The principles of science

by William Stanley Jevons

FOOTNOTES:

[1] Since the above was written Mr. Harley has read an account of Stanhope’s logical remains at the Dublin Meeting (1878) of the British Association. The paper will be printed in Mind. (Note added November, 1878.)

[2] Leibnitii Opera Philosophica quæ extant. Erdmann, Pars I. Berolini, 1840, p. 94.

[3] Erdmann, p. 102.

[4] Ibid. p. 98.

[5] Erdmann, p. 100.

[6] Fifth Edition, 1860, p. 158.

[7] Section 120.

[8] See his “Remarks on Boole’s Mathematical Analysis of Logic.” Report of the 36th Meeting of the British Association, Transactions of the Sections, pp. 3–6.

[9] Hamilton’s Lectures, vol. iv. p. 319.

[10] Ibid. p. 326.

[11] Pure Logic, or the Logic of Quality apart from Quantity; with Remarks on Boole’s System, and on the Relation of Logic and Mathematics. London, 1864, p. 3.

[12] La Philosophie Positive, Mai-Juin, 1877, tom. xviii. p. 456.

[13] Inventum Novum Quadrati Logici, &c., Gissæ Hassorum, 1714, 8vo.

[14] See Ueberweg’s System of Logic, &c., translated by Lindsay, p. 302.

[15] Since the above was written M. Liard has republished this exposition as one chapter of an interesting and admirably lucid account of the progress of logical science in England. After a brief but clear introduction, treating of the views of Herschel, Mill, and others concerning Inductive Logic, M. Liard describes in succession the logical systems of George Bentham, Hamilton, De Morgan, Boole, and that contained in the present work. The title of the book is as follows:—Les Logiciens Anglais Contemporains. Par Louis Liard, Professeur de Philosophie à la Faculté des Lettres de Bordeaux. Paris: Librairie Germer Baillière. 1878. (Note added November, 1878.)

[16] Spectator, September 19, 1874, p. 1178. A second portion of the review appeared in the same journal for September 26, 1874, p. 1204.

[17] Mind: a Quarterly Review of Psychology and Philosophy. No. II. April 1876. Vol. I. p. 206.

[18] Portions of this work have already been published in my articles, entitled “John Stuart Mill’s Philosophy Tested,” printed in the Contemporary Review for December, 1877, vol. xxxi. p. 167, and for January and April, 1878, vol. xxxi. p. 256, and vol. xxxii. p. 88. (Note added in November, 1878.)

[19] Mind, vol. i. p. 222.

[20] Fortnightly Review, New Series, April 1875, p. 480. Lecture reprinted by the Sunday Lecture Society, p. 24.

[21] Sir W. Thomson’s words are as follows (Cambridge Mathematical Journal, Nov. 1842, vol. iii. p. 174). “When x is negative, the state represented cannot be the result of any possible distribution of temperature which has previously existed.” There is no limitation in the sentence to the laws of conduction, but, as the whole paper treats of the results of conduction in a solid, it may no doubt be understood that there is a tacit limitation. See also a second paper on the subject in the same journal for February, 1844, vol. iv. p. 67, where again there is no expressed limitation.

[22] Pp. 25–26. The parentheses are in the original, and show Professor Tait’s corrections in the verbatim reports of his lectures. The subject is treated again on pp. 168–9.

[23] Theory of Heat 1871, p. 245.

[24] The Senses and the Intellect, Second Ed., pp. 5, 325, &c.

[25] Max Müller, Lectures on the Science of Language, Second Series, vol. ii. p. 63; or Sixth Edition, vol. ii. p. 67. The view of the etymological meaning of “intellect” is given above on the authority of Professor Max Müller. It seems to be opposed to the ordinary opinion, according to which the Latin intelligere means to choose between, to see a difference between, to discriminate, instead of to unite.

[26] Hartley on Man, vol. i. p. 359.

[27] Principles of Psychology, Second Ed., vol. ii. p. 86.

[28] Pure Logic, or the Logic of Quality apart from Quantity, 1864, pp. 10, 16, 22, 29, 36, &c.

[29] Brewster, Treatise on New Philosophical Instruments, p. 273. Concerning this method see also Whewell, Philosophy of the Inductive Sciences, vol. ii. p. 355; Tomlinson, Philosophical Magazine, Fourth Series, vol. xl. p. 328; Tyndall, in Youmans’ Modern Culture, p. 16.

[30] Formal Logic, p. 38.

[31] Hallam’s Literature of Europe, First Ed., vol. ii. p. 444.

[32] Outline of a New System of Logic, London, 1827, pp. 133, &c.

[33] An Investigation of the Laws of Thought, pp. 27, &c.

[34] Formal Logic, pp. 82, 106. In his later work, The Syllabus of a New System of Logic, he discontinued the use of the sign.

[35] Principles of Psychology, Second Ed., vol. ii. pp. 54, 55.

[36] Pure Logic, or the Logic of Quality, p. 14.

[37] Pure Logic, pp. 18, 19.

[38] Ueberweg’s System of Logic, transl. by Lindsay, pp. 442–446, 571, 572. The anticipations of the principle of substitution to be found in the works of Leibnitz, Reusch, and perhaps other German logicians, will be noticed in the preface to this second edition.

[39] Substitution of Similars (1869), p. 9.

[40] Port-Royal Logic, transl. by Spencer Baynes, pp. 212–219. Part III. chap. x. and xi.

[41] Description of a Notation for the Logic of Relatives, resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic. By C. S. Peirce. Memoirs of the American Academy, vol. ix. Cambridge, U.S., 1870.

[42] On the Syllogism No IV., and on the Logic of Relations. By Augustus De Morgan. Transactions of the Cambridge Philosophical Society, vol. x. part ii., 1860.

[43] Observations on Boole’s Laws of Thought. By the late R. Leslie Ellis; communicated by the Rev. Robert Harley, F.R.S. Report of the British Association, 1870. Report of Sections, p. 12. Also, On Boole’s Laws of Thought. By the Rev. Robert Harley, F.R.S., ibid. p. 14.

[44] Jevons’ Elementary Lessons in Logic, pp. 41–43; Pure Logic, p. 6. See also J. S. Mill, System of Logic, Book I. chap. ii. section 5, and Shedden’s Elements of Logic, London, 1864, pp. 14, &c. Professor Robertson objects (Mind, vol. i. p. 210) that I confuse singular and proper names; if so, it is because I hold that the same remarks apply to proper names, which do not seem to me to differ logically from singular names.

[45] Professor Robertson has criticised my introduction of “Substantial Terms” (Mind, vol. i. p. 210), and objects, perhaps correctly, that the distinction if valid is extra-logical. I am inclined to think, however, that the doctrine of terms is, strictly speaking, for the most part extra-logical.

[46] Mathematical Analysis of Logic, Cambridge, 1847, p. 17. An Investigation of the Laws of Thought, London, 1854, p. 31.

[47] Pure Logic, p. 15.

[48] “Velut si dicam, Sol, Sol, Sol, non tres soles effecerim, sed uno toties prædicaverim.”

[49] Book i., Part iv., Section 5.

[50] Laws of Thought, p. 29. It is pointed out in the preface to this Second Edition that Leibnitz was acquainted with the Laws of Simplicity and of Commutativeness.

[51] Prior Analytics, i. cap. xxvii. 3.

[52] Encyclopædia Britannica, Eighth Ed. art. Logic, sect. 37, note. 8vo. reprint, p. 79.

[53] De Morgan, On the Root of any Function. Cambridge Philosophical Transactions, 1867, vol. xi. p. 25.

[54] Syllabus of a proposed System of Logic, §§ 122, 123.

[55] Elementary Lessons in Logic, p. 86.

[56] Outline of the Laws of Thought, § 87.

[57] Treatise on Natural Philosophy, vol. i. p. 161.

[58] Treatise on Natural Philosophy, vol. i. p. 6.

[59] Todhunter’s Plane Co-ordinate Geometry, chap. ii. pp. 11–14.

[60] An explanation of this and other technical terms of the old logic will be found in my Elementary Lessons in Logic, Sixth Edition, 1876; Macmillan.

[61] Elementary Lessons in Logic, pp. 67, 79.

[62] Pure Logic, p. 19.

[63] An Outline of the Necessary Laws of Thought, Fifth Ed. p. 161.

[64] Mansel’s Aldrich, p. 103, and Prolegomena Logica, p. 221.

[65] Elements of Logic, Book II. chap. iv. sect. 4.

[66] Aldrich, Artis Logicæ Rudimenta, p. 104.

[67] Examination of Sir W. Hamilton’s Philosophy, pp. 452–454.

[68] Pure Logic, pp 76, 77.

[69] Pure Logic, p. 65. See also the criticism of this point by De Morgan in the Athenæum, No. 1892, 30th January, 1864; p. 155.

[70] Boole’s Laws of Thought, p. 106. Jevons’ Pure Logic, p. 69.

[71] On the Syllogism, No. iii. p. 12. Camb. Phil. Trans. vol. x, part i.

[72] See Horsley, Philosophical Transactions, 1772; vol. lxii. p. 327. Montucla, Histoire des Mathematiques, vol. i. p. 239. Penny Cyclopædia, article “Eratosthenes.”

[73] Euclid, Book x. Prop. 117.

[74] Philosophical Magazine, December 1852; Fourth Series, vol. iv. p. 435, “On Indirect Demonstration.”

[75] Philosophical Magazine, Dec. 1852; p. 437.

[76] Mind; a Quarterly Review of Psychology and Philosophy; October, 1876, vol. i. p. 487.

[77] Whewell, History of the Inductive Sciences, vol. i. p. 222.

[78] Formal Logic, p. 124. As Professor Croom Robertson has pointed out to me, the second and third premises may be thrown into a single proposition, D = DeBC ꖌ DEbc.

[79] Pp. 55–59, 81–86.

[80] See his work called The Process of Thought adapted to Words and Language, together with a Description of the Relational and Differential Machines. Also Philosophical Transactions, [1870] vol. 160, p. 518.

[81] Philosophical Transactions [1870], vol. 160, p. 497. Proceedings of the Royal Society, vol. xviii. p. 166, Jan. 20, 1870. Nature, vol, i. p. 343.

[82] Syllabus of a proposed system of Logic, §§ 57, 121, &c. Formal Logic, p. 66.

[83] Lectures on Metaphysics, vol. iv. p. 369.

[84] Bowen, Treatise on Logic, Cambridge, U.S., 1866; p. 362.

[85] The contents of this and the following section nearly correspond with those of a paper read before the Manchester Literary and Philosophical Society on December 26th, 1871. See Proceedings of the Society, vol. xi. pp. 65–68, and Memoirs, Third Series, vol. v. pp. 119–130.

[86] Proceedings of the Manchester Literary and Philosophical Society, 6th February, 1877, vol. xvi., p. 113.

[87] Montucla. Histoire des Mathématiques, vol. iii. p. 373.

[88] British Quarterly Review, No. lxxxvii, July 1866.

[89] Mind, October 1876, vol. i. p. 484.

[90] Pure Logic, Appendix, p. 82, § 192.

[91] Elementary Lessons in Logic (Macmillan), p. 123. It is pointed out in the preface to this Second Edition, that the views here given were partially stated by Leibnitz.

[92] Syllabus of a Proposed System of Logic, p. 29.

[93] It has been pointed out to me by Mr. C. J. Monroe, that section 14 (p. 339) of this paper is erroneous, and ought to be cancelled. The problem concerning the number of paupers illustrates the answer which should have been obtained. Mr. A. J. Ellis, F.R.S., had previously observed that my solution in the paper of De Morgan’s problem about “men in the house” did not answer the conditions intended by De Morgan, and I therefore give in the text a more satisfactory solution.

[94] Montucla, Histoire, &c., vol. iii. p. 388.

[95] Wallis, Of Combinations, &c., p. 119.

[96] James Bernoulli, De Arte Conjectandi, translated by Baron Maseres. London, 1795, pp. 35, 36.

[97] Arithmeticæ Theoria. Ed. Amsterd. 1704. p. 517.

[98] Rees’s Cyclopædia, art. Cipher.

[99] Œuvres Complètes de Pascal (1865), vol. iii. p. 302. Montucla states the name as De Gruières, Histoire des Mathématiques, vol. iii. p. 389.

[100] Histoire des Mathématiques, vol. iii. p. 378.

[101] Bernoulli, De Arte Conjectandi, translated by Francis Maseres. London, 1795, p. 75.

[102] Wallis’s Algebra, Discourse of Combinations, &c., p. 109.

[103] Œuvres Complètes, vol. iii. p. 251.

[104] See also Galton’s Lecture at the Royal Institution, 27th February, 1874; Catalogue of the Special Loan Collection of Scientific Instruments, South Kensington, Nos. 48, 49; and Galton, Philosophical Magazine, January 1875.

[105] Wallis, Of Combinations, p. 116, quoting Vossius.

[106] Philosophical Transactions (1803), vol. xciii. p. 193.

[107] Hofmann’s Introduction to Chemistry, p. 36.

[108] Works, edited by Shaw, vol. i. pp. 141–145, quoted in Rees’s Encyclopædia, art. Cipher.

[109] Nature, vol. i. p. 553.

[110] Formal Logic, p. 172.

[111] Philosophical Magazine, 4th Series, vol. i. p. 355.

[112] Transactions of the Royal Society of Edinburgh, vol. xxi. part 4.

[113] Philosophical Magazine, 4th Series, vol. vii. p. 465; vol. viii. p. 91.

[114] Memoirs of the Manchester Literary and Philosophical Society, 3rd Series, vol. iv. p. 347.

[115] Letters on the Theory of Probabilities, translated by Downes, 1849, pp. 36, 37.

[116] Encyclopædia Metropolitana, art. Probabilities, p. 396.

[117] Elements of Logic, Book III. sections 11 and 18.

[118] Encyclopædia Metropolitana, art. Probabilities, p. 400.

[119] Philosophical Transactions (1767). Abridg. vol. xii. p. 435.

[120] Transactions of the Edinburgh Philosophical Society, vol. xxi. p. 375.

[121] Montucla, Histoire des Mathématiques, vol. iii. p. 386.

[122] Leibnitz Opera, Dutens’ Edition, vol. vi. part i. p. 217. Todhunter’s History of the Theory of Probability, p. 48. To the latter work I am indebted for many of the statements in the text.

[123] Positive Philosophy, translated by Martineau, vol. ii. p. 120.

[124] System of Logic, bk. iii. chap. 18, 5th Ed. vol. ii. p. 61.

[125] Montucla, Histoire, vol. iii. p. 405; Todhunter, p. 263.

[126] Essay concerning Human Understanding, bk. iv. ch. 14. § 1.

[127] Philosophical Magazine, 4th Series, vol. i. p. 354.

[128] Essay concerning Human Understanding, bk. ii. chap. xxi.

[129] De Rerum Natura, bk. ii. ll. 216–293.

[130] Cambridge Philosophical Transactions (1830), vol. iii. pp. 369–372.

[131] Observations on the Nature and Tendency of the Doctrine of Mr. Hume, concerning the Relation of Cause and Effect. Second ed. p. 44.

[132] Ibid. p. 97.

[133] System of Logic, bk. II. chap, iii.

[134] Inductive Logic, pp. 13, 14.

[135] Bain, Deductive Logic, pp. 208, 209.

[136] System of Logic. Introduction, § 4. Fifth ed. pp. 8, 9.

[137] Ibid. bk. II. chap. iii. § 5, pp. 225, &c.

[138] These are the figurate numbers considered in pages 183, 187, &c.

[139] Commercium Epistolicum. Epistola ad Oldenburgum, Oct. 24, 1676. Horsley’s Works of Newton, vol. iv. p. 541. See De Morgan in Penny Cyclopædia, art. “Binomial Theorem,” p. 412.

[140] Bk. ii. chap. iv.

[141] Philosophical Transactions (1866), vol. 146, p. 334.

[142] Budget of Paradoxes, p. 257.

[143] Proceedings of the Royal Society (1872–3), vol. xxi. p. 319.

[144] Life of Galileo, Society for the Diffusion of Useful Knowledge, p. 102.

[145] Professor Bowen has excellently stated this view. Treatise on Logic. Cambridge, U.S.A., 1866, p. 354.

[146] Roscoe’s Spectrum Analysis, 1st edit., p. 98.

[147] Euler’s Letters to a German Princess, translated by Hunter. 2nd ed., vol. ii. pp. 17, 18.

[148] Lavoisier’s Chemistry, translated by Kerr. 3rd ed., pp. 114, 121, 123.

[149] Euler’s Letters, vol. ii. p. 21.

[150] Lardner, Edinburgh Review, July 1834, p. 277.

[151] Mémoires par divers Savans, tom. vi.; quoted by Todhunter in his History of the Theory of Probability, p. 458.

[152] Poisson, Recherches sur la Probabilité des Jugements, Paris, 1837, pp. 82, 83.

[153] Kirchhoff’s Researches on the Solar Spectrum. First part, translated by Roscoe, pp. 18, 19.

[154] Edinburgh Review, No. 185, vol. xcii. July 1850, p. 32; Herschel’s Essays, p. 421; Transactions of the Cambridge Philosophical Society, vol. i. p. 43.

[155] Evans’ Ancient Stone Implements of Great Britain. London, 1872 (Longmans).

[156] Herschel, Outlines of Astronomy, 1849, p. 565; but Todhunter, in his History of the Theory of Probability, p. 335, states that the calculations do not agree with those published by Struve.

[157] Philosophical Transactions, 1767, vol. lvii. p. 431.

[158] Philosophical Magazine, 3rd Series, vol. xxxvii. p. 401, December 1850; also August 1849.

[159] History, &c., p. 334.

[160] Essai Philosophique, p. 57.

[161] Proceedings of the Royal Society; 20 January, 1870; Philosophical Magazine, 4th Series, vol. xxxix. p. 381.

[162] Principia, bk. ii. General scholium.

[163] Essai Philosophique, p. 55. Laplace appears to count the rings of Saturn as giving two independent movements.

[164] Lubbock, Essay on Probability, p. 14. De Morgan, Encyc. Metrop. art. Probability, p. 412. Todhunter’s History of the Theory of Probability, p. 543. Concerning the objections raised to these conclusions by Boole, see the Philosophical Magazine, 4th Series, vol. ii. p. 98. Boole’s Laws of Thought, pp. 364–375.

[165] Laplace, Essai Philosophique, pp. 55, 56.

[166] Chambers’ Astronomy, 2nd ed. pp. 346–49.

[167] Traité élémentaire du Calcul des Probabilités, 3rd ed. (1833), p. 148.

[168] Laws of Thought, pp. 368–375.

[169] De Morgan’s Essay on Probabilities, Cabinet Cyclopædia, p. 67.

[170] Essay on Probabilities, p. 128.

[171] J. S. Mill, System of Logic, 5th edition, bk. iii. chap. xviii. § 3.

[172] Todhunter’s History, pp. 472, 598.

[173] Todhunter’s History, pp. 378, 379.

[174] Philosophical Transactions, [1763], vol. liii. p. 370, and [1764], vol. liv. p. 296. Todhunter, pp. 294–300.

[175] Newton’s Opticks, Bk. I., Part ii. Prop. 3; Nature, vol. i. p. 286.

[176] Aristotle’s Metaphysics, xiii. 6. 3.

[177] Possunt autem omnes testes et uno annulo signare testamentum Quid enim si septem annuli una sculptura fuerint, secundum quod Pomponio visum est?—Justinian, ii. tit. x. 5.

[178] See Wills on Circumstantial Evidence, p. 148.

[179] Memoirs of the Royal Astronomical Society, vol. iv. p. 290, quoted by Lardner, Edinburgh Review, July 1834, p. 278.

[180] Baily, British Association Catalogue of Stars, pp. 7, 23.

[181] Outlines of Astronomy, 4th ed. sect. 781, p. 522. Results of Observations at the Cape of Good Hope, &c., p. 37.

[182] See De Morgan, Study of Mathematics, in U.K.S. Library, p. 81.

[183] Loomis, On the Aurora Borealis. Smithsonian Transactions, quoting Parry’s Third Voyage, p. 61.

[184] Watts’ Dictionary of Chemistry, vol. ii. p. 790.

[185] Philosophical Transactions, (1856) vol. 146, Part i. p. 297.

[186] Airy, On Tides and Waves, Encyclopædia Metropolitana, p. 345. Scott Russell, British Association Report, 1837, p. 432.

[187] Hugenii Cosmotheoros, pp. 117, 118. Laplace’s Système, translated, vol. i. p. 67.

[188] Grant’s History of Physical Astronomy, p. 129.

[189] Baily’s Account of Flamsteed, p. lix.

[190] Jamin, Cours de Physique, vol. i. p. 152.

[191] Faraday, Chemical Researches, p. 393.

[192] Proceedings of the Royal Society, 30th November, 1866.

[193] Herschel, Physical Geography, § 40.

[194] Principia, bk. iii. Prop. 37, Corollaries, 2 and 3. Motte’s translation, vol. ii. p. 310.

[195] Roscoe’s Spectrum Analysis, 1st ed. p. 296.

[196] Philosophical Transactions (1859), vol. cxlix. p. 94.

[197] Watts’ Dictionary of Chemistry, vol. ii. p. 393.

[198] Philosophical Transactions (1859), vol. cxlix. p. 119, &c.

[199] Baily’s Account of Flamsteed, pp. 378–380.

[200] Herschel’s Astronomy, § 817, 4th. ed. p. 553.

[201] Principia, bk. ii. Sect. 6. Prop. 31. Motte’s Translation, vol. ii. p. 107.

[202] Ibid. bk. i. Law iii. Corollary 6. Motte’s Translation, vol. i. p. 33.

[203] Thomson and Tait’s Natural Philosophy, vol. i. p. 333.

[204] Philosophical Transactions, (1856), vol. cxlvi. pp. 330, 331.

[205] First Annual Report of the Mint, p. 106.

[206] Jevons, in Watts’ Dictionary of Chemistry, vol. i. p. 483.

[207] British Association, Glasgow, 1856. Address of the President of the Mechanical Section.

[208] Pelicotetics, or the Science of Quantity; an Elementary Treatise on Algebra, and its groundwork Arithmetic. By Archibald Sandeman, M. A. Cambridge (Deighton, Bell, and Co.), 1868, p. 304.

[209] De Morgan’s Trigonometry and Double Algebra, p. 5.

[210] English Works of Thos. Hobbes, Edit. by Molesworth, vol. i. p. 95.

[211] Confessions, bk. xi. chapters 20–28.

[212] Sir G. C. Lewis gives many curious particulars concerning the measurement of time in his Astronomy of the Ancients, pp. 241, &c.

[213] Principia, bk. i. Scholium to Definitions. Translated by Motte, vol. i. p. 9. See also p. 11.

[214] Rankine, Philosophical Magazine, Feb. 1867, vol. xxxiii. p. 91.

[215] Treatise on Natural Philosophy, vol. i. p. 179.

[216] Proceedings of the Manchester Philosophical Society, 28th Nov. 1871, vol. xi. p. 33.

[217] The Elements of Natural Philosophy, part i. p. 119.

[218] See Harris’ Essay upon Money and Coins, part. ii. [1758] p. 127.

[219] Philosophical Magazine, (1868), 4th Series, vol. xxxvi. p. 32.

[220] Proceedings of the Royal Society, 20th June, 1872, vol. xx. p. 438.

[221] Kater’s Treatise on Mechanics, Cabinet Cyclopædia, p. 154.

[222] Grant’s History of Physical Astronomy, p. 156.

[223] Clerk Maxwell’s Theory of Heat, p. 79.

[224] Treatise on Electricity and Magnetism, vol. i. p. 3.

[225] Chemistry for Students, by A. W. Williamson. Clarendon Press Series, 2nd ed. Preface p. vi.

[226] Introduction to Chemistry, p. 131.

[227] Philosophical Transactions (1859), vol. cxlix. p. 884, &c.

[228] Théorie Analytique de la Chaleur, Paris; 1822, §§ 157–162.

[229] Tyndall’s Sound, 1st ed. p. 26.

[230] British Association, Cambridge, 1833. Report, pp. 484–490.

[231] Smithsonian Miscellaneous Collections, vol. xii., the Constants of Nature, part. i. Specific gravities compiled by F. W. Clarke, 8vo. Washington, 1873.

[232] J. W. L. Glaisher, Philosophical Magazine, 4th Series, vol. xlii. p. 421.

[233] Stokes, Philosophical Transactions (1852), vol. cxlii. p. 529.

[234] Admiralty Manual of Scientific Enquiry, 2nd ed. p. 299.

[235] Pouillet, Taylor’s Scientific Memoirs, vol. iv. p. 45.

[236] Baily’s Account of the Rev. John Flamsteed, p. 58.

[237] Jamin, Cours de Physique, vol. ii. pp. 15–28.

[238] Philosophical Magazine, 1851, 4th Series, vol. ii. passim.

[239] Hearn, Philosophical Transactions, 1847, vol. cxxxvii. pp. 217–221.

[240] The Correlation of Physical Forces, 3rd ed. p. 159.

[241] Collected Works of Sir H. Davy, vol. ii. pp. 12–14. Elements of Chemical Philosophy, p. 94.

[242] Nicholson’s Journal, vol. i. p. 241; quoted in Treatise on Heat, Useful Knowledge Society, p. 24.

[243] Clerk Maxwell, Theory of Heat, p. 228. Proceedings of the Manchester Philosophical Society, Nov. 26, 1867, vol. vii. p. 35.

[244] Leslie, Inquiry into the Nature of Heat, p. 10.

[245] Jevons, Watts’ Dictionary of Chemistry, vol. i. pp. 513–515.

[246] Philosophical Transactions, vol. li. p. 100.

[247] Philosophical Magazine, 3rd Series, vol. xxvi. p. 372.

[248] Greenwich Observations for 1866, p. xlix.

[249] Philosophical Transactions, 1856, p. 309.

[250] Penny Cyclopædia, art. Transit, vol. xxv. pp. 129, 130.

[251] Ibid. art. Observation, p. 390.

[252] Nature, vol. i. p. 85.

[253] Nature, vol. i. p 337. See references to the Memoirs describing the method.

[254] Principia, Book I. Law III. Corollary VI. Scholium. Motte’s translation, vol. i. p. 33.

[255] Graham’s Chemical Reports and Memoirs, Cavendish Society, pp. 247, 268, &c.

[256] Regnault’s Cours Elémentaire de Chimie, 1851, vol i. p. 141.

[257] Tyndall’s Faraday, pp. 114, 115.

[258] See, for instance, the Compensated Sympiesometer, Philosophical Magazine, 4th Series, vol. xxxix. p. 371.

[259] Grant, History of Physical Astronomy, pp. 146, 147.

[260] Quetelet, Sur la Physique du Globe, p. 174. Jamin, Cours de Physique, vol. i. p. 504.

[261] Baily’s Account of Flamsteed, p. 376.

[262] The Transit of Venus across the Sun, by Horrocks, London, 1859, p. 146.

[263] De Morgan, Supplement to the Penny Cyclopædia, art. Old Appellations of Numbers.

[264] Penny Cyclopædia, art. Mean.

[265] Jevons, Journal of the Statistical Society, June 1865, vol. xxviii, p. 296.

[266] Letters on the Theory of Probabilities, transl. by Downes, Part ii.

[267] Herschel’s Essays, &c. pp. 404, 405.

[268] On the Theory of Errors of Observations, Cambridge Philosophical Transactions, vol. x. Part ii. 416.

[269] Thomson and Tait, Treatise on Natural Philosophy, vol. i. p. 394.

[270] Essai Philosophique sur les Probabilités, pp. 49, 50.

[271] Grant, History of Physical Astronomy, p. 163.

[272] Gauss, Taylor’s Scientific Memoirs, vol. ii. p. 43, &c.

[273] Proceedings of the Royal Society, vol. xviii. p. 159 (Jan. 13, 1870). Philosophical Magazine (4th Series), vol. xxxix. p. 376.

[274] Airy On Tides and Waves, Encycl. Metrop. pp. 364*-366*.

[275] Outlines of Astronomy, 4th edition, § 538.

[276] Philosophical Magazine, 3rd Series, vol. xxxvii. p. 324.

[277] Letters on the Theory of Probabilities, by Quetelet, translated by O. G. Downes, Notes to Letter XXVI. pp. 286–295.

[278] On the Law of Facility of Errors of Observations, and on the Method of Least Squares, Memoirs of the Royal Astronomical Society, vol. xxxix. p. 75.

[279] Méthode des Moindres Carrés. Mémoires sur la Combinaison des Observations, par Ch. Fr. Gauss. Traduit en Français par J. Bertrand, Paris, 1855, pp. 6, 133, &c.

[280] De Morgan, Penny Cyclopædia, art. Least Squares.

[281] Edinburgh Review, July 1850, vol. xcii. p. 17. Reprinted Essays, p. 399. This method of demonstration is discussed by Boole, Transactions of Royal Society of Edinburgh, vol. xxi. pp. 627–630.

[282] Letters on the Theory of Probabilities, Letter XV. and Appendix, note pp. 256–266.

[283] Encke, On the Method of Least Squares, Taylor’s Scientific Memoirs, vol. ii. pp. 338, 339.

[284] Quetelet, Letters on the Theory of Probabilities, translated by Downes, Letter XIX. p. 88. See also Galton’s Hereditary Genius, p. 379.

[285] System of Logic, bk. iii. chap. 17, § 3. 5th ed. vol. ii. p. 56.

[286] Philosophy of the Inductive Sciences, 2nd ed. vol. ii. pp. 408, 409.

[287] Essay on Probability, Useful Knowledge Society, 1833, p. 41.

[288] Taylor’s Scientific Memoirs, vol. ii. p. 333.

[289] Philosophical Transactions, 1873, p. 83.

[290] Taylor’s Scientific Memoirs, vol. ii. pp. 330, 347, &c.

[291] Quetelet, Letters, &c. p. 116.

[292] Baily, Account of Flamsteed, p. 56.

[293] Gould’s Astronomical Journal, Cambridge, Mass., vol. ii. p. 161.

[294] Philadelphia (London, Trübner) 1863. Appendix, vol. ii. p. 558.

[295] Bakerian Lecture, Philosophical Transactions (1868), vol. clviii. p. 6.

[296] Results of Observations at the Cape of Good Hope, p. 283.

[297] The Logic of Chance, an Essay on the Foundations and Province of the Theory of Probability, with especial reference to its Logical Bearings and its Application to Moral and Social Science. (Macmillan), 1876.

[298] Gauss, translated by Bertrand, p. 25.

[299] Jamin, Cours de Physique, vol. ii. p. 60.

[300] Preliminary Discourse on the Study of Natural Philosophy, p. 77.

[301] Lavoisier’s Elements of Chemistry, translated by Kerr, 3rd ed. p. 148.

[302] Babbage, Economy of Manufactures, p. 194.

[303] System of the World, translated by Harte, vol. ii. p. 335.

[304] This curious phenomenon, which I propose to call pedesis, or the pedetic movement, from πηδόω, to jump, is carefully described in my paper published in the Quarterly Journal of Science for April, 1878, vol. viii. (N.S.) p. 167. See also Proceedings of the Literary and Philosophical Society of Manchester, 25th January, 1870, vol. ix. p. 78, Nature, 22nd August, 1878, vol. xviii. p. 440, or the Quarterly Journal of Science, vol. viii. (N.S.) p. 514.

[305] Maxwell, Theory of Heat, p. 301.

[306] Laplace, Essai Philosophique, p. 59. Todhunter’s History, pp. 491–494.

[307] Chambers’ Astronomy, 1st ed. p. 203.

[308] Essay on Probabilities, Cabinet Cyclopædia, p. 121.

[309] Philosophical Magazine, 4th Series (1867), vol. xxxiv. p. 64.

[310] See Notes to Measures of Double Stars, 1204, 1336, 1477, 1686, 1786, 1816, 1835, 1929, 2081, 2186, pp. 265, &c. See also Herschel’s Familiar Lectures on Scientific Subjects, p. 147, and Outlines of Astronomy, 7th ed. p. 285.

[311] Jevons, On the Cirrous Form of Cloud, Philosophical Magazine, July, 1857, 4th Series, vol. xiv. p. 22.

[312] Astronomy, 4th ed. p. 358.

[313] Babbage, Ninth Bridgewater Treatise, p. 67.

[314] Cuvier, Essay on the Theory of the Earth, translation, p. 61, &c.

[315] Murchison’s Siluria, 1st ed. p. 432.

[316] Darwin’s Fertilisation of Orchids, p. 48.

[317] Peacock, Algebre, vol. ii. p. 344.

[318] Ibid, p. 359. Serret, Algèbre Supérieure, 2nd ed. p. 304.

[319] Treatise on Optics, by Brewster, Cab. Cyclo. p. 117.

[320] Opticks, 3rd. ed. p. 25.

[321] Experimental Researches in Electricity, vol. i. pp. 133, 134.

[322] Ibid. vol i. pp. 127, 162, &c.

[323] Principia, bk. iii. Prop. vi. Corollary i.

[324] Lavoisier’s Chemistry, translated by Kerr, p. 103.

[325] Cuvier’s Animal Kingdom, introduction, pp. 1, 2.

[326] Experimental Researches in Electricity, vol. iii. p. 4.

[327] Philosophical Magazine, 4th Series, vol. ix. p. 327.

[328] Inquiry into the Nature of Heat, p. 95.

[329] Herschel, Preliminary Discourse, p. 161.

[330] System of Logic, bk. iii. chap. viii. § 4, 5th ed. vol. i. p. 433.

[331] Essayes of Natural Experiments made in the Accademia del Cimento. Englished by Richard Waller, 1684, p. 40, &c.

[332] Plateau, Taylor’s Scientific Memoirs, vol. iv. pp. 16–43.

[333] Philosophical Transactions [1826], vol. cxvi. pp. 388, 389. Works of Sir Humphry Davy, vol. v. pp. 1–12.

[334] National Review, July, 1861, p. 13.

[335] His published works are contained in The Edinburgh Physical and Literary Essays, vol. ii. p. 34; Philosophical Transactions [1753], vol. xlviii. p. 261; see also Morgan’s Papers in Philosophical Transactions [1785], vol. lxxv. p. 190.

[336] Edinburgh Journal of Science, vol. v. p. 79.

[337] Encyclopædia Metropolitana, art. Light, § 524; Herschel’s Familiar Lectures, p. 266.

[338] Talbot, Philosophical Magazine, 3rd Series, vol. ix. p. 1 (1836); Brewster, Transactions of the Royal Society of Edinburgh [1823], vol. ix. pp. 433, 455; Swan, ibid. [1856] vol. xxi. p. 411; Philosophical Magazine, 4th Series, vol. xx. p. 173 [Sept. 1860]; Roscoe, Spectrum Analysis, Lecture III.

[339] Balfour Stewart, Elementary Treatise on Heat, p. 192.

[340] British Association, Liverpool, 1870. Report on Rainfall, p. 176.

[341] Philosophical Magazine., Dec. 1861. 4th Series, vol. xxii. p. 421.

[342] Experimental Researches in Electricity, vol. iii. p. 84, &c.

[343] Lectures on Heat, p. 21.

[344] Baily, Memoirs of the Royal Astronomical Society, vol. xiv. pp. 29, 30.

[345] Grant, History of Physical Astronomy, p. 531.

[346] Philosophical Transactions, abridged by Lowthorp, 4th edition, vol. i. p. 202.

[347] Jevons in Watts’ Dictionary of Chemistry, vol. ii. pp. 936, 937.

[348] Discovery of Subterraneal Treasure. London, 1639, p. 48.

[349] Laplace, System of the World, translated by Harte, vol. ii. p. 322.

[350] Principia, bk. ii. sect. 6, Prop. xxxi. Motte’s translation, vol. ii. p. 108.

[351] Essayes of Natural Experiments, &c. p. 117.

[352] Hooke’s Posthumous Works, p. 182.

[353] Principia, bk. iii. Prop. vii. Corollary 1.

[354] Keill’s Introduction to Natural Philosophy, 3rd ed., London, 1733, pp. 48–54.

[355] Discovery of Subterraneal Treasure, 1639, p. 52.

[356] Elements of Inductive Logic, 1st edit. p. 175.

[357] Philosophical Transactions, vol. li. p. 138; abridgment, vol. xi. p. 355.

[358] See Bunsen and Roscoe’s researches, in Philosophical Transactions (1859), vol. cxlix. p. 880, &c., where they describe a constant flame of carbon monoxide gas.

[359] Humboldt’s Cosmos (Bohn), vol. i. p. 7.

[360] Gilbert, De Magnete, p. 109.

[361] Principia, bk. iii. Prop. vi.

[362] Philosophical Magazine, 3rd Series, vol. xxvi. p. 375.

[363] Opticks, 3rd edit. p. 159.

[364] Watts, Dictionary of Chemistry, vol. iii. p. 637.

[365] Faraday’s Life, by Bence Jones, vol. ii. p. 5.

[366] Preliminary Discourse, &c., p. 185.

[367] Philosophical Magazine, July, 1857, 4th Series, vol. xiv. p. 24.

[368] First Principles, 3rd edit. chap. x. p. 253.

[369] Laplace, System of the World, vol. i. pp. 50, 54, &c.

[370] Herschel’s Outlines of Astronomy, 4th edit. pp. 555–557.

[371] Humboldt’s Cosmos (Bohn), vol. iii. p. 229.

[372] Encyclopædia Metropolitana, art. Sound, § 323; Outlines of Astronomy, 4th edit., § 650. pp. 410, 487–88; Meteorology, Encyclopædia Britannica, Reprint, p. 197.

[373] Philosophical Transactions, (1739), vol. xli. p. 126.

[374] Principia, bk. iii. Prop. 15.

[375] Lockyer’s Lessons in Elementary Astronomy, p. 301.

[376] Treatise on Natural Philosophy, vol. i. pp. 337, &c.

[377] An Introduction to Natural Philosophy, 3rd edit. 1733, p. 5.

[378] Watts, Dictionary of Chemistry, vol. i. p. 455.

[379] Philosophical Transactions, (1866) vol. clvi. p. 809.

[380] Experimental Researches in Electricity, vol. i. p. 246.

[381] Hutton’s Mathematical Dictionary, vol. ii. pp. 287–292.

[382] Principia, bk. iii. Prop. 13.

[383] Jamin, Cours de Physique, vol. i. pp. 282, 283.

[384] Lloyd’s Lectures on the Wave Theory, pp. 22, 23.

[385] Tait’s Thermodynamics, p. 10.

[386] Lloyd’s Lectures on the Wave Theory, pp. 82, 83.

[387] Jamin, Cours de Physique, vol. i. pp. 283–288.

[388] Joule and Thomson, Philosophical Transactions, 1854, vol. cxliv. p. 337.

[389] The properties of a perfect gas have been described by Rankine, Transactions of the Royal Society of Edinburgh, vol. xxv. p. 561.

[390] Thomson and Tait’s Natural Philosophy, vol. i. p. 60.

[391] Challis, Notes on the Principles of Pure and Applied Calculation, 1869, p. 83.

[392] An Introduction to Physical Measurements, translated by Waller and Procter, 1873, p. 10.

[393] Cambridge Philosophical Transactions (1865), vol. xi. Part I.

[394] Sandeman, Pelicotetics, p. 214.

[395] The Science and Art of Arithmetic for the Use of Schools. (Whitaker and Co.)

[396] Principles of Approximate Calculations, by J. J. Skinner, C.E. (New York, Henry Holt), 1876.

[397] Leslie, Inquiry into the Nature of Heat, p. 505.

[398] System of Logic, bk. iii. chap. viii § 6.

[399] Laplace, System of the World, translated by Harte, vol. ii. p. 366.

[400] Chemical Reports and Memoirs, Cavendish Society, p. 294.

[401] Jamin, Cours de Physique, vol. ii. p. 38.

[402] On Tides and Waves, Encyclopædia Metropolitana, p. 366*.

[403] Encyclopædia Britannica, art. Meteorology. Reprint, §§ 152–156.

[404] Lagrange, Leçons sur le Calcul des Fonctions, 1806, p. 4.

[405] Haughton, Principles of Animal Mechanics, 1873, pp. 444–450. Jevons, Nature, 30th of June, 1870, vol. ii. p. 158. See also the experiments of Professor Nipher, of Washington University, St. Louis, in American Journal of Science, vol. ix. p. 130, vol. x. p. 1; Nature, vol. xi. pp. 256, 276.

[406] Jamin, Cours de Physique, vol. ii. p. 50.

[407] Philosophical Transactions, 1826, p. 544.

[408] Jamin, Cours de Physique, vol. ii. p. 24, &c.

[409] J. W. Strutt, On a correction sometimes required in curves professing to represent the connexion between two physical magnitudes. Philosophical Magazine, 4th Series, vol. xlii. p. 441.

[410] Herschel: Lacroix’ Differential Calculus, p. 551.

[411] Cours complet de Météorologie, Note A, p. 449.

[412] On the Calculation of Empirical Formulæ. The Messenger of Mathematics, New Series, No. 17, 1872.

[413] Watts’ Dictionary of Chemistry, vol. ii. p. 790.

[414] Quarterly Journal of the Chemical Society, vol. viii. p. 15.

[415] Results of Observations at the Cape of Good Hope, p. 293.

[416] Jamin, Cours de Physique, vol. ii. p. 138.

[417] Preliminary Discourse, &c., p. 152.

[418] Tyndall, On Cometary Theory, Philosophical Magazine, April 1869. 4th Series, vol. xxxvii. p. 243.

[419] See Philosophical Transactions, abridged by Lowthorp. 4th edit. vol. i. p. 130. I find that opinions similar to those in the text have been briefly expressed by De Morgan in his remarkable preface to From Matter to Spirit, by C.D., pp. xxi. xxii.

[420] Horrocks, Opera Posthuma (1673), p. 276.

[421] Young’s Works, vol. i. p. 593.

[422] Boyle’s Physical Examen, p. 84.

[423] Young’s Works, vol. i. p. 415.

[424] Familiar Lectures on Scientific Subjects, p. 282.

[425] Young’s Works, vol. i. p. 417.

[426] Principia, bk. iii. Prop. 43. General Scholium.

[427] Ibid. bk. ii. Sect. ix. Prop. 53.

[428] Brewster’s Life of Newton, 1st edit. chap. vii.

[429] Discourse on the Study of Natural Philosophy, p. 151.

[430] Ibid. p. 229.

[431] Novum Organum, bk. ii. Aphorism 36.

[432] Principia, bk. i. Sect. xiv. Prop. 96. Scholium. Opticks, Prop. vi. 3rd edit. p. 70.

[433] Airy’s Mathematical Tracts, 3rd edit. pp. 286–288.

[434] Jamin, Cours de Physique, vol. iii. p. 372.

[435] Young’s Lectures on Natural Philosophy (1845), vol. i. p. 361.

[436] Paris, Life of Davy, p. 274.

[437] Opus Majus. Edit. 1733. Cap. x. p. 460.

[438] Newton’s Opticks. Third edit. p. 249.

[439] Brewster. Treatise on New Philosophical Instruments, p. 266, &c.

[440] Roscoe, Bakerian Lecture, Philosophical Transactions (1868), vol. clviii. p. 6.

[441] Life of Faraday, vol. ii. p. 104.

[442] Watts, Dictionary of Chemistry, vol. ii, p. 39, &c.

[443] De Morgan’s Budget of Paradoxes, p. 291.

[444] Life of Faraday, vol. ii p. 396.

[445] Experimental Researches in Electricity, 1st Series, pp. 24–44.

[446] Airy, On Tides and Waves, Encyclopædia Metropolitana, p. 348*

[447] Lib. i. cap. 74.

[448] Taylor’s Scientific Memoirs, vol. v. p. 241.

[449] Airy’s Mathematical Tracts, 3rd edit. p. 312.

[450] Young’s Works, vol. i. p. 412.

[451] Lloyd’s Wave Theory, Part ii. pp. 52–58. Babbage, Ninth Bridgewater Treatise, p. 104, quoting Lloyd, Transactions of the Royal Irish Academy, vol. xvii. Clifton, Quarterly Journal of Pure and Applied Mathematics, January 1860.

[452] Encyclopædia Metropolitana, art. Sound, p. 753.

[453] Tyndall’s Sound, pp. 261, 273.

[454] Whewell’s History of the Inductive Sciences, vol. ii. p. 471. Herschel’s Physical Geography, § 77.

[455] Maxwell’s Theory of Heat, p. 174. Philosophical Magazine, August 1850. Third Series, vol. xxxvii. p. 123.

[456] Philosophical Transactions, 1858, vol. cxlviii. p. 127.

[457] Tyndall’s Faraday, pp. 73, 74; Life of Faraday, vol. ii. pp. 82, 83.

[458] Tait’s Thermodynamics, p. 77.

[459] On the Analytical Forms called Trees, with Application to the Theory of Chemical Combinations. Report of the British Association, 1875, p. 257.

[460] Hofmann’s Introduction to Chemistry, pp. 224, 225.

[461] Philosophical Transactions (1855), vol. cxlv. pp. 100, &c.

[462] Proceedings of the Manchester Philosophical Society, Feb. 1870.

[463] Balfour Stewart, Elementary Treatise on Heat, 1st edit. p. 198.

[464] Jevons, Proceedings of the Manchester Literary and Philosophical Society, 25th January, 1870, vol. ix. p. 78.

[465] Philosophical Transactions, vol. cxlvi. p. 249.

[466] Grant’s History of Physical Astronomy, p. 162.

[467] Philosophical Transactions (1854), vol. cxliv. p. 364.

[468] Monthly Notices of the Royal Astronomical Society, vol. xxviii. p. 264.

[469] It would seem to be absurd to repeat the profuse expenditure of 1874 at the approaching transit in 1882. The aggregate sum spent in 1874 by various governments and individuals can hardly be less than £200,000, a sum which, wisely expended on scientific investigations, would give a hundred important results.

[470] Philosophical Transactions (1856), vol. cxlvi. p. 342.

[471] Monthly Notices of the Royal Astronomical Society, for 8th Nov. 1844, No. X. vol. vi. p. 89.

[472] Philosophical Magazine, 2nd Series, vol. xxvi. p. 61.

[473] Clausius in Philosophical Magazine, 4th Series, vol. ii. p. 119.

[474] Watts’ Dictionary of Chemistry, vol. iii. p. 129.

[475] Preliminary Discourse, §§ 158, 174. Outlines of Astronomy, 4th edit. § 856.

[476] Proceedings of the Manchester Literary and Philosophical Society, 28th November, 1871, vol. xi. p. 33. Since the above remarks were written, Professor Balfour Stewart has pointed out to me his paper in the Proceedings of the Manchester Literary and Philosophical Society for 15th November, 1870 (vol. x. p. 32), in which he shows that a body moving in an enclosure of uniform temperature would probably experience resistance independently of the presence of a ponderable medium, such as gas, between the moving body and the enclosure. The proof is founded on the theory of the dissipation of energy, and this view is said to be accepted by Professors Thomson and Tait. The enclosure is used in this case by Professor Stewart simply as a means of obtaining a proof, just as it was used by him on a previous occasion to obtain a proof of certain consequences of the Theory of Exchanges. He is of opinion that in both of these cases when once the proof has been obtained, the enclosure may be dispensed with. We know, for instance, that the relation between the inductive and absorptive powers of bodies—although this relation may have been proved by means of an enclosure, does not depend upon its presence, and Professor Stewart thinks that in like manner two bodies, or at least two bodies possessing heat such as the sun and the earth in motion relative to each other, will have the differential motion retarded until perhaps it is ultimately destroyed.

[477] British Association Catalogue of Stars, p. 49.

[478] Experimental Researches in Chemistry and Physics, p. 372. Philosophical Magazine, 3rd Series, May 1846, vol. xxviii. p. 350.

[479] See also Nature, September 18, 1873; vol. viii. p. 398.

[480] Theory of Political Economy, pp. 3–14.

[481] Principia, bk. i. Prop. iv.

[482] Opticks, bk. i. part ii. Prop. 3. 3rd ed. p. 115.

[483] Experimental Inquiry into the Nature of Heat. Preface, p. xv.

[484] Bence Jones, Life of Faraday, vol. i. p. 362.

[485] Ibid. vol. ii. p. 199.

[486] See also his more formal statement in the Experimental Researches in Electricity, 24th Series, § 2702, vol. iii. p. 161.

[487] Printed in Modern Culture, edited by Youmans, p. 219.

[488] Life of Faraday, vol. i. p. 225.

[489] Aristotle’s Rhetoric, Liber I. 2. 11.

[490] Essai Philosophique sur les Probabilités, p. 86.

[491] Kant’s Logik, § 84, Königsberg, 1800, p. 207.

[492] Syllabus of a Proposed System of Logic, p. 34.

[493] Principia, bk. iii. Prop. VI. Motte’s translation, vol. ii. p. 220.

[494] Professor Lovering has pointed out how obscure and uncertain the ideas of scientific men about this ether are, in his interesting Presidential Address before the American Association at Hartford, 1874. Silliman’s Journal, October 1874, p. 297. Philosophical Magazine, vol. xlviii. p. 493.

[495] Novum Organum, bk. ii. Aphorisms, 24, 25.

[496] Ibid. Aph. 28.

[497] Philosophical Transactions (1856) vol. cxlvi. p. 246.

[498] Philosophical Magazine, 4th Series, January 1870, vol. xxxix. p. 2.

[499] Novum Organum, bk. ii. Aphorism 25.

[500] Faraday’s Experimental Researches in Chemistry and Physics, p. 93.

[501] Memorabilia, iv. 7.

[502] Experimental Researches in Electricity, Series xii. vol. i. p. 420.

[503] Life of Faraday, vol. ii. p. 7.

[504] Nature, vol. ii. p. 278.

[505] Journal of the Chemical Society, vol. viii. p. 51.

[506] Correlation of Physical Forces, 3rd edit. p. 184.

[507] Philosophical Magazine, 4th Series, vol. xlii. p. 451.

[508] Grove, Correlation of Physical Forces, 3rd edit. p. 118.

[509] Ibid. pp. 166, 199, &c.

[510] Philosophical Transactions, 1861. Chemical and Physical Researches, p. 598.

[511] Life of Sir W. Hamilton, p. 439.

[512] Powell’s History of Natural Philosophy, p. 201. Novum Organum, bk. ii. Aphorisms 5–7.

[513] Thomson and Tait, Treatise on Natural Philosophy, vol. i. pp. 346–351.

[514] Philosophical Transactions (1740), vol. xli. p. 454.

[515] Principia, bk. i. Law iii. Corollary 6.

[516] Helmholtz, Taylor’s Scientific Memoirs (1853), vol. vi. p. 118.

[517] Lucretius, bk. i. lines 232–264.

[518] Novum Organum, bk. 1 Aphorism 104.

[519] The Unity of Worlds and of Nature, 2nd edit. p. 116.

[520] Principia, bk. iii, ad initium.

[521] Keill, Introduction to Natural Philosophy, p. 89.

[522] Jeremiæ Horroccii Opera Posthuma (1673), pp. 26, 27.

[523] Young’s Works, vol. ii. p. 564.

[524] Essay on Logic, Works, vol. viii. p. 276.

[525] Life of Faraday, by Bence Jones, vol. ii. p. 206.

[526] Lacroix, Traité Élémentaire de Calcul Différentiel et de Calcul Intégral, 5^me édit. p. 699.

[527] Histoire des Mathématiques, vol. i. p. 298.

[528] See Goodwin, Cambridge Philosophical Transactions (1845), vol. viii. p. 269. O’Brien, “On Symbolical Statics,” Philosophical Magazine, 4th Series, vol. i. pp. 491, &c. See also Professor Clerk Maxwell’s delightful Manual of Elementary Science, called Matter and Motion, published by the Society for Promoting Christian Knowledge. In this admirable little work some of the most advanced results of mechanical and physical science are explained according to the method of quaternions, but with hardly any use of algebraic symbols.

[529] Birch, History of the Royal Society, vol. iii. p. 262, quoted by Young, Works, vol. i. p. 246.

[530] Opticks, Query 28, 3rd edit. p. 337.

[531] Rankine, Philosophical Transactions (1856), vol. cxlvi. p. 282.

[532] Cosmotheoros (1699), p. 16.

[533] Laplace, System of the World, vol. ii. p. 316.

[534] Cosmotheoros (1699), p. 17.

[535] Ibid. p. 36.

[536] System of the World, vol. ii. p. 326. Essai Philosophique, p. 87.

[537] Principia, bk. ii. Section ii. Prop. x.

[538] De Morgan, Cambridge Philosophical Transactions, vol. xi. Part ii. p. 246.

[539] Life of Faraday, vol. i. p. 216.

[540] Babbage, The Exposition of 1851, p. 1.

[541] Daubeny’s Atomic Theory, p. 76.

[542] Bakerian Lecture, Philosophical Transactions (1868), vol. clviii. p. 2.

[543] Principia, bk. ii. Prop. 20. Corollaries, 5 and 6.

[544] Treatise on Natural Philosophy, vol. i. p. 50.

[545] Maxwell’s Theory of Heat, (1871), p. 175.

[546] Galton, on the Height and Weight of Boys. Journal of the Anthropological Institute, 1875, p. 174.

[547] Grant’s History of Physical Astronomy, p. 116.

[548] Discourse to the Royal Society, 28th May, 1684.

[549] Robert Hooke’s Posthumous Works, p. 365.

[550] Experimental Researches in Electricity, vol. ii. pp. 240–245.

[551] Murchison’s Silurian System, vol. ii. p. 733, &c.

[552] Philosophical Transactions (1872), vol. clxii. No. 23.

[553] Philosophical Transactions (1852), vol. cxlii. pp. 465, 548, &c.

[554] Philosophical Magazine, 4th Series, vol. i. p. 182.

[555] Maxwell, Theory of Heat, p. 123.

[556] Prior Analytics, ii. 2, 8, and elsewhere.

[557] Hofmann’s Introduction to Chemistry, p. 198.

[558] Stewart’s Elementary Treatise on Heat, p. 80.

[559] Jevons, Proceedings of the Manchester Literary and Philosophical Society, 6th March, 1877, vol. xvi. p. 164. See also Mr. W. E. A. Axon’s note on the same subject, ibid. p. 166.

[560] A Treatise on Logic, or, the Laws of Pure Thought, by Francis Bowen, Professor of Moral Philosophy in Harvard College, Cambridge, United States, 1866, p. 315.

[561] Proceedings of the Royal Society, November, 1873, vol. xxi. p. 512.

[562] Lectures on the Elements of Comparative Anatomy, 1864, p. 1.

[563] Essai sur la Philosophie des Sciences, p. 9.

[564] Lectures on the Elements of Comparative Anatomy, and on the Classification of Animals, 1864, p. 3.

[565] Ossemens Fossiles, 4th edit. vol. i. p. 164. Quoted by Huxley, Lectures, &c., p. 5.

[566] Chambers, Descriptive Astronomy, 1st edit. p. 23.

[567] Philosophical Magazine, 4th Series, vol. xxxix. p. 396; vol. xl. p. 183; vol. xli. p. 44. See also Proctor, Popular Science Review, October 1874, p. 350.

[568] Humboldt, Cosmos (Bohn), vol. iii. p. 224.

[569] Baily, British Association Catalogue, p. 48.

[570] Outlines of Astronomy, § 850, 4th edit. p. 578.

[571] Life of Faraday, vol. ii. p. 87.

[572] Proceedings of the Royal Society, vol. xvii. p. 212. Chemical and Physical Researches, reprint, by Young and Angus Smith, p. 290.

[573] Essai sur la Nomenclature et la Classification, Paris, 1823, pp. 107, 108.

[574] George Bentham, Outline of a New System of Logic, p. 115.

[575] Outline of a New System of Logic, 1827, p. 117.

[576] Porphyrii Isagoge, Caput ii. 24.

[577] Jevons, Elementary Lessons in Logic, p. 104.

[578] Chrestomathia; being a Collection of Papers, &c. London, 1816, Appendix V.

[579] The Classification of the Sciences, &c., 3rd edit. p. 7. Essays: Scientific, Political, and Speculative, vol. iii. p. 13.

[580] Owen, Essay on the Classification and Geographical Distribution of the Mammalia, p. 20.

[581] Dana’s Mineralogy, vol. i. p. 123; quoted in Watts’ Dictionary of Chemistry, vol. ii. p. 166.

[582] Instructions for the Discrimination of Minerals by Simple Chemical Experiments, by Franz von Kobell, translated from the German by R. C. Campbell. Glasgow, 1841.

[583] Edition of 1866, p. lxiii.

[584] Philosophia Botanica (1770), § 154, p. 98.

[585] Philosophical Magazine, 3rd Series (1845), vol. xxvi. p. 522. See also De Morgan’s evidence before the Royal Commission on the British Museum in 1849, Report (1850), Questions, 5704*-5815*, 6481–6513. This evidence should be studied by every person who wishes to understand the elements of Bibliography.

[586] English Cyclopædia, Arts and Sciences, vol. v. p. 233.

[587] Swainson, “Treatise on the Geography and Classification of Animals,” Cabinet Cyclopædia, p. 201.

[588] Darwin, Fertilisation of Orchids, p. 159.

[589] Descent of Man, vol. i. p. 214.

[590] Laws of Botanical Nomenclature, p. 16.

[591] Waterhouse, quoted by Woodward in his Rudimentary Treatise of Recent and Fossil Shells, p. 61.

[592] Bentham’s Handbook of the British Flora (1866), p. 25.

[593] Philosophia Botanica (1770), § 157, p. 99.

[594] Ibid. § 159, p. 100.

[595] Amœnitates Academicæ (1744), vol. i. p. 70. Quoted in Edinburgh Review, October 1868, vol. cxxviii. pp. 416, 417.

[596] Descent of Man, vol. i. p. 228.

[597] Agassiz, Essay on Classification, p. 219.

[598] Ibid. p. 249.

[599] Philosophia Botanica, § 155, p. 98.

[600] Laws of Botanical Nomenclature, by Alphonse Decandolle, translated from the French, 1868, p. 19.

[601] Darwin, The Variation of Animals and Plants, vol. ii. pp. 293, 359, &c.; quoting Paget, Lectures on Pathology, 1853, pp. 152, 164.

[602] Ibid. vol. ii. p. 372.

[603] Théorie Analytique des Probabilités, quoted by Babbage, Ninth Bridgewater Treatise, p. 173.

[604] First Bridgewater Treatise (1834), pp. 16–24.

[605] System of Logic, 5th edit. bk. III. chap. V. § 7; chap. XVI. § 3.

[606] System of Logic, vol. i. p. 384.

[607] Ninth Bridgewater Treatise, p. 140.

[608] Ibid. pp. 34–43.

[609] Professor Clifford, in his most interesting lecture on “The First and Last Catastrophe” (Fortnightly Review, April 1875, p. 480, reprint by the Sunday Lecture Society, p. 24), objects that I have erroneously substituted “known laws of nature” for “known laws of conduction of heat.” I quite admit the error, without admitting all the conclusions which Professor Clifford proceeds to draw; but I maintain the paragraph unchanged, in order that it may be discussed in the Preface.

[610] Tait’s Thermodynamics, p. 38. Cambridge Mathematical Journal, vol. iii. p. 174.

[611] Clerk Maxwell’s Theory of Heat, p. 245.

[612] Maxwell’s Theory of Heat, p. 92.

[613] Report of the British Association (1852), Report of Sections, p. 12.

[614] Mr. C. J. Monroe objects that in this statement I do injustice to Comte, who, he thinks, did impress upon his readers the inadequacy of our mental powers compared with the vastness of the subject matter of science. The error of Comte, he holds, was in maintaining that science had been carried about as far as it is worth while to carry it, which is a different matter. In either case, Comte’s position is so untenable that I am content to leave the question undecided.

[615] Fragments of Science, p. 362.

[616] Familiar Lectures on Scientific Subjects, p. 458.

[617] Philosophical Magazine, 3rd Series, vol. xxvi. p. 406.

[618] History of the Theory of Probability, p. 398.

[619] Trigonometry and Double Algebra, chap. ix.

[620] Agassiz, Essay on Classification, p. 75.

Return to [transcriber’s notes]

Spelling corrections:
acording → according
aklaline → alkaline
an an → an
aws → laws
beween → between
BOOK III → BOOK IV
errror → error
incapadle → incapable
interpretion → interpretation
justifed → justified
longtitude → longitude
Marriotte → Mariotte
melecules → molecules
Meropolitana → Metropolitana
necesssarily → necessarily
nnmber → number
or → of
probabilty → probability
quantites → quantities
secresy → secrecy
sucession → succession
suficiently → sufficiently
telecope → telescope
verifiy → verify

Return to [transcriber’s notes]