contingent truth in William Whewell's antithetical theory of knowledge”, Studies in history and philosophy of science, xvi (1985), 275–314; idem, “A philosopher's coming of age — A study in erotetic intellectual history”, in Fisch Menachem Schaffer Simon (eds), William Whewell — a composite portrait — studies of his life, work, and influence (Oxford, forthcoming); also Smith Wise , Energy and empire (ref. 62), ch. 11.

Smith Wise , Energy and empire (ref. 62), chs 6–8, 11, and Smith , “Hopkins and the shaping of dynamical geology” (ref. 88).

Gregory : “a considerable Whig (both in mathematics and politics)”; Smith: “my dearest radical Archy”; Ellis: “he … always professed himself a Whig”; Thomson: Son of “a most pestilent Whig”. William Thomson to Dr James Thomson, February or March 1842, Kelvin Collection, T201, University Library, Cambridge. Joanna Smith to Archibald Smith, 8 January 1835, TD 1/715, Smith papers, Strathclyde regional archives. Harvey Goodwin, “Biographical momoir”, in Walton William (ed.), Mathematical and other writings of R. L. Ellis (Cambridge, 1863), p. xvii. Allan Maconochie to Dr James Thomson, 22 June 1846, in Thompson, Life (ref. 87), i, 182–3. For the character and context of the calculus of operations in relation to natural philosophy see Smith Wise , Energy and empire (ref. 62), ch. 6.

Again, see Schaffer , “Charles Babbage and the religion of the computer”.

ane Herschel Babbage , “Preface”, Memoirs of the Analytical Society (ref. 59), p. ii. Quotation and useful discussion, if whiggish and hagiographic, in Dubbey , Mathematical work of Charles Babbage (ref. 50), 100–6, from Charles Babbage, “The philosophy of analysis”, an unpublished series of essays held in the British Museum, Additional Manuscripts 37202, and Peacock George , A treatise on algebra (Cambridge, 1830), pp. xviii–xix.

Richards J. L. , “The art and science of British algebra: A study in the perception of mathematical truth”, Historia mathematica, vii (1980), 343–65, and “Augustus de Morgan, the history of mathematics and the foundations of algebra”, Isis, lxxviii (1987), 7–30, discusses the principle of equivalent forms as interpreted by Peacock and Whewell and contrasts Whewell's nativism with Augustus de Morgan's progressive empiricism (below). She emphasizes what most historians of mathematics have missed, that the symbolic algebra of operations was not the abstract algebra of modern theory. All sides in the British debate agreed on either an intuitive or an empirical foundation for mathematics. Babbage Charles , “Observations on the analogy which subsists between the calculus of functions and other branches of analysis”. Philosophical transactions, cvii (1817), 197–216; “Philosophy of analysis” (ref. 100), 5. Dubbey , Mathematical work of Charles Babbage (ref. 50), 77. Cf. Condillac on the known and the unknown in Part One, at ref. 20.

Babbage Herschel , “Preface”, Memoirs of the Analytical Society (ref. 59), p. xvi; Babbage Charles , “An essay towards the calculus of functions, Part I”, Philosophical transactions, cv (1815), 389–423, p. 389.

Babbage Charles , Passages from the life of a philosopher (1864) (New York, 1969), 435.

Gregory D. F. , “On the solution of linear differential equations with constant coefficients”, Cambridge mathematical journal, i (1839), 22–32. Boole George , “On the integration of linear differential equations with constant coefficients”, Cambridge mathematical journal, ii (1841), 114–19.

Gregory D. F. , “On the elementary principles of the application of algebraical symbols to geometry”, Cambridge mathematical journal, ii (1841), 1–9.

Cayley Arthur , “On the geometrical representation of the motion of a solid body”, Cambridge and Dublin mathematical journal, i (1846), 164–7, epitomizes a “kinematical theorem”.

Ellis R. L. , “The course of mathematical studies”, in Walton (ed.), Mathematical and other writings (ref. 98), 417–27, 423n, from Ellis's testimony to the Commission investigating the Cambridge curriculum in 1852. Richards J. L. , “Projective geometry and mathematical progress in mid-Victorian Britain”, Studies in history and philosophy of science, xvii (1986), 297–395, p. 314, discusses the relation of ‘the new geometry’ to the intuitive and generative perspective of projective geometry, as developed especially by Cayley and Sylvester. See Daston , “Physicalist tradition” (ref. 95), for the French background.

Babbage Charles , “An essay towards the calculus of functions. Part II”, Philosophical transactions, cvi (1816), 179–256, p. 197.

Herschel J. F. W. , “Presidential address”, Report of the British Association for the Advancement of Science, xv (1835), pp. xxvii–xliv, reprinted in Essays (ref. 39), 634–82, pp. 638–9. Thomson William , “Presidential address to the British Association”, in his Popular lectures and addresses (3 vols, London, 1889–94), ii, 138–9, my emphasis.

de Morgan Augustus to Herschel J. F. W. , 28 May 1845, in de Morgan Sophie , Memoir of Augustus de Morgan (London, 1882), 150–1. Richards , “Augustus de Morgan, the history of mathematics, and the foundations of algebra” (ref. 101).

de Morgan Augustus , Formal logic, or, the calculus of inference, necessary and probable (London, 1847).

Boole George , The mathematical analysis of logic: Being an essay towards a calculus of deductive reasoning (Cambridge, 1847), 9, 13. Laita L. M. , “Influences on Boole's logic: The controversy between William Hamilton and Augustus de Morgan”, Annals of science, xxxvi (1979), 45–65; idem, “Boolean logic and its extra-logical sources: The testimony of Mary Everest Boole”, History and philosophy of logic, i (1980), 37–60. Boole George , An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities (London, 1854).

Hankins Thomas L. , Sir William Rowan Hamilton (Baltimore, 1980).