[763] There was a second edition of this work in 1846. The author's Astronomy Simplified was published in 1838, and the Thoughts on Physical Astronomy in 1840, with a second edition in 1842.

[764] This was The Science of the Weather, by several authors... edited by B., Glasgow, 1867.

[765] This was Y. Ramachandra, son of Sundara Lāla. He was a teacher of science in Delhi College, and the work to which De Morgan refers is A Treatise on problems of Maxima and Minima solved by Algebra, which appeared at Calcutta in 1850. De Morgan's edition was published at London nine years later.

[766] Abraham de Moivre (1667-1754), French refugee in London, poor, studying under difficulties, was a man with tastes in some respects like those of De Morgan. For one thing, he was a lover of books, and he had a good deal of interest in the theory of probabilities to which De Morgan also gave much thought. His introduction of imaginary quantities into trigonometry was an event of importance in the history of mathematics, and the theorem that bears his name, (cos [phi] + i sin [phi])^{n} = cos n[phi] + i sin n[phi], is one of the most important ones in all analysis.

[767] John Dolland (1706-1761), the silk weaver who became the greatest maker of optical instruments in his time.

[768] Thomas Simpson (1710-1761), also a weaver, taking his leisure from his loom at Spitalfields to teach mathematics. His New Treatise on Fluxions (1737) was written only two years after he began working in London, and six years later he was appointed professor of mathematics at Woolwich. He wrote many works on mathematics and Simpson's Formulas for computing trigonometric tables are still given in the text-books.

[769] Nicholas Saunderson (1682-1739), the blind mathematician. He lost his eyesight through smallpox when only a year old. At the age of 25 he began lecturing at Cambridge on the principles of the Newtonian philosophy. His Algebra, in two large volumes, was long the standard treatise on the subject.

[770] He was not in the class with the others mentioned.

[771] Not known in the literature of mathematics.

[772] Probably J. Butler Williams whose Practical Geodesy appeared in 1842, with a third edition in 1855.

[773] Benjamin Gompertz (1779-1865) was debarred as a Jew from a university education. He studied mathematics privately and became president of the Mathematical Society. De Morgan knew him professionally through the fact that he was prominent in actuarial work.

[774] Referring to the contributions of Archimedes (287-212 B.C.) to the mensuration of the sphere.

[775] The famous Alexandrian astronomer (c. 87-c. 165 A.D.), author of the Almagest, a treatise founded on the works of Hipparchus.

[776] Dr. Whewell, when I communicated this song to him, started the opinion, which I had before him, that this was a very good idea, of which too little was made.—A. De M.

[777] See note 117, page 76.

[778] The common epithet of rank: nobilis Tycho, as he was a nobleman. The writer had been at history.—A. De M.

See note 117, page 76.

[779] He lost it in a duel, with Manderupius Pasbergius. A contemporary, T. B. Laurus, insinuates that they fought to settle which was the best mathematician! This seems odd, but it must be remembered they fought in the dark, "in tenebris densis"; and it is a nice problem to shave off a nose in the dark, without any other harm.—A. De M.

Was this T. B. Laurus Joannes Baptista Laurus or Giovanni Battista Lauro (1581-1621), the poet and writer?

[780] See note 117, page 76.

[781] Referring to Kepler's celebrated law of planetary motion. He had previously wasted his time on analogies between the planetary orbits and the polyhedrons.—A. De M.

[782] See note 117, page 76.

[783] "It does move though."

[784] As great a lie as ever was told: but in 1800 a compliment to Newton without a fling at Descartes would have been held a lopsided structure.—A. De M.

[785] Jean-le-Rond D'Alembert (1717-1783), the foundling who was left on the steps of Jean-le-Rond in Paris, and who became one of the greatest mathematical physicists and astronomers of his century.

[786] Leonhard Euler (1707-1783), friend of the Bernoullis, the greatest of Swiss mathematicians, prominent in the theory of numbers, and known for discoveries in all lines of mathematics as then studied.

[787] See notes 478, 479, page 219.

[788] See note 621, page 288.

[789] See note 584, page 255.

[790] The siderial day is about four minutes short of the solar; there are 366 sidereal days in the year.—A. De M.

[791] The founding of the London Mathematical Society is discussed by Mrs. De Morgan in her Memoir (p. 281). The idea came from a conversation between her brilliant son, George Campbell De Morgan, and his friend Arthur Cowper Ranyard in 1864. The meeting of organization was held on Nov. 7, 1864, with Professor De Morgan in the chair, and the first regular meeting on January 16, 1865.

[792] See note 33, page 43.

[793] See note 119, page 80.

[794] John Russell Hind (b. 1823), the astronomer. Between 1847 and 1854 he discovered ten planetoids.

[795] Sir Roderick Impey Murchison (1792-1871), the great geologist. He was knighted in 1846 and devoted the latter part of his life to the work of the Royal Geographical Society and to the geology of Scotland.

[796] Friedrich Wilhelm Bessel (1784-1846), the astronomer and physicist. He was professor of astronomy at Koenigsberg.

[797] This was the Reduction of the Observations of Planets made ... from 1750 to 1830: computed ... under the superintendence of George Biddell Airy (1848). See note 129, page 85.

[798] The expense of this magnificent work was defrayed by Government grants, obtained, at the instance of the British Association, in 1833—A. De M.

[799] See note 32, page 43.

[800] Franz Friedrich Ernst Bruennow (1821-1891) was at that time or shortly before director of the observatory at Dusseldorf. He then went to Berlin and thence (1854) to Ann Arbor, Michigan. He then went to Dublin and finally became Royal Astronomer of Ireland.

[801] Johann Gottfried Galle (1812-1910), at that time connected with the Berlin observatory, and later professor of astronomy at Breslau.

[802] George Bishop (1785-1861), in whose observatory in Regent's Park important observations were made by Dawes, Hind, and Marth.

[803] James Challis (1803-1882), director of the Cambridge observatory, and successor of Airy as Plumian professor of astronomy.

[804] On Leverrier and Arago see note 33, page 43, and note 561, page 243.

[805] Robert Grant's (1814-1892) History of Physical Astronomy from the Earliest Ages to the Middle of the Nineteenth Century appeared in 1852. He was professor of astronomy and director of the observatory at Glasgow.

[806] John Debenham was more interested in religion than in astronomy. He wrote The Strait Gate; or, the true scripture doctrine of salvation clearly explained, London, 1843, and Tractatus de magis et Bethlehemae stella et Christi in deserto tentatione, privately printed at London in 1845.

[807] More properly the Sydney Smirke reading room, since it was built from his designs.

[808] The Antinomians were followers of Johannes Agricola (1494-1566). They believed that Christians as such were released from all obligations to the Old Testament. Some went so far as to assert that, since all Christians were sanctified, they could not lose this sanctity even though they disobeyed God. The sect was prominent in England in the seventeenth century, and was transferred to New England. Here it suffered a check in the condemnation of Mrs. Ann Hutchinson (1636) by the Newton Synod.

[809] Aside from this work and his publications on Reeve and Muggleton he wrote nothing. With Joseph Frost he published A list of Books and general index to J. Reeve and L. Muggleton's works (1846), Divine Songs of the Muggletonians (1829), and the work mentioned on page 396. The works of J. Reeve and L. Muggleton (1832).

[810] About 1650 he and his cousin John Reeve (1608-1658) began to have visions. As part of their creed they taught that astronomy was opposed by the Bible. They asserted that the sun moves about the earth, and Reeve figured out that heaven was exactly six miles away. Both Muggleton and Reeve were imprisoned for their unitarian views. Muggleton wrote a Transcendant Spirituall Treatise (1652). I have before me A true Interpretation of All the Chief Texts ... of the whole Book of the Revelation of St. John.... By Lodowick Muggleton, one of the two last Commissioned Witnesses & Prophets of the onely high, immortal, glorious God, Christ Jesus (1665), in which the interpretation of the "number of the beast" occupies four pages without arriving anywhere.

[811] In 1652 he was, in a vision, named as the Lord's "last messenger," with Muggleton as his "mouth," and died six years later, probably of nervous tension resulting from his divine "illumination." He was the more spiritual of the two.

[812] William Guthrie (1708-1770) was a historian and political writer. His History of England (1744-1751) was the first attempt to base history on parliamentary records. He also wrote a General History of Scotland in 10 volumes (1767). The work to which Frost refers is the Geographical, Historical, and Commercial Grammar (1770) which contained an astronomical part by J. Ferguson. By 1827 it had passed through 24 editions.

[813] George Fox (1624-1691), founder of the Society of Friends; a mystic and a disciple of Boehme. He was eight times imprisoned for heresy.

[814] If they were friends they were literary antagonists, for Muggleton wrote against Fox The Neck of the Quakers Broken (1663), and Fox replied in 1667. Muggleton also wrote A Looking Glass for George Fox.

[815] John Conduitt (1688-1737), who married (1717) Newton's half niece, Mrs. Katherine Barton. See note 284, page 136.

[816] Probably Peter Mark Roget's (1779-1869) Thesaurus of English Words (1852) is not much used at present, but it went through 28 editions in his lifetime. Few who use the valuable work are aware that Roget was a professor of physiology at the Royal Institution (London), that he achieved his title of F. R. S. because of his work in perfecting the slide rule, and that he followed Sir John Herschel as secretary of the Royal Society.

[817] See note 703, page 327. This work went into a second edition in the year of its first publication.

[818] See note 398, page 177.

[819] See note 528, page 233.

[820] George Jacob Holyoake (1817-1906) entered into a controversial life at an early age. In 1841 he was imprisoned for six months for blasphemy. He founded and edited The Reasoner (Vols. 1-26, 1846-1861). In his later life he did much to promote cooperation among the working class.

[821] See note 176, page 102.

[822] William Thomas Lowndes (1798-1843), whose Bibliographer's Manual of English Literature, 4 vols., London, 1834 (also 1857-1864, and 1869) is a classic in its line.

[823] Jacques Charles Brunet (1780-1867), the author of the great French bibliography, the Manuel du Libraire (1810).

* * * * *

Corrections made to printed original.

Page 5, "direct acquaintance with the whole of his mental ancestry": 'acquantance' in original.

Page 100, "The error is at the rate": 'it' (for 'is') in original.

Page 192, "the lineal successor of the Repository association": 'successsor' in original.

Page 211, "the doctors had finished their compliments": 'docters' in original.

Page 302, "causing mutual perturbations": 'peturbations' in original.

Page 344, "The work itself is described": 'decribed' in original.

Page 370, The entry for 1852 is printed as 19, it appears that the correct value should be 9.

Page 392, "Sir John Herschel's previous communication": 'pervious' in original.

Note 317, "he constructed a working model of a steam road carriage": 'contructed' in original.

Note 380, "the variation of the Earth's Diameters": 'Diaameters' in original.

Note 550, "The first edition of the anonymous [Greek]": 'anonynous' in original.

THE END