Chapter XVI: Part 16

[478] He was born at Paris in 1713, and died there in 1765.

[479] _Recherches sur les courbes a double courbure_, Paris, 1731. Clairaut was then only eighteen, and was in the same year made a member of the Academie des sciences. His _Elemens de geometrie_ appeared in 1741. Meantime he had taken part in the measurement of a degree in Lapland (1736-1737). His _Traite de la figure de la terre_ was published in 1741. The Academy of St. Petersburg awarded him a prize for his _Theorie de la lune_ (1750). His various works on comets are well known, particularly his _Theorie du mouvement des cometes_ (1760) in which he applied the "problem of three bodies" to Halley's comet as retarded by Jupiter and Saturn.

[480] Joseph Privat, Abbe de Molieres (1677-1742), was a priest of the Congregation of the Oratorium. In 1723 he became a professor in the College de France. He was well known as an astronomer and a mathematician, and wrote in defense of Descartes's theory of vortices (1728, 1729). He also contributed to the methods of finding prime numbers (1705).

[481] "Deserves not only to be printed, but to be admired as a marvel of imagination, of understanding, and of ability."

[482] Blaise Pascal (1623-1662), the well-known French philosopher and mathematician. He lived for some time with the Port Royalists, and defended them against the Jesuits in his _Provincial Letters_. Among his works are the following: _Essai pour les coniques_ (1640); _Recit de la grande experience de l'equilibre des liqueurs_ (1648), describing his experiment in finding altitudes by barometric readings; _Histoire de la roulette_ (1658); _Traite du triangle arithmetique_ (1665); _Aleae geometria_ (1654).

[483] This proposition shows that if a hexagon is inscribed in a conic (in particular a circle) and the opposite sides are produced to meet, the three points determined by their intersections will be in the same straight line.

[484] Jacques Curabelle, _Examen des Oeuvres du Sr. Desargues_, Paris, 1644. He also published without date a work entitled: _Foiblesse pitoyable du Sr. G. Desargues employee contre l'examen fait de ses oeuvres_.

[485] See page 119, note 233.

[486] Until "this great proposition called Pascal's should see the light."

[487] The story is that his father, Etienne Pascal, did not wish him to study geometry until he was thoroughly grounded in Latin and Greek. Having heard the nature of the subject, however, he began at the age of twelve to construct figures by himself, drawing them on the floor with a piece of charcoal. When his father discovered what he was doing he was attempting to demonstrate that the sum of the angles of a triangle equals two right angles. The story is given by his sister, Mme. Perier.

[488] Sir John Wilson (1741-1793) was knighted in 1786 and became Commissioner of the Great Seal in 1792. He was a lawyer and jurist of recognized merit. He stated his theorem without proof, the first demonstration having been given by Lagrange in the Memoirs of the Berlin Academy for 1771,--_Demonstration d'un theoreme nouveau concernant les nombres premiers_. Euler also gave a proof in his _Miscellanea Analytica_ (1773). Fermat's works should be consulted in connection with the early history of this theorem.

[489] He wrote, in 1760, a tract in defense of Waring, a point of whose algebra had been assailed by a Dr. Powell. Waring wrote another tract of the same date.--A. De M.

William Samuel Powell (1717-1775) was at this time a fellow of St. John's College, Cambridge. In 1765 he became Vice Chancellor of the University. Waring was a Magdalene man, and while candidate for the Lucasian professorship he circulated privately his _Miscellanea Analytica_. Powell attacked this in his _Observations on the First Chapter of a Book called Miscellanea_ (1760). This attack was probably in the interest of another candidate, a man of his own college (St. John's), William Ludlam.

[490] William Paley (1743-1805) was afterwards a tutor at Christ's College, Cambridge. He never contributed anything to mathematics, but his _Evidences of Christianity_ (1794) was long considered somewhat of a classic. He also wrote _Principles of Morality and Politics_ (1785), and _Natural Theology_ (1802).

[491] Edward, first Baron Thurlow (1731-1806) is known to Americans because of his strong support of the Royal prerogative during the Revolution. He was a favorite of George III, and became Lord Chancellor in 1778.

[492] George Wilson Meadley (1774-1818) published his _Memoirs of ... Paley_ in 1809. He also published _Memoirs of Algernon Sidney_ in 1813. He was a merchant and banker, and had traveled extensively in Europe and the East. He was a convert to unitarianism, to which sect Paley had a strong leaning.

[493] Watson (1737-1816) was a strange kind of man for a bishopric. He was professor of chemistry at Cambridge (1764) at the age of twenty-seven. It was his experiments that led to the invention of the black-bulb thermometer. He is said to have saved the government L100,000 a year by his advice on the manufacture of gunpowder. Even after he became professor of divinity at Cambridge (1771) he published four volumes of _Chemical Essays_ (vol. I, 1781). He became Bishop of Llandaff in 1782.

[494] James Adair (died in 1798) was counsel for the defense in the trial of the publishers of the _Letters of Junius_ (1771). As King's Serjeant he assisted in prosecuting Hardy and Horne Tooke.

[495] Morgan (1750-1833) was actuary of the Equitable Assurance Society of London (1774-1830), and it was to his great abilities that the success of that company was due at a time when other corporations of similar kind were meeting with disaster. The Royal Society awarded him a medal (1783) for a paper on _Probability of Survivorship_. He wrote several important works on insurance and finance.

[496] Dr. Price (1723-1791) was a non-conformist minister and a writer on ethics, economics, politics, and insurance. He was a defender of the American Revolution and a personal friend of Franklin. In 1778 Congress invited him to America to assist in the financial administration of the new republic, but he declined. His famous sermon on the French Revolution is said to have inspired Burke's _Reflections on the Revolution in France_.

[497] Elizabeth Gurney (1780-1845), a Quaker, who married Joseph Fry (1800), a London merchant. She was the prime mover in the Association for the Improvement of the Female Prisoners in Newgate, founded in 1817. Her influence in prison reform extended throughout Europe, and she visited the prisons of many countries in her efforts to improve the conditions of penal servitude. The friendship of Mrs. Fry with the De Morgans began in 1837. Her scheme for a female benefit society proved worthless from the actuarial standpoint, and would have been disastrous to all concerned if it had been carried out, and it was therefore fortunate that De Morgan was consulted in time. Mrs. De Morgan speaks of the consultation in these words: "My husband, who was very sensitive on such points, was charmed with Mrs. Fry's voice and manner as much as by the simple self-forgetfulness with which she entered into this business; her own very uncomfortable share of it not being felt as an element in the question, as long as she could be useful in promoting good or preventing mischief. I can see her now as she came into our room, took off her little round Quaker cap, and laying it down, went at once into the matter. 'I have followed thy advice, and I think nothing further can be done in this case; but all harm is prevented.' In the following year I had an opportunity of seeing the effect of her most musical tones. I visited her at Stratford, taking my little baby and nurse with me, to consult her on some articles on prison discipline, which I had written for a periodical. The baby--three months old--was restless, and the nurse could not quiet her, neither could I entirely, until Mrs. Fry began to read something connected with the subject of my visit, when the infant, fixing her large eyes on the reader, lay listening till she fell asleep." _Memoirs_, p. 91.

[498] Mrs. Fry certainly believed that the writer was the old actuary of the Equitable, when she first consulted him upon the benevolent Assurance project; but we were introduced to her by our old and dear friend Lady Noel Byron, by whom she had been long known and venerated, and who referred her to Mr. De Morgan for advice. An unusual degree of confidence in, and appreciation of each other, arose on their first meeting between the two, who had so much that was externally different, and so much that was essentially alike, in their natures.--S. E. De M.

Anne Isabella Milbanke (1792-1860) married Lord Byron in 1815, when both took the additional name of Noel, her mother's name. They were separated in 1816.

[499] An obscure writer not mentioned in the ordinary biographies.

[500] Not mentioned in the ordinary biographies, and for obvious reasons.

[501] "Before" and "after."

[502] On Bishop Wilkins see note 171 on page 100.

[503] Provision for a journey.

[504] See note 179 on page 103.

[505] Thomas Bradwardine (1290-1349), known as _Doctor Profundus_, proctor and professor of theology at Oxford, and afterwards Chancellor of St. Paul's and confessor to Edward III. The English ascribed their success at Crecy to his prayers.

[506] He was consecrated Archbishop of Canterbury by the Pope at Avignon, July 13, 1349, and died of the plague at London in the same year.

[507] "One paltry little year."

[508] The title is carelessly copied, as is so frequently the case in catalogues, even of the Libri class. It should read: _Arithmetica thome brauardini_ || _Olivier Senant_ || _Venum exponuntur ab Oliuiario senant in vico diui Jacobi sub signo beate Barbare sedente_. The colophon reads: _Explicit arithmetica speculatiua th[=o]e brauardini b[=n] reuisa et correcta a Petro sanchez Ciruelo aragonensi mathematicas leg[=e]te Parisius, [=i]pressa per Thom[=a] anguelart_. There were Paris editions of 1495, 1496, 1498, s. a. (c. 1500), 1502, 1504, 1505, s. a. (c. 1510), 1512, 1530, a Valencia edition of 1503, two Wittenberg editions of 1534 and 1536, and doubtless several others. The work is not "very rare," although of course no works of that period are common. See the editor's _Rara Arithmetica_, page 61.

[509] This is his _Tractatus de proportionibus_, Paris, 1495; Venice, 1505; Vienna, 1515, with other editions.

[510] The colophon of the 1495 edition reads: _Et sic explicit Geometria Thome brauardini c[=u] tractatulo de quadratura circuli bene reuisa a Petro sanchez ciruelo: operaqz Guidonis mercatoris dilig[=e]tissime impresse parisi^o in c[=a]po gaillardi. Anno d[=n]i. 1495. die. 20, maij._

This Petro Ciruelo was born in Arragon, and died in 1560 at Salamanca. He studied mathematics and philosophy at Paris, and took the doctor's degree there. He taught at the University of Alcala and became canon of the Cathedral at Salamanca. Besides his editions of Bradwardine he wrote several works, among them the _Liber arithmeticae practicae qui dicitur algorithmus_ (Paris, 1495) and the _Cursus quatuor mathematicarum artium liberalium_ (Alcala, 1516).

[511] Star polygons, a subject of considerable study in the later Middle Ages. See note 35 on page 44.

[512] "A new theory that adds lustre to the fourteenth century."

[513] There is nothing in the edition of 1495 that leads to this conclusion.

[514] The full title is: _Nouvelle theorie des paralleles, avec un appendice contenant la maniere de perfectionner la theorie des paralleles de A. M. Legendre_. The author had no standing as a scientist.

[515] Adrien Marie Legendre (1752-1833) was one of the great mathematicians of the opening of the nineteenth century. His _Elements de geometrie_ (1794) had great influence on the geometry of the United States. His _Essai sur la theorie des nombres_ (1798) is one of the classics upon the subject. The work to which Kircher refers is the _Nouvelle theorie des paralleles_ (1803), in which the attempt is made to avoid using Euclid's postulate of parallels, the result being merely the substitution of another assumption that was even more unsatisfactory. The best presentations of the general theory are W. B. Frankland's _Theories of Parallelism_, Cambridge, 1910, and Engel and Staeckel's _Die Theorie der Parallellinien von Euclid bis auf Gauss_, Leipsic, 1895. Legendre published a second work on the theory the year of his death, _Reflexions sur ... la theorie des paralleles_ (1833). His other works include the _Nouvelles methodes pour la determination des orbites des cometes_ (1805), in which he uses the method of least squares; the _Traite des fonctions elliptiques et des integrales_ (1827-1832), and the _Exercises de calcul integral_ (1811, 1816, 1817).

[516] Johann Joseph Ignatz von Hoffmann (1777-1866), professor of mathematics at Aschaffenburg, published his _Theorie der Parallellinien_ in 1801. He supplemented this by his _Kritik der Parallelen-Theorie_ in 1807, and his _Das eilfte Axiom der Elemente des Euclidis neu bewiesen_ in 1859. He wrote other works on mathematics, but none of his contributions was of any importance.

[517] Johann Karl Friedrich Hauff (1766-1846) was successively professor of mathematics at Marburg, director of the polytechnic school at Augsburg, professor at the Gymnasium at Cologne, and professor of mathematics and physics at Ghent. The work to which Kircher refers is his memoirs on the Euclidean _Theorie der Parallelen_ in Hindenburg's _Archiv_, vol. III (1799), an article of no merit in the general theory.

[518] Wenceslaus Johann Gustav Karsten (1732-1787) was professor of logic at Rostock (1758) and Butzow (1760), and later became professor of mathematics and physics at Halle. His work on parallels is the _Versuch einer voellig berichtigten Theorie der Parallellinien_ (1779). He also wrote a work entitled _Anfangsgruende der mathematischen Wissenschaften_ (1780), but neither of these works was more than mediocre.

[519] Johann Christoph Schwab (not Schwal) was born in 1743 and died in 1821. He was professor at the Karlsschule at Stuttgart. De Morgan's wish was met, for the catalogues give "c. fig. 8," so that it evidently had eight illustrations instead of eight volumes. He wrote several other works on the principles of geometry, none of any importance.

[520] Gaetano Rossi of Catanzaro. This was the libretto writer (1772-1855), and hence the imperfections of the work can better be condoned. De Morgan should have given a little more of the title: _Solusione esatta e regolare ... del ... problema della quadratura del circolo_. There was a second edition, London, 1805.

[521] This identifies Rossi, for Josephine Grassini (1773-1850) was a well-known contralto, _prima donna_ at Napoleon's court opera.

[522] William Spence (1783-1860) was an entomologist and economist of some standing, a fellow of the Royal Society, and one of the founders of the Entomological Society of London. The work here mentioned was a popular one, the first edition appearing in 1807, and four editions being justified in a single year. He also wrote _Agriculture the Source of Britain's Wealth_ (1808) and _Objections against the Corn Bill refuted_ (1815), besides a work in four volumes on entomology (1815-1826) in collaboration with William Kirby.

[523] "That used to be so, but we have changed all that."

[524] "Meet the coming disease."

[525] George Douglas (or Douglass) was a Scotch writer. He got out an edition of the _Elements of Euclid_ in 1776, with an appendix on trigonometry and a set of tables. His work on _Mathematical Tables_ appeared in 1809, and his _Art of Drawing in Perspective, from mathematical principles_, in 1810.

[526] See note 443, on page 197.

[527] John Playfair (1748-1848) was professor of mathematics (1785) and natural philosophy (1805) at the University of Edinburgh. His _Elements of Geometry_ went through many editions.

[528] "Tell Apella" was an expression current in classical Rome to indicate incredulity and to show the contempt in which the Jew was held. Horace says: _Credat Judaeus Apella_, "Let Apella the Jew believe it." Our "Tell it to the marines," is a similar phrase.

[529] As De Morgan says two lines later, "No mistake is more common than the natural one of imagining that the"--University of Virginia is at Richmond. The fact is that it is not there, and that it did not exist in 1810. It was not chartered until 1819, and was not opened until 1825, and then at Charlottesville. The act establishing the Central College, from which the University of Virginia developed, was passed in 1816. The Jean Wood to whom De Morgan refers was one John Wood who was born about 1775 in Scotland and who emigrated to the United States in 1800. He published a _History of the Administration of J. Adams_ (New York, 1802) that was suppressed by Aaron Burr. This act called forth two works, a _Narrative of the Suppression, by Col. Burr, of the 'History of the Administration of John Adams'_ (1802), in which Wood was sustained; and the _Antidote to John Wood's Poison_ (1802), in which he was attacked. The work referred to in the "printed circular" may have been the _New theory of the diurnal rotation of the earth_ (Richmond, Va., 1809). Wood spent the last years of his life in Richmond, Va., making county maps. He died there in 1822. A careful search through works relating to the University of Virginia fails to show that Wood had any connection with it.

[530] There seems to be nothing to add to Dobson's biography beyond what De Morgan has so deliciously set forth.

[531] "Give to each man his due."

[532] Hester Lynch Salusbury (1741-1821), the friend of Dr. Johnson, married Henry Thrale (1763), a brewer, who died in 1781. She then married Gabriel Piozzi (1784), an Italian musician. Her _Anecdotes of the late Samuel Johnson_ (1786) and _Letters to and from Samuel Johnson_ (1788) are well known. She also wrote numerous essays and poems.

[533] Samuel Pike (c. 1717-1773) was an independent minister, with a chapel in London and a theological school in his house. He later became a disciple of Robert Sandeman and left the Independents for the Sandemanian church (1765). The _Philosophia Sacra_ was first published at London in 1753. De Morgan here cites the second edition.

[534] Pike had been dead over forty years when Kittle published this second edition. Kittle had already published a couple of works: _King Solomon's portraiture of Old Age_ (Edinburgh, 1813), and _Critical and Practical Lectures on the Apocalyptical Epistles to the Seven Churches of Asia Minor_ (London, 1814).

[535] See note 334, on page 152.

[536] William Stukely (1687-1765) was a fellow of the Royal Society and of the College of Physicians and Surgeons. He afterwards (1729) entered the Church. He was prominent as an antiquary, especially in the study of the Roman and Druidic remains of Great Britain. He was the author of numerous works, chiefly on paleography.

[537] William Jones (1726-1800), who should not be confused with his namesake who is mentioned in note 281 on page 135. He was a lifelong friend of Bishop Horne, and his vicarage at Nayland was a meeting place of an influential group of High Churchmen. Besides the _Physiological Disquisitions_ (1781) he wrote _The Catholic Doctrine of the Trinity_ (1756) and _The Grand Analogy_ (1793).

[538] Robert Spearman (1703-1761) was a pupil of John Hutchinson, and not only edited his works but wrote his life. He wrote a work against the Newtonian physics, entitled _An Enquiry after Philosophy and Theology_ (Edinburgh, 1755), besides the _Letters to a Friend concerning the Septuagint Translation_ (Edinburgh, 1759) to which De Morgan refers.

[539] A writer of no importance, at least in the minds of British biographers.

[540] Alexander Catcott (1725-1779), a theologian and geologist, wrote not only a work on the creation (1756) but a _Treatise on the Deluge_ (1761, with a second edition in 1768). Sir Charles Lyell considered the latter work a valuable contribution to geology.

[541] James Robertson (1714-1795), professor of Hebrew at the University of Edinburgh. Probably De Morgan refers to his _Grammatica Linguae Hebraeae_ (Edinburgh, 1758; with a second edition in 1783). He also wrote _Clavis Pentateuchi_ (1770).

[542] Benjamin Holloway (c. 1691-1759), a geologist and theologian. He translated Woodward's _Naturalis Historia Telluris_, and was introduced by Woodward to Hutchinson. The work referred to by De Morgan appeared at Oxford in two volumes in 1754.

[543] His work was _The Christian plan exhibited in the interpretation of Elohim: with observations upon a few other matters relative to the same subject_, Oxford, 1752, with a second edition in 1755.

[544] Duncan Forbes (1685-1747) studied Oriental languages and Civil law at Leyden. He was Lord President of the Court of Sessions (1737). He wrote a number of theological works.

[545] Should be 1756.

[546] Edward Henry Bickersteth (1825-1906), bishop of Exeter (1885-1900); published _The Rock of Ages; or scripture testimony to the one Eternal Godhead of the Father, and of the Son, and of the Holy Ghost_ at Hampstead in 1859. A second edition appeared at London in 1860.

[547] Thomas Sadler (1822-1891) took his Ph.D. at Erlangen in 1844, and became a Unitarian minister at Hampstead, where Bickersteth's work was published. Besides writing the _Gloria Patri_ (1859), he edited Crabb Robinson's Diaries.

[548] This was his _Virgil's Bucolics and the two first Satyrs of Juvenal_, 1634.

[549] Possibly in his _Twelve Questions or Arguments drawn out of Scripture, wherein the commonly received Opinion touching the Deity of the Holy Spirit is clearly and fully refuted_, 1647. This was his first heretical work, and it was followed by a number of others that were written during the intervals in which the Puritan parliament allowed him out of prison. It was burned by the hangman as blasphemous. Biddle finally died in prison, unrepentant to the last.

[550] The first edition of the anonymous [Greek: Haireseon anastasis] (by Vicars?) appeared in 1805.

[551] Possibly by Thomas Pearne (c. 1753-1827), a fellow of St. Peter's College, Cambridge, and a Unitarian minister.

[552] Thomas Wentworth, Earl of Strafford, was borne in London in 1593, and was executed there in 1641. He was privy councilor to Charles I, and was Lord Deputy of Ireland. On account of his repressive measures to uphold the absolute power of the king he was impeached by the Long Parliament and was executed for treason. The essence of his defence is in the sentence quoted by De Morgan, to which Pym replied that taken as a whole, the acts tended to show an intention to change the government, and this was in itself treason.

[553] The name assumed by a writer who professed to give a mathematical explanation of the Trinity, see farther on.--S. E. De M.

[554] Sabellius (fl. 230 A.D.) was an early Christian of Libyan origin. He taught that Father, Son, and Holy Spirit were different names for the same person.

[555] Sir Richard Phillips was born in London in 1767 (not 1768 as stated above), and died there in 1840. He was a bookseller and printer in Leicester, where he also edited a radical newspaper. He went to London to live in 1795 and started the _Monthly Magazine_ there in 1796. Besides the works mentioned by De Morgan he wrote on law and economics.

[556] It was really eighteen months.

[557] While he was made sheriff in 1807 he was not knighted until the following year.

[558] James Mitchell (c. 1786-1844) was a London actuary, or rather a Scotch actuary living a good part of his life in London. Besides the work mentioned he compiled a _Dictionary of Chemistry, Mineralogy, and Geology_ (1823), and wrote _On the Plurality of Worlds_ (1813) and _The Elements of Astronomy_ (1820).

[559] Richarda Smith, wife of Sir George Biddell Airy (see note 129, page 85) the astronomer. In 1835 Sir Robert Peel offered a pension of L300 a year to Airy, who requested that it be settled on his wife.

[560] Mary Fairfax (1780-1872) married as her second husband Dr. William Somerville. In 1826 she presented to the Royal Society a paper on _The Magnetic Properties of the Violet Rays of the Solar Spectrum_, which attracted much attention. It was for her _Mechanism of the Heavens_ (1831), a popular translation of Laplace's _Mecanique Celeste_, that she was pensioned.

[561] Dominique Francois Jean Arago (1786-1853) the celebrated French astronomer and physicist.

[562] For there is a well-known series

1 + 1/2^2 + 1/3^2 + ... = [pi]^2/6.

If, therefore, the given series equals 1, we have

2 = 1/6 [pi]^2

or [pi]^2 = 12,

whence [pi] = 2 [root]3.

But c = [pi]d, and twice the diagonal of a cube on the diameter is 2d [root]3.

[563] There was a second edition in 1821.

[564] London, 1830.

[565] He was a resident of Chatham, and seems to have published no other works.

[566] Richard Whately (1787-1863) was, as a child, a calculating prodigy (see note 132, page 86), but lost the power as is usually the case with well-balanced minds. He was a fellow of Oriel College, Oxford, and in 1825 became principal of St. Alban Hall. He was a friend of Newman, Keble, and others who were interested in the religious questions of the day. He became archbishop of Dublin in 1831. He was for a long time known to students through his _Logic_ (1826) and _Rhetoric_ (1828).

[567] William King, D.C.L. (1663-1712), student at Christ Church, Oxford, and celebrated as a wit and scholar. His _Dialogues of the Dead_ (1699) is a satirical attack on Bentley.

[568] Thomas Ebrington (1760-1835) was a fellow of Trinity College, Dublin, and taught divinity, mathematics, and natural philosophy there. He became provost of the college in 1811, bishop of Limerick in 1820, and bishop of Leighlin and Ferns in 1822. His edition of Euclid was reprinted a dozen times. The _Reply to John Search's Considerations on the Law of Libel_ appeared at Dublin in 1834.

[569] Joseph Blanco White (1775-1841) was the son of an Irishman living in Spain. He was born at Seville and studied for orders there, being ordained priest in 1800. He lost his faith in the Roman Catholic Church, and gave up the ministry, escaping to England at the time of the French invasion. At London he edited _Espanol_, a patriotic journal extensively circulated in Spain, and for this service he was pensioned after the expulsion of the French. He then studied at Oriel College, Oxford, and became intimate with men like Whately, Newman, and Keble. In 1835 he became a Unitarian. Among his theological writings is his _Evidences against Catholicism_ (1825). The "rejoinder" to which De Morgan refers consisted of two letters: _The law of anti-religious Libel reconsidered_ (Dublin, 1834) and _An Answer to some Friendly Remarks on "The Law of Anti-Religious Libel Reconsidered"_ (Dublin, 1834).

[570] The work was translated from the French.

[571] J. Hoene Wronski (1778-1853) served, while yet a mere boy, as an artillery officer in Kosciusko's army (1791-1794). He was imprisoned after the battle of Maciejowice. He afterwards lived in Germany, and (after 1810) in Paris. For the bibliography of his works see S. Dickstein's article in the _Bibliotheca Mathematica_, vol. VI (2), page 48.

[572] Perhaps referring to his _Introduction a la philosophie des mathematiques_ (1811).

[573] Read "equation of the."

[574] Thomas Young (1773-1829), physician and physicist, sometimes called the founder of physiological optics. He seems to have initiated the theory of color blindness that was later developed by Helmholtz. The attack referred to was because of his connection with the Board of Longitude, he having been made (1818) superintendent of the Nautical Almanac and secretary of the Board. He opposed introducing into the Nautical Almanac anything not immediately useful to navigation, and this antagonized many scientists.

[575] Isaac Milner (1750-1820) was professor of natural philosophy at Cambridge (1783) and later became, as De Morgan states, president of Queens' College (1788). In 1791 he became dean of Carlisle, and in 1798 Lucasian professor of mathematics. His chief interest was in chemistry and physics, but he contributed nothing of importance to these sciences or to mathematics.

[576] Thomas Perronet Thompson (1783-1869), fellow of Queens' College, Cambridge, saw service in Spain and India, but after 1822 lived in England. He became major general in 1854, and general in 1868. Besides some works on economics and politics he wrote a _Geometry without Axioms_ (1830) that De Morgan includes later on in his _Budget_. In it Thompson endeavored to prove the parallel postulate.

[577] De Morgan's father-in-law. See note 441, page 196.

[578] Johann Friedrich Herbart (1776-1841), successor of Kant as professor of philosophy at Koenigsberg (1809-1833), where he established a school of pedagogy. From 1833 until his death he was professor of philosophy at Goettingen. The title of the pamphlet is: _De Attentionis mensura causisque primariis. Psychologiae principia statica et mechanica exemplo illustraturus.... Regiomonti,... 1822_. The formulas in question are given on pages 15 and 17, and De Morgan has omitted the preliminary steps, which are, for the first one:

[beta] ([phi] - z) [delta]t = [delta]z

unde [beta]t= Const / ([phi] - z).

Pro t = 0 etiam z = 0; hinc [beta]t = log [phi]/([phi] - z).

z = [phi] (1 - [epsilon]^{-[beta]t});

et [delta]z/[delta]t = [beta][phi][epsilon]^{-[beta]t}

These are, however, quite elementary as compared with other portions of the theory.

[579] See note 371, page 168.

[580] William Law (1686-1761) was a clergyman, a fellow of Emanuel College, Cambridge, and in later life a convert to Behmen's philosophy. He was so free in his charities that the village in which he lived became so infested by beggars that he was urged by the citizens to leave. He wrote _A serious call to a devout and holy life_ (1728).

[581] He was a curate at Cheshunt, and wrote the _Spiritual voice to the Christian Church and to the Jews_ (London, 1760), _A second warning to the world by the Spirit of Prophecy_ (London, 1760), and _Signs of the Times; or a Voice to Babylon_ (London, 1773).

[582] His real name was Thomas Vaughan (1622-1666). He was a fellow of Jesus College, Oxford, taking orders, but was deprived of his living on account of drunkenness. He became a mystic philosopher and gave attention to alchemy. His works had a large circulation, particularly on the continent. He wrote _Magia Adamica_ (London, 1650), _Euphrates; or the Waters of the East_ (London, 1655), and _The Chymist's key to shut, and to open; or the True Doctrine of Corruption and Generation_ (London, 1657).

[583] Emanuel Swedenborg, or Svedberg (1688-1772) the mystic. It is not commonly known to mathematicians that he was one of their guild, but he wrote on both mathematics and chemistry. Among his works are the _Regelkonst eller algebra_ (Upsala, 1718) and the _Methodus nova inveniendi longitudines locorum, terra marique, ope lunae_ (Amsterdam, 1721, 1727, and 1766). After 1747 he devoted his attention to mystic philosophy.

[584] Pierre Simon Laplace (1749-1827), whose _Exposition du systeme du monde_ (1796) and _Traite de mecanique celeste_ (1799) are well known.

[585] See note 117, page 76.

[586] John Dalton (1766-1844), who taught mathematics and physics at New College, Manchester (1793-1799) and was the first to state the law of the expansion of gases known by his name and that of Gay-Lussac. His _New system of Chemical Philosophy_ (Vol. I, pt. i, 1808; pt. ii, 1810; vol. II, 1827) sets forth his atomic theory.

[587] Howison was a poet and philosopher. He lived in Edinburgh and was a friend of Sir Walter Scott. This work appeared in 1822.

[588] He was a shoemaker, born about 1765 at Haddiscoe, and his "astro-historical" lectures at Norwich attracted a good deal of attention at one time. He traced all geologic changes to differences in the inclination of the earth's axis to the plane of its orbit. Of the works mentioned by De Morgan the first appeared at Norwich in 1822-1823, and there was a second edition in 1824. The second appeared in 1824-1825. The fourth was _Urania's Key to the Revelation; or the analyzation of the writings of the Jews..._, and was first published at Norwich in 1823, there being a second edition at London in 1833. His books were evidently not a financial success, for Mackey died in an almshouse at Norwich.

[589] Godfrey Higgins (1773-1833), the archeologist, was interested in the history of religious beliefs and in practical sociology. He wrote _Horae Sabbaticae_ (1826), _The Celtic Druids_ (1827 and 1829), and _Anacalypsis, an attempt to draw aside the veil of the Saitic Isis; or an Inquiry into the Origin of Languages, Nations, and Religions_ (posthumously published, 1836), and other works. See also page 274, _infra_.

[590] The work also appeared in French. Wirgman wrote, or at least began, two other works: _Divarication of the New Testament into Doctrine and History; part I, The Four Gospels_ (London, 1830), and _Mental Philosophy; part I, Grammar of the five senses; being the first step to infant education_ (London, 1838).

[591] He was born at Shandrum, County Limerick, and supported himself by teaching writing and arithmetic. He died in an almshouse at Cork.

[592] George Boole (1815-1864), professor of mathematics at Queens' College, Cork. His _Laws of Thought_ (1854) was the first work on the algebra of logic.

[593] Oratio Grassi (1582-1654), the Jesuit who became famous for his controversy with Galileo over the theory of comets. Galileo ridiculed him in _Il Saggiatore_, although according to the modern view Grassi was the more nearly right. It is said that the latter's resentment led to the persecution of Galileo.

[594] De Morgan might have found much else for his satire in the letters of Walsh. He sought, in his _Theory of Partial Functions_, to substitute "partial equations" for the differential calculus. In his diary there is an entry: "Discovered the general solution of numerical equations of the fifth degree at 114 Evergreen Street, at the Cross of Evergreen, Cork, at nine o'clock in the forenoon of July 7th, 1844; exactly twenty-two years after the invention of the Geometry of Partial Equations, and the expulsion of the differential calculus from Mathematical Science."

[595] "It has been ordered, sir, it has been ordered."

[596] Bartholomew Prescot was a Liverpool accountant. De Morgan gives this correct spelling on page 278. He died after 1849. His _Inverted Scheme of Copernicus_ appeared in Liverpool in 1822.

[597] Robert Taylor (1784-1844) had many more ups and downs than De Morgan mentions. He was a priest of the Church of England, but resigned his parish in 1818 after preaching against Christianity. He soon recanted and took another parish, but was dismissed by the Bishop almost immediately on the ground of heresy. As stated in the text, he was convicted of blasphemy in 1827 and was sentenced to a year's imprisonment, and again for two years on the same charge in 1831. He then married a woman who was rich in money and in years, and was thereupon sued for breach of promise by another woman. To escape paying the judgment that was rendered against him he fled to Tours where he took up surgery.

[598] Herbert Marsh, Bishop of Peterborough. See note 449 on page 199.

[599] "Argument from the prison."

[600] Richard Carlile (1790-1843), one of the leading radicals of his time. He published Hone's parodies (see note 250, page 124) after they had been suppressed, and an edition of Thomas Paine (1818). He was repeatedly imprisoned, serving nine years in all. His continued conflict with the authorities proved a good advertisement for his bookshop.

[601] Wilhelm Ludwig Christmann (1780-1835) was a protestant clergyman and teacher of mathematics. For a while he taught under Pestalozzi. Disappointed in his ambition to be professor of mathematics at Tubingen, he became a confirmed misanthrope and is said never to have left his house during the last ten years of his life. He wrote several works: _Ein Wort ueber Pestalozzi und Pestalozzismus_ (1812); _Ars cossae promota_ (1814); _Philosophia cossica_ (1815); _Aetas argentea cossae_ (1819); _Ueber Tradition und Schrift, Logos und Kabbala_ (1829), besides the one mentioned above. The word _coss_ in the above titles was a German name for algebra, from the Italian _cosa_ (thing), the name for the unknown quantity. It appears in English in the early name for algebra, "the cossic art."

[602] See note 174, page 101.

[603] See note 589, page 257.

[604] He seems to have written nothing else.

[605] See note 596 on page 270. The name is here spelled correctly.

[606] Joseph Jacotot (1770-1840), the father of this Fortune Jacotot, was an infant prodigy. At nineteen he was made professor of the humanities at Dijon. He served in the army, and then became professor of mathematics at Dijon. He continued in his chair until the restoration of the Bourbons, and then fled to Louvain. It was here that he developed the method with which his name is usually connected. He wrote a _Mathematiques_ in 1827, which went through four editions. The _Epitome_ is by his son, Fortune.

[607] He wrote on educational topics and a _Sacred History_ that went through several editions.

[608] "All is in all."

[609] "Know one thing and refer everything else to it," as it is often translated.

[610] A writer of no reputation.

[611] Sir John Lubbock (1803-1865), banker, scientist, publicist, astronomer, one of the versatile men of his time.

[612] See note 165, page 99.

[613] "Those about to die salute you."

[614] Georges Louis Leclerc Buffon (1707-1788), the well-known biologist. He also experimented with burning mirrors, his results appearing in his _Invention des miroirs ardens pour bruler a une grande distance_ (1747). The reference here may be to his _Resolution des problemes qui regardent le jeu du franc carreau_ (1733). The prominence of his _Histoire naturelle_ (36 volumes, 1749-1788) has overshadowed the credit due to him for his translation of Newton's work on Fluxions.

[615] See page 285. This article was a supplement to No. 14 in the _Athenaeum_ Budget.--A. De M.

[616] There are many similar series and products. Among the more interesting are the following:

[pi] 2.2.4.4.6.6.8...
---- = ----------------,
2 1.3.3.5.5.7.7...

[pi]-3 = 1 1 1
------ = ----- - ----- + ----- - ...,
4 2.3.4 4.5.6 6.7.8

[pi] 1 1 1 1 1
---- = sqrt - . (1 - --- + ----- - ----- + ----- - ...),
6 3 3.3 3^2.5 3^3.7 3^4.9

[pi] 1 1 1 1
---- = 4 ( - - ----- + ----- - ----- + ...)
4 5 3.5^3 5.5^5 7.5^7

1 1 1
- ( --- - ------- + ------- - ...).
239 3.239^3 5.239^5

[617] "To a privateer, a privateer and a half."

[618] Joshua Milne (1776-1851) was actuary of the Sun Life Assurance Society. He wrote _A Treatise on the Valuation of Annuities and Assurances on Lives and Survivorships; on the Construction of tables of mortality; and on the Probabilities and Expectations of Life_, London, 1815. Upon the basis of the Carlisle bills of mortality of Dr. Heysham he reconstructed the mortality tables then in use and which were based upon the Northampton table of Dr. Price. His work revolutionized the actuarial science of the time. In later years he devoted his attention to natural history.

[619] See note 576, page 252. He also wrote the _Theory of Parallels. The proof of Euclid's axiom looked for in the properties of the equiangular spiral_ (London, 1840), which went through four editions, and the _Theory of Parallels. The proof that the three angles of a triangle are equal to two right angles looked for in the inflation of the sphere_ (London, 1853), of which there were three editions.

[620] For the latest summary, see W. B. Frankland, _Theories of Parallelism, an historical critique_, Cambridge, 1910.

[621] Joseph Louis Lagrange (1736-1813), author of the _Mecanique analytique_ (1788), _Theorie des functions analytiques_ (1797), _Traite de la resolution des equations numeriques de tous degres_ (1798), _Lecons sur le calcul des fonctions_ (1806), and many memoirs. Although born in Turin and spending twenty of his best years in Germany, he is commonly looked upon as the great leader of French mathematicians. The last twenty-seven years of his life were spent in Paris, and his remarkable productivity continued to the time of his death. His genius in the theory of numbers was probably never excelled except by Fermat. He received very high honors at the hands of Napoleon and was on the first staff of the Ecole polytechnique (1797).

[622] "I shall have to think it over again."

[623] Henry Goulburn (1784-1856) held various government posts. He was under-secretary for war and the colonies (1813), commissioner to negotiate peace with America (1814), chief secretary to the Lord Lieutenant of Ireland (1821), and several times Chancellor of the Exchequer. On the occasion mentioned by De Morgan he was standing for parliament, and was successful.

[624] On Drinkwater Bethune see note 165, page 99.

[625] Charles Henry Cooper (1808-1866) was a biographer and antiquary. He was town clerk of Cambridge (1849-1866) and wrote the _Annals of Cambridge_ (1842-1853). His _Memorials of Cambridge_ (1874) appeared after his death. Thompson Cooper was his son, and the two collaborated in the _Athenae Cantabrigiensis_ (1858).

[626] William Yates Peel (1789-1858) was a brother of Sir Robert Peel, he whose name degenerated into the familiar title of the London "Bobby" or "Peeler." Yates Peel was a member of parliament almost continuously from 1817 to 1852. He represented Cambridge at Westminster from 1831 to 1835.

[627] Henry John Temple, third Viscount of Palmerston (1784-1865), was member for Cambridge in 1811, 1818, 1820, 1826 (defeating Goulburn), and 1830. He failed of reelection in 1831 because of his advocacy of reform. This must have been the time when Goulburn defeated him. He was Foreign Secretary (1827) and Secretary of State for Foreign Affairs (1830-1841, and 1846-1851). It is said of him that he "created Belgium, saved Portugal and Spain from absolutism, rescued Turkey from Russia and the highway to India from France." He was Prime Minister almost continuously from 1855 to 1865, a period covering the Indian Mutiny and the American Civil War.

[628] William Cavendish, seventh Duke of Devonshire (1808-1891). He was member for Cambridge from 1829 to 1831, but was defeated in 1831 because he had favored parliamentary reform. He became Earl of Burlington in 1834, and Duke of Devonshire in 1858. He was much interested in the promotion of railroads and in the iron and steel industries.

[629] Richard Sheepshanks (1794-1855) was a brother of John Sheepshanks the benefactor of art. (See note 314, p. 147.) He was a fellow of Trinity College, Cambridge, a fellow of the Royal Society and secretary of the Astronomical Society. Babbage (See note 469, p. 207) suspected him of advising against the government support of his calculating machine and attacked him severely in his _Exposition of 1851_, in the chapter on _The Intrigues of Science_. Babbage also showed that Sheepshanks got an astronomical instrument of French make through the custom house by having Troughton's (See note 332, page 152) name engraved on it. Sheepshanks admitted this second charge, but wrote a _Letter in Reply to the Calumnies of Mr. Babbage_, which was published in 1854. He had a highly controversial nature.

[630] See note 469, page 207. The work referred to is _Passages from the Life of a Philosopher_, London, 1864.

[631] Drinkwater Bethune. See note 165, page 99.

[632] Simeon-Denis Poisson (1781-1840) was professor of calculus and mechanics at the Ecole polytechnique. He was made a baron by Napoleon, and was raised to the peerage in 1837. His chief works are the _Traite de mecanique_ (1811) and the _Traite mathematique de la chaleur_ (1835).

[633] "As to M. Poisson, I really wish I had a thousandth part of his mathematical knowledge that I might prove my system to the incredulous."

[634] This list includes most of the works of Antoine-Louis-Guenard Demonville. There was also the _Nouveau systeme du monde ... et hypotheses conformes aux experiences sur les vents, sur la lumiere et sur le fluide electro-magnetique_, Paris, 1830.

[635] Paris, 1835.

[636] Paris, 1833.

[637] The second part appeared in 1837. There were also editions in 1850 and 1852, and one edition appeared without date.

[638] Paris, 1842.

[639] Parsey also wrote _The Art of Miniature Painting on Ivory_ (1831), _Perspective Rectified_ (1836), and _The Science of Vision_ (1840), the third being a revision of the second.

[640] William Ritchie (1790-1837) was a physicist who had studied at Paris under Biot and Gay-Lussac. He contributed several papers on electricity, heat, and elasticity, and was looked upon as a good experimenter. Besides the geometry he wrote the _Principles of the Differential and Integral Calculus_ (1836).

[641] Alfred Day (1810-1849) was a man who was about fifty years ahead of his time in his attempt to get at the logical foundations of geometry. It is true that he laid himself open to criticism, but his work was by no means bad. He also wrote _A Treatise on Harmony_ (1849, second edition 1885), _The Rotation of the Pendulum_ (1851), and several works on Greek and Latin Grammar.

[642] Walter Forman wrote a number of controversial tracts. His first seems to have been _A plan for improving the Revenue without adding to the burdens of the people_, a letter to Canning in 1813. He also wrote _A New Theory of the Tides_ (1822). His _Letter to Lord John Russell, on Lord Brougham's most extraordinary conduct; and another to Sir J. Herschel, on the application of Kepler's third law_ appeared in 1832.

[643] Lord John Russell (1792-1878) first Earl Russell, was one of the strongest supporters of the reform measures of the early Victorian period. He became prime minister in 1847, and again in 1865.

[644] Lauder seems never to have written anything else.

[645] See note 22, page 40.

[646] The names of Alphonso Cano de Molina, Yvon, and Robert Sara have no standing in the history of the subject beyond what would be inferred from De Morgan's remark.

[647] Claude Mydorge (1585-1647), an intimate friend of Descartes, was a dilletante in mathematics who read much but accomplished little. His _Recreations mathematiques_ is his chief work. Boncompagni published the "Problemes de Mydorge" in his _Bulletino_.

[648] Claude Hardy was born towards the end of the 16th century and died at Paris in 1678. In 1625 he edited the _Data Euclidis_, publishing the Greek text with a Latin translation. He was a friend of Mydorge and Descartes, but an opponent of Fermat.

[649] That is, in the _Bibliotheca Realis_ of Martin Lipen, or Lipenius (1630-1692), which appeared in six folio volumes, at Frankfort, 1675-1685.

[650] See note 29, page 43.

[651] Baldassare Boncompagni (1821-1894) was the greatest general collector of mathematical works that ever lived, possibly excepting Libri. His magnificent library was dispersed at his death. His _Bulletino_ (1868-1887) is one of the greatest source books on the history of mathematics that we have. He also edited the works of Leonardo of Pisa.

[652] He seems to have attracted no attention since De Morgan's search, for he is not mentioned in recent bibliographies.

[653] Joseph-Louis Vincens de Mouleon de Causans was born about the beginning of the l8th century. He was a Knight of Malta, colonel in the infantry, prince of Conti, and governor of the principality of Orange. His works on geometry are the _Prospectus apologetique pour la quadrature du cercle_ (1753), and _La vraie geometrie transcendante_ (1754).

[654] See note 119, page 80.

[655] See note 120, page 81.

[656] Lieut. William Samuel Stratford (1791-1853), was in active service during the Napoleonic wars but retired from the army in 1815. He was first secretary of the Astronomical Society (1820) and became superintendent of the Nautical Almanac in 1831. With Francis Baily he compiled a star catalogue, and wrote on Halley's (1835-1836) and Encke's (1838) comets.

[657] See Sir J. Herschel's _Astronomy_, p. 369.--A. De M.

[658] Captain Ross had just stuck a bit of brass there.--A. De M.

Sir James Clark Ross (1800-1862) was a rear admiral in the British navy and an arctic and antarctic explorer of prominence. De Morgan's reference is to Ross's discovery of the magnetic pole on June 1, 1831. In 1838 he was employed by the Admiralty on a magnetic survey of the United Kingdom. He was awarded the gold medal of the geographical societies of London and Paris in 1842.

[659] John Partridge (1644-1715), the well-known astrologer and almanac maker. Although bound to a shoemaker in his early boyhood, he had acquired enough Latin at the age of eighteen to read the works of the astrologers. He then mastered Greek and Hebrew and studied medicine. In 1680 he began the publication of his almanac, the _Merlinus Liberatus_, a book that acquired literary celebrity largely through the witty comments upon it by such writers as Swift and Steele.

[660] See note 642 on page 296.

[661] William Woodley also published several almanacs (1838, 1839, 1840) after his rejection by the Astronomical Society in 1834.

[662] It appeared at London.

[663] The first edition appeared in 1830, also at London.

[664] See note 441, page 196.

[665] Thomas Kerigan wrote _The Young Navigator's Guide to the siderial and planetary parts of Nautical Astronomy_ (London, 1821, second edition 1828), a work on eclipses (London, 1844), and the work on tides (London, 1847) to which De Morgan refers.

[666] Jean Sylvain Bailly, who was guillotined. See note 365, page 166.

[667] See note 670, page 309.

[668] Laurent seems to have had faint glimpses of the modern theory of matter. He is, however, unknown.

[669] See note 133, page 87.

[670] Francis Baily (1774-1844) was a London stockbroker. His interest in science in general and in astronomy in particular led to his membership in the Royal Society and to his presidency of the Astronomical Society. He wrote on interest and annuities (1808), but his chief works were on astronomy.

[671] If the story is correctly told Baily must have enjoyed his statement that Gauss was "the oldest mathematician now living." As a matter of fact he was then only 58, three years the junior of Baily himself. Gauss was born in 1777 and died in 1855, and Baily was quite right in saying that he was "generally thought to be the greatest" mathematician then living.

[672] Margaret Cooke, who married Flamsteed in 1692.

[673] John Brinkley (1763-1835), senior wrangler, first Smith's prize-man (1788), Andrews professor of astronomy at Dublin, first Astronomer Royal for Ireland (1792), F.R.S. (1803), Copley medallist, president of the Royal Society and Bishop of Cloyne. His _Elements of Astronomy_ appeared in 1808.

[674] See note 248, page 124.

[675] See note 276, page 133.

[676] See note 352, page 161.

[677] "It becomes the doctors of the Sorbonne to dispute, the Pope to decree, and the mathematician to go to Paradise on a perpendicular line."

[678] See note 124, page 83.

[679] See note 621, page 288.

[680] Sylvain van de Weyer, who was born at Louvain in 1802. He was a jurist and statesman, holding the portfolio for foreign affairs (1831-1833), and being at one time ambassador to England.

[681] Henry Crabb Robinson (1775-1867), correspondent of the _Times_ at Altona and in the Peninsula, and later foreign editor. He was one of the founders of the Athenaeum Club and of University College, London. He seems to have known pretty much every one of his day, and his posthumous _Diary_ attracted attention when it appeared.

[682] Was this Whewell, who was at Trinity from 1812 to 1816 and became a fellow in 1817?

[683] Tom Cribb (1781-1848) the champion pugilist. He had worked as a coal porter and hence received his nickname, the Black Diamond.

[684] John Finleyson, or Finlayson, was born in Scotland in 1770 and died in London in 1854. He published a number of pamphlets that made a pretense to being scientific. Among his striking phrases and sentences are the statements that the stars were made "to amuse us in observing them"; that the earth is "not shaped like a garden turnip as the Newtonians make it," and that the stars are "oval-shaped immense masses of frozen water." The first edition of the work here mentioned appeared at London in 1830.

[685] Richard Brothers (1757-1824) was a native of Newfoundland. He went to London when he was about 30, and a little later set forth his claim to being a descendant of David, prince of the Hebrews, and ruler of the world. He was confined as a criminal lunatic in 1795 but was released in 1806.

[686] Charles Grey (1764-1845), second Earl Grey, Viscount Howick, was then Prime Minister. The Reform Bill was introduced and defeated in 1831. The following year, with the Royal guarantees to allow him to create peers, he finally carried the bill in spite of "the number of the beast."

[687] The letters of obscure men, the _Epistolae obscurorum virorum ad venerabilem virum Magistrum Ortuinum Gratium Dauentriensem_, by Joannes Crotus, Ulrich von Hutten, and others appeared at Venice about 1516.

[688] The lamentations of obscure men, the _Lamentationes obscurorum virorum, non prohibete per sedem Apostolicam. Epistola D. Erasmi Roterodami: quid de obscuris sentiat_, by G. Ortwinus, appeared at Cologne in 1518.

[689] The criticism was timely when De Morgan wrote it. At present it would have but little force with respect to the better class of algebras.

[690] Thomas Ignatius Maria Forster (1789-1860) was more of a man than one would infer from this satire upon his theory. He was a naturalist, astronomer, and physiologist. In 1812 he published his _Researches about Atmospheric Phenomena_, and seven years later (July 3, 1819) he discovered a comet. With Sir Richard Phillips he founded a Meteorological Society, but it was short lived. He declined a fellowship in the Royal Society because he disapproved of certain of its rules, so that he had a recognized standing in his day. The work mentioned by De Morgan is the second edition, the first having appeared at Frankfort on the Main in 1835 under the title, _Recueil des ouvrages et des pensees d'un physicien et metaphysicien_.