The use of the commutation table was independently developed in England-apparently between the years 1788 and 1811by George Barrett, of Petworth, Sussex, who was the son of a yeoman farmer, and was himself a village schoolmaster, and afterwards farm steward or bailiff. It has been usual to consider Barrett as the originator in England of the method of calculating the values of annuities by means of a commutation table, and this method is accordingly sometimes called Barrett's method. (It is also called the commutation method and the columnar method.) Barrett's method of calculating annuities was explained by him to Francis Baily in the year 1811, and was first made known to the world in a paper written by the latter and read before the Royal Society in 1812.

By what has been universally considered an unfortunate error of judgment, this paper was not recommended by the council of the Royal Society to be printed, but it was given by Baily as an appendix to the second issue (in 1813) of his work on life annuities and assurances. Barrett had calculated extensive tables, and with Baily's aid attempted to get them published by subscription, but without success; and the only printed tables calculated according to his manner, besides the specimen tables given by Baily, are the tables contained in Babbage's Comparative View of the various Institutions for the Assurance of Lives, 1826.

In the year 1825 Griffith Davies published his Tables of Life Contingencies, a work which contains, among others, two tables, which are confessedly derived from Baily's explanation of Barrett's tables.

Those who desire to pursue the subject further can refer to the appendix to Baily's Life Annuities and Assurances, De Morgan's paper" On the Calculation of Single Life Contingencies," Assurance Magazine, xii. 348-349; Gray's Tables and Formulae, chap. viii.; the preface to Davies's Treatise on Annuities; also Hendriks's papers in the Assurance Magazine, No. 1, p. 1, and No. 2, p. 12; and in particular De Morgan's "Account of a Correspondence between Mr George Barrett and Mr Francis Baily," in the Assurance Magazine, vol. iv. p. 185.

The principal commutation tables published in England are contained in the following works:-David Jones, Value of Annuities and Reversionary Payments, issued in parts by the Useful Knowledge Society, completed in 1843; Jenkin Jones, New Rate of Mortality, 1843: G. Davies, Treatise on Annuities, 1825 (issued 1855); David Chisholm, Commutation Tables, 1858; Neison's Contributions to Vital Statistics, 1857; Jardine Henry, Government Life Annuity Commutation Tables, 1866 and 1873; Institute of Actuaries Life Tables, 1872; R. P. Hardy, Valuation Tables, 1873; and Dr William Farr's contributions to the sixth (1844), twelfth (1849), and twentieth (1857) Reports of the Registrar General in England (English Tables, 1, 2), and to the English Life Table, 1864.

The theory of annuities may be further studied in the discussions in the English Journal of the Institute of Actuaries. The institute was founded in the year 1848, the first sessional meeting being held in January 1849. Its establishment has contributed in various ways to promote the study of the theory of life contingencies. Among these may be specified the following:-Before it was formed, students of the subject worked for the most part alone, and without any concert; and when any person had made an improvement in the theory, it had little chance of becoming publicly known unless he wrote a formal treatise on the whole subject. But the formation of the institute led to much greater interchange of opinion among actuaries, and afforded them a ready means of making known to their professional associates any improvements, real or supposed, that they thought they had made. Again, the discussions which follow the reading of papers before the institute have often served, first, to bring out into bold relief differences of opinion that were previously unsuspected, and afterwards to soften down those differences, to correct extreme opinions in every direction, and to bring about a greater agreement of opinion on many important subjects. In no way, probably, have the objects of the institute been so effectually advanced as by the publication of its Journal. The first number of this work, which was originally called the Assurance Magazine, appeared in September 1850, and it has been continued quarterly down to the present time. It was originated by the public spirit of two well-known actuaries (Mr Charles Jellicoe and Mr Samuel Brown), and was adopted as the organ of the Institute of

Journal of the Institute of Actuaries, Mr Jellicoe continuing to be the by Mr T. B. Sprague (who contributed to the 9th edition of this editor, a post he held until the year 1867, when he was succeeded Encyclopaedia an elaborate article on "Annuities," on which the above account is based). The name was again changed in 1866, the words "Assurance Magazine" being dropped; but in the following year it was considered desirable to resume these, for the purpose of showing the continuity of the publication, and it is now called the Journal of the Institute of Actuaries and Assurance Magazine. This work contains not only the papers read before the institute (to which have been appended of late years short abstracts of the discussions on together with correspondence, but also reprints of many papers them), and many original papers which were unsuitable for reading, published elsewhere, which from various causes had become difficult of access to the ordinary reader, among which may be specified Transactions, the Philosophical Magazine, the Mechanics' Magazine, various papers which originally appeared in the Philosophical and the Companion to the Almanac; also translations of various papers from the French, German, and Danish. Among the useful objects which the continuous publication of the Journal of the institute has served, we may specify in particular two:-that any supposed improvement in the theory was effectually submitted to the criticisms of the whole actuarial profession, and its real value speedily discovered; and that any real improvement, whether great or small, being placed on record, successive writers have been able, one after the other, to take it up and develop it, each commencing where the previous one had left off.

ANNULAR, ANNULATE, &c. (Lat. annulus, a ring), ringed. "Annulate" is used in botany and zoology in connexion with certain plants, worms, &c. (see ANNELIDA), either marked with rings or composed of ring-like segments. The word "annulated" is also used in heraldry and architecture. An annulated cross is one with the points ending in an "annulet" (an heraldic ring, supposed to be taken from a coat of mail), while the annulet in architecture is a small fillet round a column, which encircles the lower part of the Doric capital immediately above the neck or trachelium. The word "annulus" (for "ring") is itself used technically in geometry, astronomy, &c., and the adjective" annular " corresponds. An annular space is that between an inner and outer ring. The annular finger is the ring finger. An annular eclipse is an eclipse of the sun in which the visible part of the latter completely encircles the dark body of the moon; for this to happen, the centres of the sun and moon, and the point on the earth where the observer is situated, must be collinear. Certain nebulae having the form of a ring are also called "annular."

ANNUNCIATION, the announcement made by the angel Gabriel to the Virgin Mary of the incarnation of Christ (Luke i. 26-38). The Feast of the Annunciation in the Christian Church is celebrated on the 25th of March. The first authentic allusions to it are in a canon of the council of Toledo (656), and another of the council of Constantinople "in Trullo" (692), forbidding the celebration of all festivals in Lent, excepting the Lord's day and the Feast of the Annunciation. An earlier origin has been Athanasius and of Gregory Thaumaturgus, but both of these claimed for it on the ground that it is mentioned in sermons of documents are now admitted to be spurious. A synod held at Worcester, England (1240), forbade all servile work on this feast day. See further LADY DAY.

ANNUNZIO, GABRIELE D' (1863 ), Italian novelist and poet, of Dalmatian extraction, was born at Pescara (Abruzzi) in 1863. The first years of his youth were spent in the freedom of the open fields; at sixteen he was sent to school in Tuscany. While still at school he published a small volume of verses called Primo Vere (1879), in which, side by side with some almost brutal imitations of Lorenzo Stecchetti, the then fashionable poet of Postuma, were some translations from the Latin, distinguished by such agile grace that Giuseppe Chiarini on reading them brought the unknown youth before the public in an enthusiastic article. The young poet then went to Rome, where he was received as one of their own by the Cronaca Bizantina group (see CARDUCCI). Here he published Canto Nuovo (1882), Terra Vergine (1882), L' Intermezzo di Rime (1883), Il Libro delle afterwards collected under the general title of San Pantaleone Vergini (1884), and the greater part of the short stories that were (1886). In Canto Nuovo we have admirable poems full of pulsating youth and the promise of power, some descriptive

of the sea and some of the Abruzzi landscape, commented on and completed in prose by Terra Vergine, the latter a collection of short stories dealing in radiant language with the peasant life of the author's native province. With the Intermezzo di Rime we have the beginning of d'Annunzio's second and characteristic manner. His conception of style was new, and he chose to express all the most subtle vibrations of voluptuous life. Both style and contents began to startle his critics; some who had greeted him as an enfant prodige-Chiarini amongst othersrejected him as a perverter of public morals, whilst others hailed him as one bringing a current of fresh air and the impulse of a new vitality into the somewhat prim, lifeless work hitherto produced. Meanwhile the Review of Angelo Sommaruga perished in the midst of scandal, and his group of young authors found itself dispersed. Some entered the teaching career and were lost to literature, others threw themselves into journalism. Gabriele d'Annunzio took this latter course, and joined the staff of the Tribuna. For this paper, under the pseudonym of "Duca Minimo," he did some of his most brilliant work, and the articles he wrote during that period of originality and exuberance would well repay being collected. To this period of greater maturity and deeper culture belongs Il Libro d' Isotta (1886), a love poem, in which for the first time he drew inspiration adapted to modern sentiments and passions from the rich colours of the Renaissance. Il Libro d' Isotta is interesting also, because in it we find most of the germs of his future work, just as in Intermezzo melico and in certain ballads and sonnets we find descriptions and emotions which later went to form the aesthetic contents of Il Piacere, Il Trionfo della Morte, and Elegie Romane (1892).

D' Annunzio's first novel Il Piacere (1889)-translated into English as The Child of Pleasure-was followed in 1891 by L' Innocente (The Intruder), and in 1892 by Giovanni Episcopo. These three novels created a profound impression. L'Innocente, admirably translated into French by Georges Herelle, brought its author the notice and applause of foreign critics. His next work, Il Trionfo della Morte (The Triumph of Death) (1894), was followed at a short distance by Le Vergini della Roccio (1896) and Il Fuoco (1900), which in its descriptions of Venice is perhaps the most ardent glorification of a city existing in any language.

D' Annunzio's poetic work of this period, in most respects his finest, is represented by Il Poema Paradisiaco (1893), the Odi Navali (1893), a superb attempt at civic poetry, and Laudi (1900).

A later phase of d' Annunzio's work is his dramatic production, represented by Il Sogno di un mattino di primavera (1897), a lyrical fantasia in one act; his Cilla Morta (1898), written for Sarah Bernhardt, which is certainly among the most daring and original of modern tragedies, and the only one which by its unity, persistent purpose, and sense of fate seems to continue in a measure the traditions of the Greek theatre. In 1898 he wrote his Sogno di un Pomeriggio d' Autunno and La Gioconda; in the succeeding year La Gloria, an attempt at contemporary political tragedy which met with no success, probably through the audacity of the personal and political allusions in some of its scenes; and then Francesca da Rimini (1901), a perfect reconstruction of medieval atmosphere and emotion, magnificent in style, and declared by one of the most authoritative Italian critics-Edoardo Boutet-to be the first real although not perfect tragedy which has ever been given to the Italian theatre.

The work of d' Annunzio, although by many of the younger generation injudiciously and extravagantly admired, is almost the most important literary work given to Italy since the days when the great classics welded her varying dialects into a fixed language. The psychological inspiration of his novels has come to him from many sources-French, Russian, Scandinavian, German-and in much of his earlier work there is little fundamental originality. His creative power is intense and searching, but narrow and personal; his heroes and heroines are little more than one same type monotonously facing a different

problem at a different phase of life. But the faultlessness of his style and the wealth of his language have been approached by none of his contemporaries, whom his genius has somewhat paralysed. In his later work, when he begins drawing his inspiration from the traditions of bygone Italy in her glorious centuries, a current of real life seems to run through the veins of his personages. And the lasting merit of d' Annunzio, his real value to the literature of his country, consists precisely in that he opened up the closed mine of its former life as a source of inspiration for the present and of hope for the future, and created a language, neither pompous nor vulgar, drawn from every source and district suited to the requirements of modern thought, yet absolutely classical, borrowed from none, and, independently of the thought it may be used to express, a thing of intrinsic beauty. As his sight became clearer and his purpose strengthened, as exaggerations, affectations, and moods dropped away from his conceptions, his work became more and more typical Latin work, upheld by the ideal of an Italian Renaissance.

ANOA, the native name of the small wild buffalo of Celebes, Bos (Bubalus) depressicornis, which stands but little over a yard at the shoulder, and is the most diminutive of all wild cattle. It is nearly allied to the larger Asiatic buffaloes, showing the same reversal of the direction of the hair on the back. The horns are peculiar for their upright direction and comparative straightness, although they have the same triangular section as in other buffaloes. White spots are sometimes present below the eyes, and there may be white markings on the legs and back; and the absence or presence of these white markings may be indicative of distinct races. The horns of the cows are very small. The nearest allies of the anoa appear to be certain extinct buffaloes, of which the remains are found in the Siwalik Hills of northern India. In habits the animal appears to resemble the Indian buffalo.

ANODYNE (from Gr. áv-, privative, and ódúvŋ, pain), a cause which relieves pain. The term is commonly applied to medicines which lessen the sensibility of the brain or nervous system, such as morphia, &c.

ANOINTING, or greasing with oil, fat, or melted butter, a process employed ritually in all religions and among all races, civilized or savage, partly as a mode of ridding persons and things of dangerous influences and diseases, especially of the demons (Persian drug, Greek kĥpes, Armenian dev) which are or cause those diseases; and partly as a means of introducing into things and persons a sacramental or divine influence, a holy emanation, spirit or power. The riddance of an evil influence is often synonymous with the introduction of the good principle, and therefore it is best to consider first the use of anointing in consecrations.

The Australian natives believed that the virtues of one killed could be transferred to survivors if the latter rubbed themselves with his caul-fat. So the Arabs of East Africa anoint themselves with lion's fat in order to gain courage and inspire the animals with awe of themselves. Such rites are often associated with the actual eating of the victim whose virtues are coveted. Human fat is a powerful charm all over the world; for, as R. Smith points out, after the blood the fat was peculiarly the vehicle and seat of life. This is why fat of a victim was smeared on a sacred stone, not only in acts of homage paid to it, but in the actual consecration thereof. In such cases the influence of the god, communicated to the victim, passed with the unguent into the stone. But the divinity could by anointing be transferred into men no less than into stones; and from immemorial antiquity, among the Jews as among other races, kings were anointed or greased, doubtless with the fat of the victims which, like the blood, was too holy to be eaten by the common votaries.

Butter made from the milk of the cow, the most sacred of animals, is used for anointing in the Hindu religion. A newlybuilt house is smeared with it, so are demoniacs, care being taken to smear the latter downwards from head to foot.

In the Christian religion, especially where animal sacrifices, together with the cult of totem or holy animals, have been given up, it is usual to hallow the oil used in ritual anointings with

return to the pericentre. If the pericentre is fixed, this is an actual revolution; but if it moves the anomalistic revolution is greater or less than a complete circumference.

The holy oil, chrism, or uúpov, as the Easterns call it, was prepared and consecrated on Maundy Thursday, and in the Gelasian sacramentary the formula used runs thus: "Send forth, O Lord, we beseech thee, thy Holy Spirit the Paraclete from heaven into this fatness of oil, which thou hast deigned to bring forth out of the green wood for the refreshing of mind and body; and through thy holy benediction may it be for all who anoint with it, taste it, touch it, a safeguard of mind and body, of soul and spirit, for the expulsion of all pains, of every infirmity, of every sickness of mind and body. For with the same thou hast anointed priests, kings, and prophets and martyrs with this thy chrism, perfected by thee, O Lord, blessed, abiding within our bowels in the name of our Lord Jesus Christ."

In various churches the dead are anointed with holy oil, to guard them against the vampires or ghouls which ever threaten to take possession of dead bodies and live in them. In the Armenian church, as formerly in many Greek churches, a cross is not holy until the Spirit has been formally led into it by means of prayer and anointing with holy oil. A new church is anointed at its four corners, and also the altar round which it is built; similarly tombs, church gongs, and all other instruments and utensils dedicated to cultual uses. In churches of the Greek rite a little of the old year's chrism is left in the jar to communicate its sanctity to that of the new. (F. C. C.) ANOMALY (from Gr. ȧvwpala, unevenness, derived from av-, privative, and duaλós, even), a deviation from the common rule. In astronomy the word denotes the angular distance of a body from the pericentre of the orbit in which it is moving. Let AB be the major axis of the orbit, B the pericentre, F the focus or centre of motion, P the position of the body. The anomaly is then the angle BFP which the radius vector makes with the major axis. This is the actual or true anomaly. Mean anomaly is the anomaly which the body would have if it moved from the pericentre around F with a uniform angular motion such that its revolution would be completed in its actual time (see ORBIT). B Eccentric anomaly is defined thus:Draw the circumscribing circle of the elliptic orbit around the centre C of the orbit. Drop the perpendicular RPQ through P, the position of the planet, upon the major axis. Join CR; the angle CRQ is then the eccentric anomaly.

In the ancient astronomy the anomaly was taken as the angular distance of the planet from the point of the farthest recession from the earth.

Kepler's Problem, namely, that of finding the co-ordinates of a planet at a given time, which is equivalent-given the mean anomaly to that of determining the true anomaly, was solved approximately by Kepler, and more completely by Wallis, Newton and others.

The anomalistic revolution of a planet or other heavenly body is the revolution between two consecutive passages through the

An Anomalistic year is the time (365 days, 6 hours, 13 minutes, 48 seconds) in which the earth (and similarly for any other planet) passes from perihelion to perihelion, or from any given value of the anomaly to the same again. Owing to the precession of the equinoxes it is longer than a tropical or sidereal year by 25 minutes and 2-3 seconds. An Anomalistic month is the time in which the moon passes from perigee to perigee, &c. For the mathematics of Kepler's problem see E. W. Brown, Lunar Theory (Cambridge 1896), or the work of Watson or of Bauschinger on Theoretical Astronomy.

ANORTHITE, an important mineral of the felspar group, being one of the end members of the plagioclase (q.v.) series. It is a calcium and aluminium silicate, CaAl Si2Os, and crystallizes in the anorthic system. Like all the felspars, it possesses two cleavages, one perfect and the other less so, here inclined to one another at an angle of 85° 50'. The colour is white, greyish or reddish, and the crystals are transparent to translucent. The hardness is 6-6, and the specific gravity 2.75.

M

Anorthite is an essential constituent of many basic igneous rocks, such as gabbro and basalt, also of some meteoric stones. The best developed crystals are those which accompany mica, augite, sanidine, &c., in the ejected blocks of metamorphosed limestone from Monte Somma, the ancient portion of Mount Vesuvius; these Anorthite. perfectly colourless and transparent, and are bounded by numerous brilliant faces, Distinctly developed crystals are also met with in the basalts of Japan, but are usually rare at other localities.

are

The name anorthite was given to the Vesuvian mineral by G. Rose in 1823, on account of its anorthic crystallization. The species had, however, been earlier described by the comte de Bournon under the name indianite, this name being applied to a greyish or reddish granular mineral forming the matrix of corundum from the Carnatic in India. Several unimportant varieties have been distinguished. (L. J. S.)

ANQUETIL, LOUIS PIERRE (1723-1808), French historian, was born in Paris, on the 21st of February 1723. He entered the congregation of Sainte-Geneviève, where he took holy orders and became professor of theology and literature. Later, he became director of the seminary at Reims, where he wrote his Histoire civile et politique de Reims (3 vols., 1756-1757), perhaps his best work. He was then director of the college of Senlis, where he composed his Esprit de la Ligue ou histoire politique des troubles de la Fronde pendant le XVI et le XVII° siècles (1767). During the Reign of Terror he was imprisoned at St Lazare; there he began his Précis de l'histoire universelle, afterwards published in nine volumes. On the establishment of the national institute he was elected a member of the second group (moral and political sciences), and was soon afterwards employed in the office of the ministry of foreign affairs, profiting by his experience to write h Motifs des guerres et des traités de paix sous Louis XIV., Louis XV. et Louis XVI. He is said to have been asked by Napoleon to write his Histoire de France (14 vols., 1805), a mediocre compilation at second or third hand, with the assistance of de Mézeray and of Paul François Velly (1709-1759). This work, nevertheless, passed through numerous editions, and by it his name is remembered. He died on the 6th of September 1808.

ANQUETIL DUPERRON, ABRAHAM HYACINTHE (17311805), French orientalist, brother of Louis Pierre Anquetil, the historian, was born in Paris on the 7th of December 1731. He was educated for the priesthood in Paris and Utrecht, but his taste for Hebrew, Arabic, Persian, and other languages of the East

Little more than a year after, fresh trouble arose with the king, and Anselm resolved to proceed to Rome and seek the counsel of his spiritual father. With great difficulty he obtained a reluctant permission to leave, and in October 1097 he set out for Rome. William immediately seized on the revenues of the see, and retained them to his death. Anselm was received with high honour by Urban, and at a great council held at Bari, he was put forward to defend the doctrine of the procession of the Holy Ghost against the representatives of the Greek Church. But Urban was too politic to embroil himself with the king of England, and Anselm found that he could obtain no substantial result. He withdrew from Rome, and spent some time at the little village of Schiavi, where he finished his treatise on the atonement, Cur Deus homo, and then retired to Lyons.

In 1100 William was killed, and Henry, his successor, at once recalled Anselm. But Henry demanded that he should again receive from him in person investiture in his office of archbishop, thus making the dignity entirely dependent on the royal authority. Now, the papal rule in the matter was plain; all homage and lay investiture were strictly prohibited. Anselm represented this to the king; but Henry would not relinquish a privilege possessed by his predecessors, and proposed that the matter should be laid before the Holy See. The answer of the pope reaffirmed the law as to investiture. A second embassy was sent, with a similar result. Henry, however, remained firm, and at last, in 1103, Anselm and an envoy from the king set out for Rome. The pope, Paschal, reaffirmed strongly the rule of investiture, and passed sentence of excommunication against all who had infringed the law, except Henry. Practically this left matters as they were, and Anselm, who had received a message forbidding him to return to England unless on the king's terms, withdrew to Lyons, where he waited to see if Paschal would not take stronger measures. At last, in 1105, he resolved himself to excommunicate Henry. His intention was made known to the king through his sister, and it seriously alarmed him, for it was a critical period in his affairs. A meeting was arranged, and a reconciliation between them effected. In 1106 Anselm crossed to England, with power from the pope to remove the sentence of excommunication from the illegally invested churchmen. In 1107 the long dispute as to investiture was finally ended by the king resigning his formal rights. The remaining two years of Anselm's life were spent in the duties of his archbishopric. He died on the 21st of April 1109. He was canonized in 1494 by Alexander VI.

Anselm may, with some justice, be considered the first scholastic philosopher and theologian. His only great predecessor, Scotus Erigena, had more of the speculative and mystical element than is consistent with a schoolman; but in Anselm are found that recognition of the relation of reason to revealed truth, and that attempt to elaborate a rational system of faith, which form the special characteristics of scholastic thought. His constant endeavour is to render the contents of the Christian consciousness clear to reason, and to develop the intelligible truths interwoven with the Christian belief. The necessary preliminary for this is the possession of the Christian conscious"He who does not believe will not experience; and he who has not experienced will not understand." That faith must precede knowledge is reiterated by him. Neque enim quaero

ncss.

intelligere ut credam, sed credo ut intelligam. Nam et hoc credo, quia, nisi credidero, non intelligam." (" Nor do I seek to understand that I may believe, but I believe that I may understand. For this too I believe, that unless I first believe, I shall not under. stand.") But after the faith is held fast, the attempt must be made to demonstrate by reason the truth of what we believe. It is wrong not to do so. "Negligentiae mihi esse videtur, si, intelligere." ("I hold it to be a failure in duty if after we have become steadfast in the faith we do not strive to understand what we believe.") To such an extent does he carry this demand for rational explanation that, at times, it seems as if he claimed for unassisted intelligence the power of penetrating even to the mysteries of the Christian faith. On the whole, however, the qualified statement is his real view; merely rational proofs are always, he affirms, to be tested by Scripture. (Cur Deus homo, i. 2 and 38; De Fide Trin. 2.)

The groundwork of his theory of knowledge is contained in the tract De Veritate, in which, from the consideration of truth as in knowledge, in willing, and in things, he rises to the affirma tion of an absolute truth, in which all other truth participates. This absolute truth is God himself, who is therefore the ultimate ground or principle both of things and of thought. The notion of God comes thus into the foreground of the system; before all things it is necessary that it should be made clear to reason, that it should be demonstrated to have real existence. This demonstration is the substance of the Monologion and Proslogion. In the first of these the proof rests on the ordinary grounds of realism, and coincides to some extent with the earlier theory of Augustine, though it is carried out with singular boldness and fulness. Things, he says, are called good in a variety of ways and degrees; this would be impossible if there were not some absolute standard, some good in itself, in which all relative goods participate. Similarly with such predicates as great, just; they involve a certain greatness and justice. The very existence of things is impossible without some one Being, by whom they are. This absolute Being, this goodness, justice, greatness, is God. Anselm was not thoroughly satisfied with this reasoning; it started from a posteriori grounds, and contained several converging lines of proof. He desired to have some one short demonstration. Such a demonstration he presented in the Proslogion; it is his celebrated ontological proof. God is that being than whom none greater can be conceived. Now, if that than which nothing greater can be conceived existed only in the intellect, it would not be the absolutely greatest, for we could add to it existence in reality. It follows, then, that the being than whom nothing greater can be conceived, i.e. God, necessarily has real existence. This reasoning, in which Anselm partially anticipated the Cartesian philosophers, has rarely seemed satisfactory. It was opposed at the time by the monk Gaunilo, in his Liber pro Insipiente, on the ground that we cannot pass from idea to reality. The same criticism is made by several of the later schoolmen, among others by Aquinas, and is in substance what Kant advances against all ontological proof. Anselm replied to the objections of Gaunilo in his Liber Apologeticus. The existence of God being thus held proved, he proceeds to state the rational grounds of the Christian doctrines or creation and of the Trinity. With reference to this last, he says we cannot know God from himself, but only after the analogy of his creatures; and the special analogy used is the self-consciousness of man, its peculiar double nature, with the necessary elements, memory and intelligence, representing the relation of the Father to the Son. The mutual love of these two, proceeding from the relation they hold to one another, symbolizes the Holy Spirit. The further theological doctrines of man, original sin, free will, are developed, partly in the Monologion, partly in other mixed treatises. Finally, in his greatest work, Cur Deus homo, he undertakes to make plain, even to infidels, the rational necessity of the Christian mystery of the atonement. The theory rests on three positions: that satisfaction is necessary on account of God's honour and justice; that such satisfaction can be given only by the peculiar personality