DEMONOLOGY (L1alµwv, demon,

See also:

• GENIUS (from Lat. genere, gignere)

genius, spirit)  , the branch of the science of religions which relates to superhuman beings which are not gods . It deals both with benevolent beings which have no circle of worshippers or so limited a circle as to be below the rank of gods, and with malevolent beings of all kinds . It may be noted that the original sense of " demon " was a benevolent being; but in English the name now connotes malevolence; in German it has a neutral sense, e.g . Korndamonen . Demons, when they are regarded as spirits, may belong to either of the classes of spirits recognized by primitive animism (q.v.); that is to say, they may be human, or non-human, separable souls, or discarnate spirits which have never inhabited a body; a. sharp DEMONOLOGY 5 distinction is often drawn between these two classes, notably by the Melanesians, the West Africans and others; the Arab jinn, for example, are not reducible to modified human souls; at the same time these classes are frequently conceived as producing identical results, e.g. diseases . Under the head of demons are classified only such spirits as are believed to enter into relations with the human race; the term therefore includes (I) human souls regarded as genii or familiars, (2) such as receive a cult (for which see ANCESTOR WORSHIP), and (3) ghosts or other malevolent revenants; excluded are souls conceived as inhabiting another world . But just as gods are not necessarily spiritual, demons may also be regarded as corporeal; vampires for example are sometimes described as human heads with appended entrails, which issue from the tomb to attack the living during the night watches± The so-called Spectre Huntsman of the Malay Peninsula is said to be a man who scours the firmament with his dogs, vainly seeking for what he could not find on earth-a buck mouse-deer pregnant with male offspring; but he seems to be a living man; there is no statement that he ever died, nor yet that he is a spirit . The incubus and succubus of the middle ages are some-times regarded as spiritual beings; but they were held to give very real proof of their bodily existence . It should, however, be remembered that primitive peoples do not distinguish clearly between material and immaterial beings . Prevalence of Demons.—According to a conception of the world frequently found among peoples of the lower cultures, all the affairs of life are supposed to be under the control of spirits, each ruling a certain element or even object, and them-selves in subjection to a greater spirit . Thus, the Eskimo are said to believe in spirits of the sea, earth and say, the winds, the clouds and everything in nature . Every cove of the seashore, every point, every island and prominent rock has its guardian spirit .

All are of the

malignant type, to be propitiated only by acceptable offerings from persons who desire to visit the locality where it is supposed to reside . A rise in culture often results in an increasein the number of spiritual beings with whom man surrounds himself . Thus, the Koreans go far beyond the Eskimo and number their demons by thousands of billions; they fill the chimney, the shed, the living-room, the kitchen, they are on every shelf and jar; in thousands they waylay the traveller as he leaves his home, beside him, behind him, dancing in front of him, whirring. over his head, crying out upon him from air, earth and water . Especially complicated was the ancient Babylonian demonology; all the petty annoyances of life—a sudden fall, a headache, a quarrel—were set down to the agency of fiends; all the stronger emotions—love, hate, jealousy and so on—were regarded as the work of demons; in fact so numerous were they, that there were special fiends for various parts of the human body—one for the head, another for the neck, and so on . Similarly in Egypt at the present day the jinn are believed to swarm so thickly that it is necessary to ask their permission before pouring water on the ground, lest one should accidentally be soused and vent his anger on the offending human being . But these beliefs are far from being confined to the uncivilized; Greek philosophers like Porphyry, no less than the fathers of the Church, held that the world was pervaded with spirits; side by side with the belief in witchcraft, we can trace through the middle ages the survival of primitive animistic views; and in our own day even these beliefs subsist in unsuspected vigour among the peasantry of the more uneducated European countries . In fact the ready acceptance of spiritualism testifies to the force with which the primitive animistic way of looking at things appealed to the white races in the middle of the last century . Character of Spiritual World.—The ascription of malevolence to the world of spirits is by no means universal . In West Africa the Mpongwe believe in local spirits, just as do the Eskimo; but they are regarded as inoffensive in the main; true, the passer-by must make some trifling offering as he nears their place of abode; but it is only occasionally that mischievous acts, such as the throwing down of a tree on a passer-by, are, in the view of the natives, perpetuated by the Ombuiri . So too, many of the spirits especially concerned with the operations of nature are conceived as neutral or even benevolent; the European peasant fears the corn-spirit only when he irritates him by trenching on his domain and taking his property by cutting the corn; similarly, there is no reason why the more insignificant personages of the pantheon should be conceived as malevolent, and we find that the Petara of the Dyaks are far from indiscriminating and malignant, though disease and death are laid at their door . Classification.—Besides the distinctions of human and non-human, hostile and friendly, the demons in which the lower races believe are classified by them according to function, each class with a distinctive name, with extraordinary minuteness, the list in the case of the Malays running to several score . They have, fbr example, a demon of the waterfall, a demon of wild-beast tracks, a demon which interferes with snares for wild-fowl, a baboon demon, which takes possession of dancers and causes them to perform wonderful feats of climbing, &c .

But it is impossible to do more than

deal with a few types, which will illustrate the main features of the demonology of savage, barbarous and semi-civilized peoples . (a) Natural causes, either of death or of disease, are hardly, if at all, recognized by the uncivilized; everything is attributed to spirits or magical influence of some sort . The spirits which cause disease may be human or non-human and their influence is shown in more than one way; they may enter the body of the victim (see POSSESSION), and either dominate his mind as well as his body, inflict specific diseases, or cause pains of various sorts . Thus the Mintra of the Malay Peninsula have a demon corresponding to every kind of disease known to them; the Tasmanian ascribed a gnawing pain to the presence within him of the soul of a dead man, whom he had unwittingly summoned by mentioning his name and who was devouring his liver; the Samoan held that the violation of a food tabu would result in the animal being formed within the body of the offender and cause his death . The demon theory of disease is still attested by some of our medical terms; epilepsy (Gr. ini?tnihs, seizure) points to the belief that the patient is possessed . As a logical consequence of this view of disease the mode of treatment among peoples in the lower stages of culture is mainly magical; they endeavour to propitiate the evil spirits by sacrifice, to expel them by spells, &c . (see EXORCISM), to drive them away by blowing, &c.; conversely we find the Khonds attempt to keep away smallpox ;,v placing thorns and brushwood in the paths leading to places decimated by that disease, in the hope of making the disease demon retrace his steps . This theory of disease disappeared sooner than did the belief in possession; the energumens (Evep'yobuevoL) of the early Christian church, who were under the care of a special clerical order of exorcists, testify to a belief in possession; but the demon theory of disease receives no recognition; the energumens find their analogues in the converts of missionaries in China, Africa and elsewhere . Another way in which a demon is held to cause disease is by introducing itself into the patient's body and sucking his blood; the Malays believe that a woman who dies in childbirth becomes a langsuir and sucks the blood of children; victims of the lycanthrope are sometimes said to be done to death in the same way; and it is commonly believed in Africa that the wizard has the power of killing people in this way, probably with the aid of a familiar . (b) One of the primary meanings of Saloom is that of genius or familiar, tutelary spirit; according to Hesiod the men of the golden race became after death guardians or watchers over mortals . The idea is found among the Romans also; they attributed to every man a genius who accompanied him through life . A Norse belief found in Iceland is that the fylgia, a genius in animal form, attends human beings; and these animal guardians may sometimes be seen fighting; in the same way the Siberian shamans send their animal familiars to do battle instead of deciding their quarrels in person .

The animal guardian re-appears in the nagual of Central

America (see article TOTEMISM), the yunbeai of some Australian tribes, the manitou of the Red Indian and the bush soul of some West African tribes;among the latter the link between animal and human being is said to be established by the ceremony of the blood bond . Corresponding to the animal guardian of the ordinary man, we have the familiar of the witch or wizard . All the world over it is held that such people can assume the form of animals; some-times the power of the shaman is held to depend on his being able to summon his familiar; among the Ostiaks the shaman's coat was covered with representations of birds and beasts; two bear's claws were on his hands; his wand was covered with mouse-skin; when he wished to divine he beat his drum till a black bird appeared and perched on his hut; then the shaman swooned, the bird vanished, and the divination could begin . Similarly the Greenland angekok is said to summon his torngak (which may be an ancestral ghost or an animal) by drumming; he is heard by- the bystanders to carry on a conversation and obtain advice as to how to treat diseases, the prospects of good weather and other matters of importance . The familiar, who is sometimes replaced by the devil, commonly figured in witchcraft trials; and a statute of James I. enacted that all persons invoking an -evil spirit or consulting, covenanting with, entertaining, employing, feeding or rewarding any evil spirit should be guilty of felony and suffer death . In modern spiritualism the familiar is represented by the " guide," corresponding to which we have the theosophical " guru." (c) The familiar is sometimes an ancestral spirit, and here we touch the fringe of the cult of the dead (see also ANCESTOR WORSHIP) . Especially among the lower races the dead are regarded as hostile; the Australian avoids the grave even of a kinsman and elaborate ceremonies of mourning are found amongst most primitive peoples, whose object seems to be to rid the living of the danger they, run by association with the ghost of the dead . Among the Zulu the spirits of the dead are held to be friendly or hostile, just as they were in life; on the Congo a man after death joins the good or bad spirits according as his life has been good or bad . Especially feared among many peoples are the souls of those who have committed suicide or died a violent death; the woman who dies in childbed is held to become a demon of the most dangerous , kind; even the unburied, as restless, dissatisfied spirits, are more feared than ordinary ghosts . Naturally spirits of these latter kinds are more valuable as familiars than ordinary dead men's souls . We find many recipes for securing their aid . In the Malay Peninsula the blood of a.murdered man must be put in a bottle and prayers said over; after seven days of this worship a sound is heard and the operator puts his finger into the bottle for the polong, as the demon is called, to suck; it will fly through the air in the shape of an exceedingly diminutive female figure, and is always preceded by its pet, the, pelesit, in the shape of a grasshopper .

In

Europe a similar demon is said to be obtainable from a cock's egg . In South Africa and India, on the other hand, the magician digs up a dead-body, especially of a child, to secure a familiar . The evocation of spirits, especially in the form of necromancy, is an important branch of the demonology of many peoples; and the peculiarities of trance medium-ship, which seem sufficiently established by modern research, go far to explain the vogue of this art . It seems to have been common among the Jews, and the case of the witch of Endor is narrated in a way to suggest something beyond fraud; in the book of magic which bears the name of Dr Faustus may be found many of the formulae for raising demons; in England may be mentioned especially Dr Dee as one of the most famous of those who claimed before the days of modern spiritualism (q.v.) to have intercourse with the unseen world and to summon demons at his will . Sometimes the spirits were summoned to appear as did the phantoms of the Greek heroes to Odysseus; some-times they were called to enter a crystal (see CRYSTAL-GAZING); sometimes they are merely asked to declare the future or communicate by moving external objects without taking a visible form; thus among the Karens at the close of the burial ceremonies the ghost of the dead man, which is said to hover round till the rites are completed, is believed to make a ring swing round and snap the string from which it hangs . (d) The vampire is a particular form of demon which calls fo7 some notice . In the Malay Peninsula, parts of Polynesia, &e., it is conceived as a head with attached enerails, which issues, it may be from the grave, to suck the blood of living human beings . According to the Malays a penanggalan (vampire) is a living witch, and can be killed if she can be caught; she is especially feared in houses where a birth has taken place and it is the custom to hang up a bunch of thistle in order to catch her; she is said to keep vinegar at home to aid her in re-entering her own body . In Europe the Slavonic area is the principal seat of vampire beliefs, and here too we find, as a natural development, that means of preventing the dead from injuring the living have been evolved by the popular mind . The corpse of the vampire, which may often be recognized by its unnaturally ruddy and fresh appearance, should be staked down in the grave or its head should be cut off; it is interesting to note that the cutting off of heads of the dead was a neolithic burial rite . (e) The vampire is frequently blended in popular idea with the Poltergeist (q.v.) or knocking spirit, and also with the werwolf (see LYCANTHROPY) . (f) As might be expected, dream demons are very common; in fact the word " nightmare " (A.S. mar, spirit, elf) preserves for us a record of this form of belief, which is found right down to the lowest planes of culture .

The Australian, when he suffers from an oppression in his

sleep, says that Koin is trying to throttle him; the Caribs say that Maboya beats them in their sleep; and the belief persists to this day in some parts of Europe; horses too are said to be subject to the persecutions of demons, which ride them at night . Another class of nocturnal demons are the incubi and succubi, who are said to consort with human beings in their sleep; in the Antilles these were the ghosts of the dead; in New Zealand likewise ancestral deities formed liaisons with females; in the Samoan Islands the inferior gods were regarded as the fathers of children otherwise unaccounted for; the Hindus have rites prescribed by which a companion nymph may be secured . The question of the real existence of incubi and succubi, whom the Romans identified with the fauns, was gravely discussed by the fathers of the church; and in 1418 Innocent VIII. set forth the doctrine of lecherous demons as an indisputable fact; and in the history of the Inquisition and of trials for witch-craft may be found the confessions of many who bore witness to their reality . In the Anatomy of Melancholy Burton assures us that they were never more numerous than in A.D . 1600 . (g) Corresponding to the personal tutelary spirit (supra, b) we have the genii of buildings and places . The Romans celebrated the birthday of a town and of its genius, just as they celebrated that of a man; and a snake was a frequent form for this kind of demon; when we compare with this the South African belief that the snakes which are in the neighbourhood of the kraal are the incarnations. of the ancestors of the residents, it seems probable that some similar idea lay at the bottom of the Roman belief; to this day in European folklore the house snake or toad, which lives in the cellar, is regarded as the " life index " or other self of the father of the house; the death of one involves the death of the other, according to popular belief . The assignment of genii to buildings and gates is connected with an important class of sacrifices; in order to provide a tutelary spirit, or to appease chthonic deities, it was often the custom to sacrifice a human being or an animal at the foundation of a building; sometimes we find a similar guardian provided for the frontier of a country or of a tribe . The house spirit is, however, not necessarily connected with this idea . In Russia the domovoi (house spirit) is an important personage in folk-belief; he may object to certain kinds of animals, or to certain colours in cattle; and must, generally speaking, be propitiated and cared for . Corresponding to him we have the drudging goblin of English folklore . (h) It has been shown above how the animistic creed postulates the existence of all kinds of local spirits, which are sometimes tied to their habitats, sometimes free to wander .

Especially prominent in Europe, classical,

medieval and modern, and in East Asia, is the spirit of the lake, river, spring, or well, often conceived as human, but also in the form of a bull or horse; the term Old Nick may refer to the water-horse Nok . Less specializedin their functions are many of the figures of modern folklore, some of whom have perhaps replaced some ancient goddess, e.g . Fran Holda; others, like the Welsh Pwck, the Lancashire boggarts or the more widely found Jack-o'-Lantern (Will o' the Wisp), are sprites who do no ,more harm than leading the wanderer astray . The banshee is perhaps connected with ancestral or house spirits; the Wild Huntsman, the Gabriel hounds, the Seven Whistlers, &c., are traceable to some actual phenomenon; but the great mass of British goblindom cannot now be traced back to savage or barbarous analogues . Among other local sprites may be mentioned the kobolds or spirits of the mines . The fairies (see FAIRY), located in the fairy knolls by the inhabitants of the Shetlands, may also be put under this head . (i) The subject of plant souls is referred to in connexion with animism (q.v.); but certain aspects of this phase of belief demand more detailed treatment . Outside the European area vegetation spirits of all kinds seem to be conceived, as a rule, as anthropomorphic; in classical Europe, and parts of the Slavonic area at the present day, the tree spirit was believed to have the form of a goat, or to have goats' feet . Of special importance in Europe is the conception of the so-called " corn spirit "; W . Mannhardt collected a mass of information proving that the life of the corn is supposed to exist apart from the corn itself and to take the form, sometimes of an animal, sometimes of a man or woman, sometimes of a child . There is, however, no proof that the belief is animistic in the proper sense . The animal which popular belief identified with the corn demon is sometimes killed in the spring in order to mingle its blood or bones with the seed; at harvest-time it is supposed to sit in the last corn and the animals driven out from it are sometimes killed; at others the reaper who cuts the last ear is said to have killed the " wolf " or the " dog,?" and sometimes receives the name of " wolf " or " dog " and retains it till the next harvest .

The corn spirit is also said to be hiding in the

barn till the corn is threshed, or it may be said to reappear at midwinter, when the farmer begins to think of his new year of labour and harvest . Side by side with the conception of the corn spirit as an animal is the anthropomorphic view of it; and this element must have predominated in the evolution of the cereal deities like Demeter; at the same time traces of the association of gods and goddesses of corn with animal embodiments of the corn spirit are found . (j) In many parts of the world, and especially in Africa, is found the conception termed the " otiose creator "; that is to say, the belief in a great deity, who is the author of all that exists but is too remote from the world and too high above terrestrial things to concern himself with the details of the universe . As a natural result of this belief we find the view that the operations of nature are conducted by a multitude of more or less obedient subordinate deities; thus, in Portuguese West Africa the Kimbunda believe in Suku-Vakange, but hold that he has committed the government of the universe to innumerable kilulu good and bad; the latter kind are held to be far more numerous, but Suku-Vakange is said to keep them in order by occasionally smiting them with his thunderbolts; were it not for this, man's lot would be insupportable . Sometimes the gods of an older religion degenerate into the demons of the belief *hich supersedes it . A conspicuous example of this is found in the attitude of the Hebrew prophets to the gods of the nations, whose power they recognize without admitting their claim to reverence and sacrifice . The same tendency is seen in many early missionary works and is far from being without influence even at the present day . In the folklore of European countries goblindom is peopled by gods and nature-spirits of an earlier heathendom . We may also compare the Persian devs with the Indian devas . Expulsion of Demons.—In connexion with demonology mention must be made of the custom of expelling ghosts, spirits or evils generally . Primitive peoples from the Australians upwards celebrate, usually at fixed intervals, a driving out of hurtful influences . Sometimes, as among the Australians, it is merely the ghosts of those who have died in the year which are thus driven out; from this custom must be distinguished another, which consists in dismissing the souls of the dead at the close of the year and sending them on their journey to the other world; this latter custom seems to have an entirely different origin and to be due to love and not fear of the dead .

In other cases it is believed that evil spirits generally or even non-personal evils such as sins are believed to be expelled . In these customs originated perhaps the scapegoat, some forms of sacrifice (q.v.) and other cathartic ceremonies . (N . W . T.) DE

MORGAN, AUGUSTUS (1806-1871), English mathematician and logician, was born in June 18o6, at Madura, in the Madras presidency . His father, Colonel John De Morgan, was employed in the East India Company's service, and his grand-father and great-grandfather had served under Warren Hastings . On the mother's side he was descended from JamesDodson,F.R.S., author of the Anti-logarithmic Canon and other mathematical works of merit, and a friend of Abraham Demoivre . Seven months after the birth of Augustus, Colonel De Morgan brought his wife, daughter and infant son to England, where he left them during a subsequent period of service in India, dying in 1816 on his way home . Augustus De Morgan received his early education in several private schools, and before the age of fourteen years had learned Latin, Greek and some Hebrew, in addition to acquiring much general knowledge . At the age of sixteen years and a half he entered Trinity College, Cambridge, and studied mathematics, partly under the tuition of Sir G . B . Airy .

In 1825 he gained a Trinity scholarship . De Morgan's love of wide

reading some-what interfered with his success in the mathematical tripos, in which he took the fourth place in 1827 . He was prevented from taking his M.A. degree, or from obtaining a fellowship, by his conscientious objection to signing the theological tests then required from masters of arts and fellows at Cambridge . A career in his own university being closed against him, he entered Lincoln's Inn; but had hardly done so when the establishment, in 1828, of the university of London, in Gower Street, afterwards known as University College, gave him an opportunity of continuing his mathematical pursuits . At the early age of twenty-two he gave his first lecture as professor of mathematics in the college which he served with the utmost zeal and success for a third of a century . His connexion with the college, indeed, was interrupted in 1831, when a disagreement with the governing body caused De Morgan and some other professors to resign their chairs simultaneously . When, in 1836, his successor was accidentally drowned, De Morgan was requested to resume the professorship . In 1837 he married Sophia Elizabeth,' daughter of William Frend, a Unitarian in faith, a mathematician and actuary in occupation, a notice of whose life, written by his son-in-law, will be found in the Monthly Notices of the Royal Astronomical Society (vol. v.) . They settled in Chelsea (30 Cheyne Row), where in later years Mrs De Morgan had a large circle of intellectual and artistic friends . As a teacher of mathematics De Morgan was unrivalled . He gave instruction in the form of continuous lectures delivered extempore from brief notes . The most prolonged mathematical reasoning, and the most intricate formulae, were given with almost infallible accuracy from the resources of his extraordinary memory .

De Morgan's writings, however excellent, give little idea of the perspicuity and elegance of his viva voce expositions, which never failed to

fix the attention of all who were worthyof hearing him . Many of his pupils have distinguished them-selves, and, through'Isaac Todhunter and E . J . Routh, he had an important influence on the later Cambridge school . For thirty years he took an active part in the business of the Royal Astronomical Society, editing its publications, supplying obituary notices of members, and for eighteen years acting as one of the honorary secretaries . He was also frequently employed as consulting actuary, a business in which his mathematical powers, combined with sound judgment and business-like habits, fitted him to take the highest place . De Morgan's mathematical writings contributed powerfully towards the progress of the science . His memoirs on the " Foundation of Algebra," in the 7th and 8th volumes of the Cambridge Philosophical Transactions, contain some of the most important contributions which have been made to the philosophy of mathematical method; and Sir W . Rowan Hamilton, in the preface to his Lectures on Quaternions, refers more than once to those papers as having led and encouraged him in the working out of the new system of quaternions . The work on Trigonometry and Double Algebra (1849) contains in the latter part a most luminous and philosophical view of existing and possible systems of symbolic calculus . But De Morgan's influence on mathematical science in England can only be estimated by a review of his long series of publications, which commence, in 1828, with a translation of part of Bourdon's Elements of Algebra, prepared for his students . In 1830 appeared the first edition of his well-known Elements of Arithmetic, which did much to raise the character of elementary training .

It is distinguished by a

simple yet thoroughly philosophical treatment of the ideas of number and magnitude, as well as by the introduction of new abbreviated processes of computation, to which De Morgan always attributed much practical importance . Second and third editions were called for in 1832 and 1835; a sixth edition was issued in 1876 . De Morgan's other principal mathematical works were The Elements of Algebra (1835), a valuable but some-what dry elementary treatise; the Essay on Probabilities (1838), forming the Io7th volume of Lardner's Cyclopaedia, which forms a valuable introduction to the subject; and The Elements of Trigonometry and Trigonometrical Analysis, preliminary to the Differential Calculus (1837) . Several of his mathematical works were published by the Society for the Diffusion of Useful Know-ledge, of which De Morgan was at one time an active member . Among these may be mentioned the Treatise on the Differential and Integral Calculus (1842) ; the Elementary Illustrations of the Differential and Integral Calculus, first published in 1832, but often bound up with the larger treatise; the essay, On the Study and Difficulties of Mathematics (1831); and a brief treatise on Spherical Trigonometry (1834) . By some accident the work on probability in the same series, written by Sir J . W . Lubbock and J . Drinkwater-Bethune, was attributed to De Morgan, an error which seriously annoyed his nice sense of bibliographical accuracy . For fifteen years he did all in his power to correct the mistake, and finally wrote to The Times to disclaim the authorship . (See Monthly Notices of the Royal Astronomical Society, vol. xxvi. p . 118.) Two of his most elaborate treatises are to be found in the Encyclopaedia metropolitan, namely the articles on the Calculus of Functions, and the Theory of Probabilities .

De Morgan's

minor mathematical writings were scattered over various periodicals . A list of these and other papers will be found in the Royal Society's Catalogue, which contains forty-two entries under the name of De Morgan . In spite, however, of the excellence and extent of his mathematical writings, it is probably as a logical reformer that De Morgan will be best remembered . In this respect he stands alongside of his great contemporaries Sir W . R . Hamilton and George Boole, as one of several independent discoverers of the all-important principle of the quantification of the predicate . Unlike most mathematicians, De Morgan always laid much stress upon the importance of logical training . In his admirable papers upon the modes of teaching arithmetic and geometry, originally published in the Quarterly Journal of Education (reprinted in The Schoolmaster, vol ii.), he remonstrated against the neglect of logical doctrine . In 1839 he produced a small work called First Notions of Logic, giving what he had found by experience to be much wanted by students commencing with Euclid . In October 1846 he completed the first of his investigations, in the form of a paper printed in the Transactions of the Cambridge Philosophical Society (vol. viii . No . 29) .

In this paper the principle of the quantified predicate was referred to, and there immediately ensued a memorable controversy with Sir W . R . Hamilton regarding the

independence of De Morgan's discovery, some communications having passed between them in the autumn of 1846 . The details of this dispute will be found in the original pamphlets, in the Athenaeum and in the appendix to De Morgan's Formal Logic . Suffice it to say that the independence of De Morgan's discovery was subsequently recognized by Hamilton . The eight forms of proposition adopted by De Morgan as the basis of his system partially differ from those which Hamilton derived from the quantified predicate . The general character of De Morgan's development of logical forms was wholly peculiar and original on his part . Late in 1847 De Morgan published his principal logical treatise, called Formal Logic, or the Calculus of Inference, Necessary and Probable . This contains a reprint of the First Notions, an elaborate development of his doctrine of the syllogism, and of the numerical definite syllogism, together with chapters of great interest on probability, induction, old logical terms and fallacies . The severity of the treatise is relieved by characteristic touches of humour, and by quaint anecdotes and allusions furnished from his wide reading and perfect memory . There followed at intervals, in the years 185o, 1858, 186o and 1863, a series of four elaborate memoirs on the " Syllogism," printed in volumes ix. and x. of the Cambridge Philosophical Transactions . These papers taken together constitute a great treatise on logic, in which he substituted improved systems of notation, and developed a new logic of relations, and a new onymatic system of logical expression .

In 186o De Morgan endeavoured to render their contents better known by

publishing a Syllabus of a Proposed System of Logic, from which may be obtained a good idea of his symbolic system, but the more readable and interesting discussions contained in the memoirs are of necessity omitted . The article " Logic " in the English Cyclopaedia (186o) completes the list of his logical publications . Throughout his logical writings De Morgan was led by the idea that the followers of the two great branches of exact science, logic and mathematics, had made blunders,—the logicians in neglecting mathematics, and the mathematicians in neglecting logic . He endeavoured to reconcile them, and in the attempt showed how many errors an acute mathematician could detect in logical writings, and how large a field there was for discovery . But it may be doubted whether De Morgan's own system, " horrent with mysterious spiculae," as Hamilton aptly described it, is fitted to exhibit the real analogy between quantitative and qualitative reasoning, which is rather to be sought in the logical works of Boole . Perhaps the largest part, in volume, of De Morgan's writings re-mains still to be briefly mentioned; it consists of detaehed articles contributed to various periodical or composite works . During the years 1833–1843 he contributed very largely to the first edition of the Penny Cyclopaedia, writing chiefly on mathematics, astronomy, phy>ics and biography . His articles of various length cannot be less in number than 85o, and they have been estimated to constitute a sixth part of the whole Cyclopaedia, of which they formed perhaps the most valuable portion . He also wrote biographies of Sir Isaac Newton and Edmund Halley for Knight's British Worthies, various notices of scientific men for the Gallery of Portraits, and for the uncompleted Biographical Dictionary of the Useful Knowledge Society, and at least seven articles in Smith's Dictionary of Greek and Roman Biography . Some of De Morgan's most interesting and useful minor writings are to be found in the Companions to the British Almanack, to which he contributed without fail one article each year from 1831 up to 1857 inclusive . In these carefully written papers he treats a great variety of topics relating to astronomy, chronology, decimal coinage, life assurance, bibliography and the history of science . Most of them are as valuable now as when written .

Among De Morgan's

miscellaneous writings may be mentioned his Explanation of the Gnomonic Projection of the Sphere, 1836, including a description of the maps of the stars, published by the Useful Know-.ledge Society; his Treatise on the Globes, Celestial and Terrestrial,1845, and his remarkable Book of Almanacks (2nd edition, 1871), which contains a series of thirty-five almanacs, so arranged with indices of reference, that the almanac for any year, whether in old style or new, from any epoch, ancient or modern, up to A . D . 2000, may be found without difficulty, means being added for verifying the almanac and also for discovering the days of new and full moon from 2000 B . C . Up to A . D . 2000 . De Morgan expressly draws attention to the fact that the plan of this book was that of L . B . Francoeur and J . Ferguson, but the plan was developed by one who was an unrivalled master of all the intricacies of chronology . The two best tables of logarithms, the small five-figure tables of the Useful Knowledge Society 1839 and 1857), and Shroen's Seven Figure-Table (5th ed., 1865), were printed under De Morgan's superintendence .

Several works edited by him will be found mentioned in the British Museum Catalogue . He made numerous

anonymous contributions through a long series of years to the Athenaeum, and to Notes and Queries, and occasionally to The North British Review, Macmillan's Magazine, &c . Considerable labour was spent by De Morgan upon the subject of decimal coinage . He was a great advocate of the pound and mil scheme . His evidence on this subject was sought by the Royal Commission, and, besides constantly supporting the Decimal Association in periodical publications, he published several separate pamphlets on the subject . One marked characteristic of De Morgan was his intense and yet reasonable love of books . He was a true bibliophile and loved to surround himself, as far as his means allowed, with curious and rare books . He revelled in all the mysteries of watermarks, title-pages, colophons, catch-words and the like; yet he treated bibliography as an important science . As he himself wrote, " the most worthless book of a bygone day is a record worthy of preservation; like a telescopic star, its obscurity may render it unavailable for most purposes; but it serves, in hands which know how to use it, to determine the places of more important bodies." His evidence before the Royal Commission on the British Museum in 185o (Questions 5704*-5815,* 6481-6513, and 8966-8967), should be studied by all who would comprehend the principles of bibliography or the art of constructing a catalogue, his views on the latter subject corresponding with those carried out by Panizzi in the British Museum Catalogue . A sample of De Morgan's bibliographical learning is to be found in his account of Arithmetical Books, from the Invention of Printing (1847), and finally in his Budget of Paradoxes . This latter work consists of articles most of which were originally published in the Athenaeum, describing the various attempts which have been made to invent a perpetual motion, to square the circle, or to trisect the angle; but De Morgan took the opportunity to include many curious bits gathered from his extensive reading, so that the Budget, as re-printed by his widow (1872), with much additional matter prepared by himself, forms a remarkable collection of scientific ana . De Morgan's correspondence with contemporary scientific men was very extensive and full of interest .

It remains unpublished, as does also a large mass of mathematical tracts which he prepared for the use of his students, treating all parts of mathematical science, and embodying some of the matter of his lectures . De Morgan's library was

purchased by Lord Overstone, and presented to the university of London . In 1866 his life became clouded by the circumstances which led him to abandon the institution so long the scene of his labours . The refusal of the council to accept the recommendation of the senate, that they should appoint an eminent Unitarian minister to the professorship of logic and mental philosophy, revived all De Morgan's sensitiveness on the subject of sectarian freedom; and, though his feelings were doubtless excessive, there is no doubt that gloom was thrown over his life, intensified in 1867 by the loss of his son George Campbell De Morgan, a young man of the highest scientific promise, whose name, as De Morgan expressly wished, will long be connected with the London Mathematical Society, of which he was one of the founders . From this time De Morgan rapidly fell into ill-health, previously almost unknown to him, dying on the 18th of March 1871 . An interesting and truthful sketch of his life will be found in the Monthly Notices of the Royal Astronomical Society for the 9th of February 1872, Vol. xxii. p . 112, written by A . C . Ranyard, who says, " He was the kindliest, as well as the most learned of men—benignant to every one who approached him, never forgetting the claims which weakness has on strength." De Morgan left no published indications of his opinions on religious questions, in regard to which he was extremely reticent . He seldom or never entered a place of worship, and declared that he could not listen to a sermon, a circumstance perhaps due to the extremely strict religious discipline under which he was brought up . Nevertheless there is reason to believe that he was of a deeply religious disposition . Like M .

Faraday. and Sir I . Newton he entertained a confident belief in Providence, founded not on any tenuous inference, but on personal feeling . His hope of a future life also was vivid to the last . It is impossible to omit a reference to his witty sayings, some specimens of which are preserved in Dr Sadler's most interesting Diary of Henry Crabb Robinson (1869), which also contains a humorous account of H . C . R. by De Morgan . It may be added that De Morgan was a great reader and admirer of Dickens; he was also fond of music, and a fair performer on the flute . (W . S . J.) His son, WILLIAM FREND DE MORGAN (b . 1839), first became known in artistic circles as a potter, the " De Morgan " tiles being remarkable for his rediscovery of the secret of some beautiful colours and glazes . But later in life he became even better known to the literary world by his novels, Joseph Vance (1906), Alice for Short (1907), Somehow Good (1908) and It Never Can Happen Again (1909), in which the influence of Dickens and of his own earlier family life were conspicuous .