925

Asia.

TAVERNIER, BARON D'AUBONNE.

TAYLER, FREDERICK,

926

provinces to the north of Erivan, leave a favourable impression of his
talent for extracting information from the native authorities. He has
been accused of plagiarism, principally because of the striking coin-
cidence between his account of the Guebres of Kerman, published in
1676, and that which Louis Moreri published in 1671 from the papers
of Father Gabriel de Chinon. It deserves to be noticed that Moreri's
publication is lucidly arranged and neatly expressed, while the account
contained in Tavernier's travels is confused and miserable in point of
diction. Had it been taken from Moreri, it is scarcely possible that
the latter could have been so wretchedly composed. Add to this that
the information found in the papers of Father Gabriel is not said to
have been the fruit of personal observation: that Tavernier resided
three months among the Guebres at Kirman, and had frequent dealings
with them in India and elsewhere; that he and Father Gabriel
repeatedly met in Persia; and it must be allowed that the priest is
quite as likely to have derived his information from the merchant as
otherwise. In judging of the statements made by Tavernier, the
school in which he was trained, and his personal character as it appears
from his own story, must always be kept in view. He had no know.
ledge of or taste for science and literature, for art, or antiquarian
research. He acted upon impulse, and his instincts were love of
travelling, and desire to acquire money for the sake of spending it in
feasting and personal display. A diamond was a more interesting
object to him than the mysterious remains of Tchelminar. He had
no very nice or refined sense of honour, but he was frank and
veracious, and little inclined to deck himself with stolen feathers of
literature; possibly because he could not appreciate their value.
In this review we have been obliged to anticipate that part of the
history of the third period of Tavernier's life, which relates to what
may be called his literary labours. We are thus enabled to abridge
the sequel of our narrative. On Tavernier's return from his sixth
journey he was presented with lettres de noblesse, by Louis XIV., and
purchased about the same time the barony of Aubonne in the Pais de
Vaud. When his travels were published, they were, as has been inti-
mated above, fiercely attacked; in particular, most virulently by
Jurieu, in his 'Esprit de M. Arnauld' (December 1684); more tem-
perately and with a greater parade of evidence by Henrick van Quel-
lenburgh, in 'Vindicia Batavica' (Amsterdam 1684). Tavernier made
no reply. Bayle has given a characteristic account of his conduct
relative to the publication of Jurieu, which was rather a libel than a
criticism. "He made a noise in the taverns and streets, he threatened
and even named the day and hour when he would apply to the Wal-
loon consistory of Rotterdam to demand execution of the canonical
laws against the minister who had dishonoured him: but his threaten-
ings came to nothing, he retired very peaceably, and never commenced
any prosecution at all." The misconduct of a nephew, to whom he
had intrusted the management of his affairs in the Levant, obliged
him to sell, some time previous to 1688, his hotel in Paris and his
estate of Aubonne. He retired first into Switzerland, and sub-
sequently to Berlin, where he was nominated by the elector of Bran-
denburg director of a projected East India Company. From the time
of his first journey he had regretted being prevented from carrying
into execution a design which he then entertained of returning from
Persia through the Russian dominions. His new appointment afforded
him an excuse and opportunity for making that journey, and he set
out to travel to the East Indies across Russia in 1688. He was taken ill
on the way and died at Copenhagen (Bayle says at Moscow), July, 1689.
(Les six Voyages de Jean Baptiste Tavernier, Ecuyer Baron d'Aubonne,
en Turquie, en Perse, et aux Indes, à Paris, 4to, 1676-79; L'Esprit de
M. Arnauld, tiré des écrits de lui et de ses disciples, Deventer, 12mo,
1684; Henrick van Quellenburgh, Vindicia Batavice, ofte Refutatie
van het Tractaet van J. B. Tavernier, Chevalier, Baron d'Aubonne,
Amsterdam, 4to, 1684; Bayle, v. Tavernier;' Biographie Universelle,
v. Tavernier, Jean Baptiste,' par Weiss.)

1659, but we are at a loss for other dates in this journey. The sixth and last expedition that Tavernier made to the east was begun in November 1663 and was terminated in 1669. The most important novelty of this journey was his tour through the province of Bengal as far as Dacca, which occupied him from November 1665 till July or August 1666. He was at Ispahan in July 1667, and on his return to Europe visited Constantinople for the second time. The very unsatisfactory arrangement adopted in the narrative of Tavernier's journeys has rendered it advisable to extract from it the preceding incomplete chronology of them. His first publication was an account of the interior of the seraglio at Constantinople, 'Nouvelle Relation de l'Intérieur du Serail,' published at Paris, in a thin 4to volume, in 1675. This was followed by an account of his travels, 'Six Voyages en Turquie, en Perse, et aux Indes,' also at Paris, in two quarto volumes, in 1676. A third volume was added in 1679, containing an account of Japan and the origin of the persecution of the Christians in these islands; an account of the proceedings of the deputies from the king and the French company of the Indies both in Persia and India; observations on the commerce of the East Indies; account of the kingdom of Tunquin; account of the conduct of the Dutch in In preparing the account of the seraglio and the two first volumes of his Travels, Tavernier employed Chappuzeau, a dull and unintelligent writer: the memoirs contained in the third volume were prepared by Lachapelle, secretary to the president Lamaignon. The account of the seraglio, and the contents of the third volume of the travels, are partly memoirs compiled from the information of others, and partly more full expositions of topics touched upon in his narrative. It is to the first two volumes of Tavernier's travels that we must look for such information of the countries he visited, the time he spent in them, and the adventures he encountered, as is necessary to enable us to determine what he witnessed himself, what he learned from the report of others, how far his informants were worthy of belief, and how far he was qualified to understand their communications. But the arrangement of these two volumes is the very worst that could be conceived for supplying satisfactory information upon these heads. The first volume professes to give an account of the various routes by which the Parisian traveller can reach Constantinople, Ispahan, and the Persian Gulf. It is arranged as a routier; the result of all Tavernier's observations upon each line of road is given at once, and it is only from incidental remarks that we learn when and in what direction he travelled it. His remarks upon the customs, government, and commerce of the different countries are thrown into intercalary chapters. A similar arrangement is adopted in his second volume, which contains the fruits of his observations in the south of India, in the region between Surat and Delhi, in Bengal, and in the Dutch possessions in the Eastern Archipelago. The work is neither a systematic account of the geography and statistics of the countries in which Tavernier travelled, nor is it a personal narrative of the traveller. It is an ill-digested and unsatisfactory attempt to combine both. Yet are the four volumes we have mentioned full of available matter, both for the historian and the geographer. The former will find in it the fruits of the forty years' experience and observation of a European merchant in Turkey, Persia, India, and the Indian Archipelago, in the 17th century. Tavernier did not possess either the intellect or the education of Thévenot and Bernier, but his opportunities of observation were more varied and protracted. He was a part of that commercial enterprise and rivalry of which they were only spectators. He is himself a specimen of the kind of adventurers who at that time managed the commerce of Europe with the East. His unconscious revelations of his own character may be relied upon, and the naiveté with which they are made encourages us to believe what he tells us of others. His statements have not passed unchal lenged: they wounded the national pride of the Dutch too sorely to *TAYLER, FREDERICK, was born near Elstree, Hertfordshire, in be left without a reply, and the partisan feelings of the Protestant 1804. Having early acquired notice in the art-circles of the metropolis literati of Europe induced them to embrace the cause of Holland, in by his sketches and drawings, especially of animals, he was elected first opposition to the protégé of Louis XIV. Even the Roman Catholic an associate and in 1835 a member of the old Society of Painters in literati took little interest in a writer who frankly confessed that he Water-Colours. In the gallery of that society his pictures soon secured saw nothing interesting or valuable in the plain of Troy or the ruins him a considerable measure of popularity; and amid all the fluctuaof Persepolis. And yet notwithstanding the violent attacks of the tions of taste and fashion in art during the past quarter of a century Dutch and Calvinist writers, the silence of others, and even of him- he has maintained his place in the general estimation as one of the self (for Tavernier did not engage in a controversy), not one material most original and brilliant of English water-colour painters. At first, assertion he made has been disproved. Unfriendly criticism has been Mr. Tayler painted a good deal in conjunction with George Barrett, he confined to the remark that many of his statements regarding the furnishing the figures to that painter's landscapes, as Sidney Cooper Dutch are trivial, and betray a littleness of mind: this may be, but has occasionally furnished the figures to the landscapes of Lee, and they are not the less characteristic for that reason. Tavernier's Andsell to those of Creswick; but since Mr. Barrett's death Mr. Tayler accounts of the principal objects of Oriental commerce in his day, of has painted alone. His pictures have been very largely drawn from the leading markets and routes of trade, of the money of the different the Scotch Highlands, embracing Highland peasants and sportsmen, countries, and the state of the exchanges, are more full and intelli- ponies, dogs, and deer, in various scenes, occupations, and circumgible than those we find in any other cotemporary writer. His stances; and few painters have shown themselves more familiar with success in trade affords a guarantee of the correctness of the opinions the Scotch mountains, moors, and lakes, or more at home in the he states. We have collated his routes, whenever this was possible, bothies.' Another favourite class of subjects consists of hunting and with those of recent travellers, and have found them in general so bawking parties in the costume of the latter half of the 17th and the accurate, that they may be relied upon for the purposes of comparative first half of the 18th century, which his knowledge of horses and dogs, geography, and in one or two instances as affording information regard- and his tact in costume enabled him to paint with great spirit and ng tracts which have not been visited since his time. Tavernier's facility: a series of lithographic copies of his sketches has made his notices of the route from Casvin to India by Candahar, and of the skill in these classes of subjects widely known. One of Mr. Tayler's

largest and most important pictures is 'The Highland Larder-
Weighing the Stag,' which has been excellently engraved in mezzotint
by Mr. C. Lewis. The Festival of the Popinjay,' 'Morning of the
12th of August-Unkennelling the Hounds,' The Vicar of Wakefield's
Family going to Church,' &c., are among the best known of his larger
compositions. His etchings and book illustrations are popular.
*TAYLOR, ALFRED SWAINE. [See vol. vi., col. 1027.]
TAYLOR, BROOK. Referring to the ARTS AND SCIENCES Division
of our work for an account of TAYLOR'S THEOREM, and of the methods
of algebraical development which are the consequences of it, we here
confine our attention to such points in the history of Taylor himself
and that of his theorem, as can be recovered from the neglect into
which they have fallen, at least in this country.

Nothing is said of Brook Taylor in the 'Biographia Britannica,' or Martin's Biographia Philosophica;' and Hutton, &c., give nothing but the date of his birth and death, entrance into college and the Royal Society. The Biographie Universelle' was the first work which gave any detail of his life, and this is due to the following circumstance :In 1790, some members of the French Academy, struck with the scantiness of the existing information relative to so celebrated a man, requested Mr. W. Seward to make some inquiry on the subject in England. This gentleman applied to Sir William Young, Brook Taylor's grandson, who accordingly drew up an account of his ancestor from family materials, and printed and circulated it privately. This account, which was not published, was entitled 'Contemplatio Philosophica, a posthumous work of the late Brook Taylor, LL.D., F.R.S., some time secretary of the Royal Society. To which is prefixed a Life of the author, by his grandson, Sir William Young, Bart., F.R.S., A.S.S., with an appendix, containing sundry original papers, &c., London, printed by W. Bulmer and Co., Shakspeare Printing-office, 1793.' The account given by Prony in the 'Biographie Universelle' (1826) is, we are almost sure, one drawn up at the time from Sir W. Young's manuscript account as forwarded to Paris; with parenthetical sentences inserted just before publication. It is from this work that the following account is taken, as to the facts of his private life :Brook Taylor was born at Edmonton, August 18, 1685, and was the son of John Taylor, of Bifrons House in Kent, by Olivia, daughter of Sir Nicholas Tempest, of Durham, Baronet. John Taylor was the son of Nathaniel, who, to use a phrase of his own diary, "tugged and wrestled with the Lord in prayer," and was member (elected by Cromwell's summons) for the county of Bedford in the (Barebones) parliament of 1653. Brook Taylor's father was the most despotic of parents his son was educated at home, where, besides enough of the usual learning to enable him to begin residence at St. John's Cambridge in 1701, he became excellent both in music and painting. "His numerous family were generally proficient in music, but the domestic hero of the art was the subject of this memoir. In a large family picture he is represented, at the age of thirteen, sitting in the centre of his brothers and sisters, the two elder of whom crown him with laurel bearing the insignia of harmony." The paintings of the future writer on perspective are represented as not needing the allowance always made for amateurs, but as capable of bearing the closest scrutiny of artists. At Cambridge he applied himself to mathematics, and acquired early the notice of Keil, Machin, and others. His first writing was on the centre of oscillation, in 1708, as appears by a letter to Keil, (afterwards given in 'Phil. Trans.,' 1713, No. 337). In 1709 he took the degree of LL.B., in 1714 that of LL.D. in 1712 he was elected to the Royal Society. As yet he had published nothing: his letters to Machin (preserved in his family), from 1709 to 1712, treat of various subjects; and, in particular, contain a solution of Kepler's problem. We may here conveniently put together a complete list of his works.

just had a warm correspondence with the former on the Newtonian doctrine, and on the tenets of Malebranche. His posthumous work, or rather tract, the Contemplatio Philosophica,' seems to contain his latest thoughts on the opinions of Malebranche and Leibnitz. In France he formed the acquaintance of Bishop Bossuet and Lord and Lady Bolingbroke, with all of whom Sir W. Young has printed some of the correspondence. He returned to England in February 1717; but his health was now impaired, and, throwing up the secretaryship in October 1718, he retired to Aix-la-Chapelle. On returning to England early in 1719, he seems to have abandoned the mathe matics almost entirely; among his papers of this period are essays on Jewish Sacrifices, and on the lawfulness of eating blood. At the end of 1720 he went to visit Lord Bolingbroke at La Source, near Orleans, and returned to England in 1721. After the middle of this year he wrote nothing for publication, nor could his grandson find anything of a mathematical character among his papers, with the exception of reference to a treatise on logarithms, which it seems he placed in the hands of his friend Lord Paisley (afterwards Abercorn) to prepare for the press, but which was never printed.

At the end of 1721 he married a young lady of small fortune, a circumstance which occasioned a rupture with his father. Some months after his marriage, and when there appeared hope of issue, his wife was informed that the birth of a son would probably accomplish a reconciliation between her husband and his father. On this she fixed her mind with such earnestness, that on finding herself in due time actually delivered of a son, she "literally died of joy :" the infaut also perished. This melancholy event led to the reconciliation the hope of which had caused it, but not till the autumn of 1723. Dr. Taylor returned to his father's house, and in 1725, with his father's consent, married the daughter of a neighbouring proprietor. In 1729 he succeeded to the family estate by the death of his father, and in the following year his wife died in giving birth to a daughter, afterwards the mother of the writer of the memoir from which we cite. This blow was fatal; Lord Bolingbroke, now settled again in England, endeavoured to divert the thoughts of his friend by inducing him to pass some time in his house, but in about a year after the stroke, Dr. Taylor died of decline (in London, we suppose), December 29, 1731, and was buried in the churchyard of Saint Anne's, Soho. The family estate of Bifrons is still in the possession of the descendants of his brother Herbert.

We shall dismiss other points with brief notice, and as well known, in order to come to the history of the theorem: such are the celebrity of Taylor's solution of the problem of vibrating chords, the questions he proposed to the foreign mathematicians in the war of problems, his answer to those of Leibnitz, the accusation of plagiarism made against him by John Bernoulli, and his reply. With reference to the celebrated works on perspective, the first was mathematical, the second intended for artists who hardly knew anything of geometry. Bernoulli charged Taylor with having taken his method from another, and Prony states that it is in fact the one given by Guido Ubaldi, though he thinks Taylor could not have seen that method. The work referred to is Guidi Ubaldi Perspectiva Libri Sex,' Pisauri, 1600, at which we have looked in consequence. Nothing is more easy than assertion about old books: if Prony had really looked attentively at the works of Ubaldi and of Taylor together, he would have seen that whereas Ubaldi's work-the very title page of which announces by a diagram that its distinctive feature is the use of vanishing points all at the height of the eye-only introduced the use of vanishing points as to lines which are horizontal (the picture being vertical), Taylor introduced the method of vanishing points for all lines whatsoever, and made them of universal application. We cannot think that he had never seen Ubaldi's work: a man of learning, an artist from early In the Philosophical Transactions,' 1712 (No. 336), On the ascent youth, was not likely to be ignorant of so celebrated a production. of water between two glass planes; 1713 (No. 337), On the centre of He must have seen, and generalised, the method given by Ubaldi. If oscillation; also on the motion of a vibrating string in the same indeed any one between the two is asserted to have a claim, that year, a paper on Music, not printed. 1713 (No. 344), Account of claim, when proposed, must be discussed: but a general charge of experiment made with Hawksbee on the law of attraction of the plagiarism from John Bernoulli is literally no more than a record of magnet. 1717 (No. 352), Method of Approximation to the roots of the fact that the party accused and John Bernoulli had had a quarrel, equations; (No. 353), Appendix to Montmort on infinite series; while what relates to Ubaldi is only so far true in that Ubaldi used (No. 354), Solution of a problem proposed by Leibnitz. 1719 the particular and Taylor the general method. It is not credible (No. 360), Reply to the accusations of John Bernoulli. 1721 (No. that Ubaldi was ignorant of the general proposition, or if he were so, 367), Propositions on the parabolic motion of projectiles; (No. Stevinus (whose Sciagraphia' was published in 1608) was not; 368), Experiments on magnetism. 1723 (No. 376), On the expan-(Sciagraphia,' prop. iii.) but Stevinus did not use any vanishing points, sion of the thermometer. Besides these, the separate publications except those of lines parallel to the ground, nor Ubaldi neither: while Taylor did use them, which is the distinctive feature of his system. Again, it is a strong presumption in favour of Taylor's origi nality in this point, that works published abroad shortly after his time do not contain it. For example, the Kurzgefasste Einleitung zur Perspectiv, von J. C. Bischoff, 1741,' a quarter of a century after the time of Taylor's publication, contains no use of vanishing points except at the height of the eye.

are:

1715. Methodus incrementorum directa et inversa. Londini.-1715. Linear perspective, or a new method of representing justly all manner of objects as they appear to the eye in all situations. London.-1719. New principles of Linear perspective, or the art of designing on a plane the representations of all sorts of objects in a more general and simple method than has been done before. London. A different work from the former: its second edition (called the third, by an obvious mistake) bears 'revised and corrected by John Colson, London, 1749.' Joshua Kirby's well-known work, though called Brook Taylor's perspective, is not an edition of Taylor, but a new work founded on his methods.

In January 1714, he was chosen secretary of the Royal Society. In 1716, he visited his friends Montmort and Conti at Paris. He bad

The Methodus Incrementorum' is the first treatise in which what is at this day called the calculus of finite differences is proposed for consideration. Besides what are now the most common theorems in this subject, there are various purely fluxional or infinitesimal theories, such as the change of the independent variable integrations, J. Bernoulli's series, &c., and various applications to interpolation, the vibrating chord, the catenary, dome, &c., centre of oscillation and per

029

TAYLOR, BROOK.

TAYLOR, ISAAC.

930

cussion, law of density of the atmosphere, refraction of light. The first Institutions (1748), in Landen's Residual Analysis (1764), in Simpson's enunciation of the celebrated theorem is as follows:

1.222

1.2.3z3

Fluxions (1737), in Emerson's Increments (1763), in Emerson's Fluxions (1743), in Stone's Mathematical Dictionary (1743), nor in the first edition of Montucla's History (1758). We have examined various other places in which it should be, without finding it anywhere, except in the great French Encyclopædia (article Series'), and there we certainly did find it, mentioned only inci dentally, and attributed by no less a person than Condorcet to D'Alembert. The Abbé Bossut, who wrote the preliminary essay, knew nothing about the theorem at that time; though afterwards, when he published his history of mathematics, he was better informed. We found afterwards that Condorcet (Lacroix, tom. iii., p. 396) was in the habit of assigning this theorem to D'Alembert; not with any unfair intention, but in pure ignorance. The fact was that D'Alembert (Recherches sur différens points,' &c., vol. i, p. 50, according to Lacroix) gave for the first time the theorem accompanied by a method of finding the remnant of Taylor's series after a certain number of terms have been taken; and Condorcet, who probably had never seen the theorem elsewhere, thought it was D'Alembert's. In

vel mutato signo ipsius v, quo tempore z decrescendo fiet z-v, a de- fact, D'Alembert himself gave the theorem as if it were new, and

crescendo fiet

Taylor does not make much use of his own theorem in the 'Methodus Incrementorum,' but he shows his command over it in the paper above cited on the roots of equations, in which he extends Newton's method to other than algebraical equations.

One would have supposed that such a theorem as that of Taylor, the instant it was proposed, would have been hailed as the best and most useful of generalisations. Instead of this, it sunk, or rather never rose, till Lagrange pointed out its power. This is perhaps an assertion which some may doubt we proceed to make it good. The first criticism upon the whole work (without a word about the theorem) was that of Leibnitz, in a letter to John Bernoulli (June 1716, vol. ii., p. 380, of their correspondence), and it will show of what sort of view the neglect of this theorem was the consequence. The translation is as follows:-"I have received what Taylor calls his 'Method of Increments.' It is an application of the differential and integral calculus to numbers, or rather to general magnitude. Thus the English have placed the horses, according to the proverb, behind the cart. I began the differential calculus from series of numbers . . . . and so came naturally from the general calculus to the special geometrical or infinitesimal calculus. They proceed the other way, because they have not the true method of investigation..... It is written obscurely enough." noulli answers (August 1716, p. 389):-"I have at length received Taylor's book. What, in the name of God, does the man mean by the darkness in which he involves the clearest things! No doubt to conceal his habit of thieving: as far as I can make it out, I see nothing but what he has stolen from me, through his thick cloud of obscurity." The notion of Leibnitz prevailed for a long time, and is not quite extinct in our own day, though rapidly expiring; the Differential Calculus was to be used only as the medium in which pure algebra was to be applied to geometry and physics; and even a generalisation of existing theorems, expressed in the language of that Calculus, was a positively erroneous mode of proceeding.

without mentioning the name of any one, which Lacroix says is 'assez singulier,' an opinion in which we cannot agree. Unless D'Alembert read English, we cannot imagine how he should have known Taylor's theorem, nor even then, unless Taylor, Stirling, Maclaurin, or an old volume of the 'Philosophical Transactions,' be supposed to have fallen in his way. We have no doubt that D'Alembert was a new discoverer of the theorem, and that Condorcet never saw it except in his writings. Our wonder rather is where Lagrange could have found the name of Taylor in connection with it. From Lagrange's time Taylor's theorem takes that place which, if it had always occupied, we should not have had to write any history of it.

*TAYLOR, HENRY, English poet, was born in the early part of the present century. A great portion of his life has been spent as a civil servant in the department of the Colonial Office; in which office he now holds one of the five senior clerkships. His first known literary effort was 'Isaac Comnenus,' a play in five acts and in verse, published in 1827. This was followed in 1834 by his more celebrated poem Philip Van Artevelde, a Dramatic Romance, in two parts,' of which there have been six or seven editions, and which has been translated into German. In 1836 he published a prose work of a different character, entitled 'The Statesman,' embodying, in the shape of reflection, much of his experience of public and administrative life. To this succeeded, in 1842, Edwin the Fair, an Historical Drama,' in five acts and in verse. In 1847, he published The Eve of the Conquest and other Poems;' and in the same year a prose work entitled Ber-Notes from Life, in Six Essays,' of which there have been three subsequent editions. In 1849 he gave to the world another work of a similar character, entitled 'Notes from Books, in four Essays;' and in 1850 he published The Virgin Widow,' a play in five acts, and chiefly in verse. There have also been collected editions of his poetical writings. His various works have given him a high reputation with the judicious as a man of thought and scholarship, and more particularly as a dramatic poet of great and peculiar ability-one of the few English poets of our time who have produced sterling poetic works of a thoroughly English character in the dramatic form once so dominant in our literature.

But on

In Britain, two really great disciples of Taylor, soon appeared, STIRLING and MACLAURIN. The first (Meth. Diff.,' p. 102) repeated the theorem as given by Taylor himself, and adds that Herman had also given it in the Appendix to his 'Phoronomia;' and as this last work was published in 1716, were Stirling's assertion true, Herman must probably be considered an independent inventor. examining the appendix to the Phoronomia' (p. 393), to which Stirling refers, we find only the theorem in book v., lemma 3, of the Principia, and John Bernoulli's series for integration. Maclaurin (Fluxions, 1742, p. 610) proved Taylor's theorem again in the way which has since become common. But both Stirling and Maclaurin use only a particular case of Taylor's theorem, expanding not p (x+z), but (0+2), or expanding oz in powers of z. Neither thought he was doing more than proving Taylor's theorem, and both attribute the result to Taylor. Nevertheless this particular case has been since called Maclaurin's theorem, though, if not Taylor's, it is Stirling's. Maclaurin's book was, no doubt, more read than either of the other two; it was the answer to Berkeley's metaphysical objections, and contained great power and vast store of instances; and this may have been the reason why a theorem which was best used in, and best known by, Maclaurin's book, should be called after his name. It is well that it should be so, or rather, it would be well that the develop ment of (0+2) in powers of z should be called by the name of Stirling; for in truth the development of (a+b) in powers of bis one theorem or another in its uses, and in the consequences it suggests, according as a or b is looked at as the principal letter.

In the interval between Taylor's death and Lagrange's paper in the Berlin Memoirs for 1772, in which he first proposed to make Taylor's theorem the foundation of the Differential Calculus, the theorem was hardly known, and even when known, not known as Taylor's. We cannot find it in Hodgson's Fluxions (1736), in Maria Agnesi's

BIOG. DIV. VOL. V.

TAYLOR, ISAAC, the author of the 'Natural History of Enthusiasm' and 'Ancient Christianity,' belongs to a family, several of the members of which have honourably distinguished themselves, and of whom we prefix a brief notice.

ISAAC TAYLOR, senior, was a man of great decision of purpose and of considerable mental power. Originally a line-engraver, he in 1786 removed from the metropolis to Lavenham, Suffolk, for the purpose of pursuing his profession, and at the same time training his children under his own eye in a quiet country town. Being a man of strong religious feelings he was led to take an active part in the community to which he belonged, and his occasional religious addresses being found very acceptable, he was eventually, 1796, invited to become the minister of an Independent congregation at Colchester, Essex. In 1810 he removed, on the invitation of a similar congregation, to Ongar, where he remained till his death, December 11, 1829. During this period he not only laboured diligently in his ministerial calling, and carefully educated his children, but likewise found time to write numerous small books on educational subjects: Advice to the Teens,' 'Scenes for Tarry-at-Home Travellers,' 'Beginnings of Biography,' &c., which had an extensive circulation. He also published a few sermons and other religious works. His elder brother CHARLES TAYLOR (who died November 1821), was the editor of Calmet's Dictionary of the Bible,' and the author of Fragments' on subjects of Biblical exposition.

ANN TAYLOR, the wife of Isaac Taylor of Ongar, was likewise a woman of superior ability and attainments. Having herself completed the education of her daughters, she somewhat late in life took up her pen, and wrote several volumes very popular in their dayMaternal Solicitude,' and others, chiefly of an educational character. She died in 1830. ANN TAYLOR (Mrs. Gilbert), and JANE TAYLOR, daughters of the above Isaac and Ann Taylor, also became widely known as the authors of juvenile works of more than ordinary excel

30