be sufficient for all common uses. Having obtained this series, he gives (in Art. 24,) a new and very convenient formula, for computing the difference before mentioned. Mr. Hellins next (in Art. 25) adverts to p. 466 and 467 of the Philosophical Transactions for 1802, and shows that the difference between the ascending series and the descending series, there inserted, is the very expression which Mr. Landen obtained, by a very different method, in Art. 5 of his second Memoir, and on which he set a considerable value. This difference, as was before observed, (and is proved in this Article,) is the difference between the infinite arch of the Hyperbola and its asymptote; which difference he denotes by the letter d, the character by which we also, for the sake of brevity, shall denote that difference in the remaining part of our account of this Paper. It clearly appears, by the process in Art. 25 of this Paper, that, when the same geometrical progression obtains both in the ascending and in the descending series, the latter will be most eligible for arithmetical computation, on account of the absence of a column of quantities in that series which enters into the other. So that the formula for computing the value of d, by the descending series, will be more convenient in practice, than the formula for computing it by the ascending series. The first of these formule (which may be called Landen's Theorem) is given in Art. 25, the second is given in Art. 27 of this Paper. Art. 28, Mr. H. refers again to his Paper in the Philosophical Transactions for 1798, for a method of transforming the series given in Art. 25, for computing the value of d, into others which converge twice as fast : And, in the next Article, he transforms one of his own descending series for the rectification of the Hyperbola (inserted in the Philosophical Transactions for 1802,) into a pair of series for computing the value of d, each converging by the powers of the fraction where a, which denotes the transverse semi-axis, is supposed to be much greater than 1, which denotes the conjugate semiaxis; so that this series will converge very swiftly. In Art. 30, the last mentioned pair of swiftly converging series is transformed into another pair of a simpler form, but having the same rate of convergency; the operations being similar to those which he had described in his former papers inserted in the Philosophical Transactions for 1798 and 1800. Art. 31 and 32 contain the investigation of the law which the co-efficients of the new pair of series observe ad infinitum; which law is discovered by a fluxionary process, for which we must refer our mathematical readers to the Paper itself, as it cannot be abridged, nor will the nature of our plan admit of its insertion here. Mr. H. then says, with great truth, "Thus, by the common application of Sir Isaac Newton's doctrine of Fluxions and infinite series, without any assistance from, or regard to, Landen's Theorem, we have obtained a pair of series for computing the value of d, which converge by the powers of, and of which we can find as many terms as we please. And by a similar process, may Euler's series for computing the quadrantal arch of an Ellipsis be ob tained without any use of Fagnani's Theorem, or the tentative methods, and strange artifices as Mr. Woodhouse calls them, which appear in Euler's Paper." In Art. 34, that ratio of the axes of an Hyperbola is pointed out, which serves as a limit of the use of the single series, and of the pair of series, before spoken of, for computing the value of d. And in the next Article, the pair of series is accommodated to. the Hyperbola of which the semi-axes are 1 and b. Mr. Hellius had shown in Art. 24, that, even in the most disadvantageous case, the value of d might be computed by a series converging somewhat swifter than the powers of; he remarks in Art. 36, that series of much swifter convergency may be obtained for that purpose, by means of a transformation of the fluxion of the arch of the Hyperbola; but that such transformations were foreign from his present design. By the examples which are given in the remaining pages of this Paper, the great advantage of descending series over ascending series, in the rectification of the Hyperbola, is very obvious; and Mr. H. concludes his Paper with this just remark: "In these examples the use and ad vantage vantage of descending series appear: more examples of their utility might be given and it might easily be shown, that there are cases in which such series have the advantage, even when the ascending series have a good rate of convergency. I trust, how ever, that enough has been done in this Paper, to satisfy all candid and competent judges of the matter, that the rectification of the Hyperbola by means of two Ellipses is more curious than useful; that the advantage of computing by descending series, is, in many cases, very great; and that such series will often answer the end of a transformation without the trouble of making it." THE importance of the subjects of the two matheínatical articles here noticed, will be acknowledged by all scientific men, and will justify the attention here bestowed upon them. With respect to the two Authors, the distinction is very obvious. The one borrows largely from books; the other takes from his own store: the one delights in Gallicisms, and is often obscure; the other is plain and perspicuous. More might be said respecting the different tempers of the writers, but nothing that would not be self-evident to every reader of the two Papers. THE Mr. URBAN, Inner Temple. HE life of our great Poet Milton has occupied the attention of many able pens. Every minute occurrence of his memorable career, which industry, joined to the spirit of modern inquiry, could at this distance of time recover, has been laid before the publick, and points out the high estimation in which his memory is now held. Indeed no genuine admirer of the Poet will regard any circumstance connected with the family of Milton, or which serves to throw light on the transactions of those times, as trivial. Much curious information, and many valuable notices, collected by the late Mr. Thomas Warton, are prefixed to his edition of Milton's Juvenile Poems. It is owing to the commendable zeal and assiduity of a late writer of his life, the Rev. H. J. Todd, that even an additional harvest has been gleaned to adorn what the Author modestly terms an "unadorned narration:" and from his acknowledged talents and integrity, the writer is convinced he would not intentionally have inserted any thing that would not have borne the test of the strictest investigation. In one instance, however, this is not the case: and truth being the sole object in view, more especially that the character of Milton may not be liable to a charge of inconsis tency, the writer of this may easily be pardoned for attempting to clear up a point relative to the Poet's first marriage into the family of Powell, in which, according to Mr. Todd's ac count, there is most certainly a considerable inaccuracy. The first Life of Milton was written by Phillips, his sister's son, who may reasonably be supposed to know the circumstances connected with his uncle's first marriage. His words are: "About Whitsuutide (A. D. 1643) or a little after, he (Milton) took a journey into the country, nobody about him certainly knowing the reason --after about a month's stay, home he returned a married man that went out a batchelor; his wife being Mary, the eldest daughter of Mr. Richard Powell, then a Justice of the Peace, of Forrest-hill, near Shotover in Oxfordshire." (Phillips's Life of Milton, p. 22.) Mr. Todd (on the authority of the late Mr. T. B. Richards) asserts, that "Milton married a daughter of Justice Powell of Sandford, in the vici nity of Oxford, and lived at a house at Forrest-hill, about three miles from Sandford." (Todd's Life of Milton, p. 25, 2d edition.) The late Mr. Richards had certainly great opportunities of making inquiries concerning the family into which Milton married, having resided many years in the early part of his life, at Bensington, within ten miles of Oxford. But, if indeed he ever did make inquiries, he has in this instance been most strangely mistaken; having confounded the family of Richard Powell, Justice of the Peace, of Forrest-hill, with an antient Roman Ca tholic family, the Powells of Sandford. To prove this point satisfactorily, it will be necessary to pursue the following plan : 1. Give a genealogical sketch of the Powells of Sandford. 2. State the result of an accurate examination of the parish register at Sandford. 3. Col 3. Collect the incidental notices scattered through the works of those eminent Antiquaries Hearne and Authony Wood, relating to this family. The first part proposed, the writer is the better enabled to accomplish, being possessed of a curious Pedigree of the family, commencing with Maurice Ap Howel of Guernan, có. Cardigan, to the death of the late John Powell, esq. of Sandford, A. D. 1730, without issue male. 1. The manor of Sandford belonged in antient times to Sir Thomas de Saundford, who, in the reign of King Stephen, or thereabouts, gave it to the Knights Templars. At the suppression of religious houses, it was granted by King Henry VIII. to Edward [Edmund] Powell. (Tanner's Not. Mon. ed. 1744, p. 414.) Arms: Arg. a lion ramp. Sab. debruised by a fess engrailed Gules. 1. Edmond P. (to whom the manor was granted) settled at Sandford 33 Henry VIII. A. D. 1542. 2. Edinond P. his son ob. 1592, sepult. ap. Sandford. He left two sons, 1. Edmond, his successor; 2. Sir William P. of Tutbury and Rolleston Park, co. Stafford. ob. s. p. 1656. 3. Edmond P. married two wives, 1. Frances, daughter of - Gifford, of Chillington, co. Stafford, by whom he had three daughters, who died young and unmarried. Secondly, Cicely, daughter of Richard Fogge, of Dane-court, co. Kent, by whom he had two sons: 1. Edmond, born 1004, his successor; and 2. William: also six daughters. 1. Thomazine, born 1603, married Richard Spicer, of London, Doctor of Physick. 2. Philippa. 3. Anne, born 1607, married Richard Betham. 4. Mary, died young. 5. Mary, born 1609. 6. Cecilia, born 1611, buried at Sandford 1641. This Edmond P. dying in 1632, was succeeded by his eldest son. 4. Edmond P. born 1604, who married Winifred, daughter of John Throgmorton, of Coughton, co. Warr.; by whom he had four sous: 1. Edmond, died unmarried, v. p. 2. John, born 1632, who succeeded his father. 3. Francis, buried at Sandford, 1690. 4. Ambrose: also three daughters. 1. Agnes, married to William Gould of Dunscombe, co. Devon. 2. Winifred, married to Joha White. 3. Mary, died unmarr. 1703. 5. John P. eldest surviving son, born 1632, succeeded his father; married Catharine, daughter of William Petre, of Stanford Rivers, co. Essex, and died 1678. He had two sons: 1. Edmund, who married Anne, sister to Rowland fourth Lord Dormer, and died v. p. without issue. 2. John, who succeeded his father. 6. John P. married Anne, daughter of Thomas Wyndham, and dying Aug. 1730, without issue male, was suc ceeded in his estates by his two daughters and coheiresses. 1. Winifred, born 1705, married to Sir Francis Curzon, of Waterbury, co. Oxon. bart. whom she survived, and died 1764, s. p. 2. Catharine, born 1709, married in 1732 to Henry Roper, 10th Lord Teynham, and died 1765. From this short, though comprehensive extract, comprising the names of every individual of the Powell fa mily from the above-mentioned pedigree, it appears then, that from 1542, when the manor of Sandford was granted to Edmond P. till 1730, during a space of nearly 200 years, there never was any one of this family named Richard. That at the time Milton is said to have married (in 1643) Mary, the eldest daughter of Mr. Richard P. of Forrest-hill, Edmond Powell boru 1604, fourth in descent from the original grantee, both in name and possession, was Lord of the Manor of Sandford that he was then 39 years of age; and of his daughters, the third, named Mary, died unmarried in 1703. Besides, the family were rigid Roman Catholics, and connected by marriage with several antient families of that persuasion; as Gifford of Chillington, Napier of Haly well, co. Oxon. Dormer, Petre, Throgmorton, &c. as set forth in the Pedigree. That they continued in this profession is evident. The two daughters and coheiresses of the last John Powel mar ried into two of the most antient Ro man Catholic families in England, Curzon and Roper, although they have both since that time conformed to the Establishment. While Milton was a rigid Presbyterian, whose principles must have ill accorded with those of a Roman Catholic family; and when he was inveighing against Prelacy and Papal tyranny, it is quite absurd to suppose that he would become so closely allied to such an one; if he had, doubtless his enemies would not have failed to have published this circumstance to the world. II. Parish Register of Sandford. This Register, which has been kept with a very commendable neatness, has been most carefully examined. Milton, according to Phillips, was married in Oxfordshire; and it is reasonable to suppose, some notice might have been traced from this source. The entries of the Powell family commence in the middle of the 16th century, very shortly after they became seated at Sandford, and are brought down to the death of the last possessor, viz. "John P. esq. Lord of the Manor of Sandford, was buried Aug. 15, 1730;" and although these entries are numerous, yet no such marriage is noticed. III. Incidental Notices from the writings of Anthony Wood and Hearne. At Sandford" there is nothing extraordinary to be seen in the Church, besides some monuments of the Powells, Lords of the Manor here. The chief of these monuments is one in the South wall of Chancel*." (Leland's Itin. vol. II. p. 119.) Antient Crosses: Trees in orchards were often planted in the shape of them. "There was formerly such an orchard at the great Ivy-house at Sandford, near Oxford; the present trees in it are much later, though there is now (1724) in it a very old holly tree, the oldest, I think, I ever saw, round which there was formerly a bench, where, in suminer time, the present Mr. Powell's great grandfather used to entertain his friends.' (Hearne's Rob. of Glou. p. 638.). Nunnery of Littlemore, near Sandford: "I refer to Leland's Itinerary, for what I have said about the nunnery of Littlemore or Sandford; but I shall observe in this place, that the Minshery, Minchery, or Minchion Ree, belongs to the Powells of Sandford, being purchased by an ancestor of theirs in the third year of King Edward VI. of Sir John Williams (afterwards Lord Williams) of Thame. Ex cod. MS. penès amicissimum virum Joannem Powell de Sandford, armigerum." (Hist. Glaston. pref. p. 16.) A. D. 1661. June 29, "A. W. was at Sandford, near Oxon, in the house of John Powell, gent. which was a house and preceptory sometime belonging to the Knights Templars. He took a note of some arms in a bay window in a low room there.” (Aut. à Wood's Diary.) These celebrated Antiquaries passed their lives at Oxford, within three miles of Sandford, and must surely have been acquainted with the cir cumstance of Milton being connected with this family, and knowing it, would not have failed to have alluded to it. Hearne, indeed, appears tojhave lived on very friendly terms with the last possessor of the estate, whom he terms vir amicissimus. Wood made large collections relating to Oxfordshire families, now in the Ashmolean Museum, from which some extracts respecting this family, about the time of Milton's first marriage, are printed in Guillim's Heraldry (edit. 1724, p. 273); yet not the most distant bint occurs of any such marriage. From what has been written we may fairly conclude, that the antient family of Powell of Sandford was in no way connected with the family into which Milton married, as related by Mr. Todd, in his Life of the Poet. Of what family Mr. Richard Powell, Jus * Erected to the memory of Sir William Powell of Tutbury and Rolleston Park, co. Stafford, second son of Edmond, and grandson of Edmond P. to whom the manor was originally granted in 1542. He died Dec. 15, 1656, æt. 83. Hearne has printed the inscription, by which it appears that he left his estates to the Powells of Sandford, in whose possession they continued till the death of the last John Powell in 1730, when, on a division between his two daughters and coheirs, Rolleston Park was assigned to Catharine, his youngest daughter, married to Henry Roper, Lord Teynham. The present Lord T. grandson of the said Catharine P. is now the owner of them, TUTBURY. In this parish, about a mile South of the town, is Rolleston Park. Sir Simon Degge says," at Rolleston Park, a mile South of Tutbury, is the seat of [John] Powell, that was [great nephew] to Sir William P. Knight, and courtier in the time of King James; of whose son, as I take it, he purchased this Park, and made the Lodge his seat.' (Shaw's History of Staffordshire, vol. I. p. 58. MS addit. to Erdeswick.j Narrative of an Expedition to explore the Territory beyond the Blue Mountains; by an Officer of the 101st Reg. THE Territory beyond the Blue Mountains has long been an object of considerable anxiety & conjecture; not only among the inhabitants of New Holland itself, but even among the learned men of almost every civilized Country in the World-au anxiety not springing from idle curiosity, but deriving its origin from that laudable thirst of knowledge, to which may be attributed almost every great and useful discovery, of which the modern world so justly boasts. The investigation of this hitherto unknown Country presents an object in all respects worthy the speculation and research of the Philosopher and the Merchant. With this impression, a party of spirited individuals, residing af Sydney-Town, having obtained the sanction of the Governor, undertook to pass the mountain-boundary, which bad so often baffled the labours of previous Adventurers; and the result of this last effort of perseverance has not only justified the undertaking, but realized the calculations of those who have accomplished the extraordinary task. On the 9th of April 1814, the party, consisting of 27 persons, (of whom 19 were workmen, the rest being Gentlemen well acquainted with Geology, Botany, &c.) set out from Sydney; and having by the 13th reached the celebrated Cataract (which supplies the River emptying itself into Shark's Bay), where all prior attempts had ceased, they immediately com menced active operations. The Cataract issues from a large circular opening in the immense ridge of rocks composing the front line of the Blue Mountains, the terrific barrier which runs from one end of the Country to the other, preserving almost the whole way the regular perpendicular height of about three hundred GENT. MAG. January, 1815. feet. The aperture through which this awful Cataract falls in one column to its basin, is about 120 feet from the ground, being rather more than 30 feet less than the celebrated Falls of Niagara. The first idea which suggested itself to the Travellers, was to explore a passage through the fissure from whence the Cataract issued; but, on more accurate observation, it was ascertained that the column of water completely filled the whole diameter of the opening; so that no alternative remained but to scale the awful wall of rocks. - After innumerable attempts, they at length adopted a plan used many years since in repairing the great Tower of the Monastery at Raucoux in Westphalia by making a hole in the rock at about two feet from the ground, and driving the end of a strong stake into the opening, and so continuing to make fresh holes (each two feet above the former, not in a straight, but in a slanting direction of ascent), and to introduce as many stakes, they were enabled to construct a firm flight of steps, connected by coarse basket-work, about the texture of common hurdles, the materials being furnished in abundance from the neighbouring woods. This was a task requiring of necessity. much labour and considerable time, so that it was not until the 27th the workmen attained an elevation parallel with the upper part of the open ing through which the Cataract rushed; they were, however, most agreeably surprized to find that here the rock ended, the immense continuation of the precipice consisting of a kind. of bituminous Coblon earth, firin, but very yielding to the spade. By the following day was hollowed out a space sufficient for the workmen to move at will with their wheelbarrows, &c. and the noble undertaking was now determined on of excavating a flight of steps to the summit! Within about thirty feet of the top, the labourers discovered the petrified skeleton of an unknown animal, the head and body resembling those of a bear, with a tail similar to that of a croco dile, only not so long. It is a remarkable fact, that when about 140 feet from the ground, the thermometer (Farenheit) fell to 37, and continued so till the party had ascended within fifty feet of the surface, when |