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.