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 bution is valuable. Hoddesdon also wrote ‘Tho. Mori vita & exitus, or the History of Sir Thomas More … collected out of severall authours,’ dedicated to Christopher Hoddesdon, London, 1652, 8vo.

HODGE, ARTHUR (d. 1811), West Indian planter, settled about 1792 in Tortola, the chief of the Virgin Islands in the West Indies. He occupied the estate of Bellevue, in the eastern part of the island. Though a man of quarrelsome character, he rose to be a member of council for the dependency of the Virgin Islands. In 1803 the negroes on his estate numbered 140, but in 1811 they numbered only thirty-five, and the diminution was attributed to Hodge's cruelties. Early in 1811 a free negro woman named Perreen Georges deposed before three justices of the peace for Tortola that from 1805 to 1807 she had been in occasional employment at Bellevue. During that period, she declared, three negroes named Tom Boiler, Prosper, and Cuffy had been flogged at Hodge's orders with such severity that they all died within a few days of their punishment. Two female slaves named Margaret and Else, accused, for no reason it seems, of trying to poison Hodge's children, had been murdered by having boiling water forced down their throats. Lastly, a child named Samson had been flayed alive by being dipped in a cauldron of scalding water. Astonished at this catalogue of horrors, the justices summoned before them one Stephen M'Keough, formerly overseer on Hodge's plantation, then resident in the Danish island of St. Croix. M'Keough not only corroborated Perreen's statements, but brought forward numerous additional charges of gross cruelty. The justices arrested and prosecuted Hodge on a charge of murder. Five distinct counts were stated in the indictment. The case of the negro Prosper was proceeded with first. The trial began on 29 April before a special court of oyer and terminer and gaol delivery, presided over by Mr. Hetherington. Perreen Georges and m'Keough gave evidence showing that Prosper, having been accused of pulling a mango from a tree, and being unable to find the six shillings which Hodge demanded as compensation, had been laid down and cart-whipped for the space of one hour; that the next day he had been tied to a tree and flogged ‘at short quarters,’ i.e. with a short-looped lash, till he fainted; that he had then been chained up with two other negroes; and that, while his comrades managed to escape, he himself crawled into a hut, where he died unattended. M'Keough declared that sometimes three or four negroes died in a single night. Among corroborative witnesses was Mrs. Rawbone, Hodge's sister. The defence tried in vain to discredit the witnesses, and appealed to the jury in the name of Hodge's young family. The jury brought in a verdict of guilty, and Hodge was sentenced to death. He spent the last days of his life in religious exercises, and suffered the extreme penalty of the law on 8 May 1811.

HODGES, CHARLES HOWARD (1764–1837), portrait-painter and mezzotint-engraver, was born in London in 1764. His earlier years were spent in mezzotint-engraving, in which art he attained the highest excellence. He may have been a pupil of John Raphael Smith [q. v.], as that engraver's name appears on some of his earlier engravings, such as ‘Mrs. Musters as Hebe’ (1785), ‘Guardian Angels’ (1786), and others after Sir Joshua Reynolds. He engraved after Reynolds portraits of Lavinia, Lady Spencer, Lady Dashwood and child, Mary Robinson, Charles, duke of Rutland, Joshua Sharpe, the Rev. Thomas Warton, and others; after Romney, portraits of Admiral Arbuthnot, James Mingay, James Adair, Thomas Raikes, Sir James Stuart, and others; after Hoppner, portraits of Frederick, duke of York (full length), William, duke of Clarence (full length), and George IV as prince regent; after C. G. Stuart a series of portraits of notable personages in Ireland; and other portraits after Alefounder, Opie, Heins, Beechey, Sharples, Mather Brown, and others, including a portrait of William Wilberforce after Rising. Among the subject-pictures engraved by him were ‘The Shipbuilder and his Wife’ after Rembrandt, ‘The Entombment’ after Parmigiano, ‘Silenus’ after Rubens, ‘The Crucifixion’ after Vandyck, ‘Ugolino’ and ‘The Infant Hercules’ after Reynolds, and others after G. Metsu, B. Strozzi, F. Wheatley, B. West, and R. M. Paye. In 1788 Hodges being in pecuniary difficulties accompanied W. Humphreys, the print-dealer, to Amsterdam, and continued for many years to act as agent for the transmission of prints, copperplates, &c., especially rare portraits, to England. He did not settle there at once, as he continued to publish engravings in England, such as ‘Sir Abraham Hume,’ after Reynolds, dated from 17 Lambeth Row in 1791. By 1794, however, he was settled in Amsterdam, and spent the remainder of his life there or at the Hague.


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108 thus he went down the steps, and along the street, still talking to himself. I should conjecture he is one, who, having been maintained by the Jesuits, has lost his wits in consequence of the tremendous fall of the order, and now comes every day to search the empty vessel for its old inhabitants, and, after a short prayer, to pronounce a curse upon their enemies.

A young man whom I questioned about the remarkable sights in the town showed me a house which is called the "Devil's house," because the devil, who is generally too ready to destroy, is said to have built it in a single night, with stones rapidly brought to the spot. However, what is really remarkable about the house the good man had not observed; namely, that it is the only house of good taste that I have yet seen in Trent, and was certainly built by some good Italian, at an earlier period. At five o'clock in the evening I again set off. The spectacle of yesterday evening was repeated, and at sunset the grasshoppers again began to sing. For about a league the journey lies between walls above which the grape-espaliers are visible. Other walls, which are not high enough, have been eked out with stones, thorns, etc., to prevent passengers from plucking off the grapes. Many owners sprinkle the foremost rows with lime, which renders the grapes uneatable, but does not hurt the wine, as the process of fermentation drives out the heterogeneous matter.

Evening of Sept. 11.

I am now at Roveredo, where a marked distinction of language begins: hitherto it has fluctuated between German and Italian. I have now, for the first time, had a thoroughly Italian postilion. The innkeeper does not speak a word of German, and I must put my own linguistic powers to the test. How delighted I am that the language I have always loved most now becomes living,—the language of common usage!

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 He devoted most of his time in Holland to portrait-painting in crayon, in which he was very successful, and gained the highest esteem. There are several portraits by him in the Ryksmuseum at Amsterdam, including Louis Napoleon, king of Holland, William I, king of the Netherlands, his own portrait, and that of his daughter. Hodges continued to engrave in mezzotint from the portraits painted by himself, and engraved among others Napoleon as emperor, and the grand pensionary Rutger Jan Schimmelpenninck. The latter engraving, from the skilful treatment of the dress and accessories, is considered one of the best examples of mezzotint-engraving. When the kingdom of the Netherlands was formed, Hodges was appointed one of the commissioners sent to Paris to recover the pictures removed by Napoleon. He died in Amsterdam on 24 July 1837. Hodges married in 1784, at St. George's, Hanover Square, Miss Margaret Harmar. His son, J. N. Hodges, engraved a few plates himself, and became a print-dealer in Amsterdam. A daughter, Emma Jane, on her death in 1868, bequeathed some portraits by her father to the Ryksmuseum. A small portrait of Hodges at the age of twenty-eight, drawn by E. Bell, is in Anderdon's ‘Collectanea Biographica’ in the print-room, British Museum. S. W. Reynolds the elder [q. v.] was his pupil.

 HODGES, EDWARD (1796–1867), organist and composer, born at Bristol in 1796, was organist at Clifton Church, and subsequently of the two churches, St. James and St. Nicholas, both at Bristol. In 1825 he proceeded to the degree of doctor of music from Sidney Sussex College, Cambridge, and in 1838 he went with his family to America. At New York Hodges was appointed organist to St. John's episcopal chapel, and in 1846 to Trinity Church, opened on 21 May with an organ built from his specifications. Prostrated by illness he resigned his appointments and returned in 1863 to England. He died at Clifton 1 Sept. 1867.

Hodges composed a morning and evening service and two anthems for the reopening of St. James's organ, Bristol, 2 May 1824, and published them in the following year. A second edition of the evening service, in C, was published at New York in 1863. Hodges also published: 1. ‘An Apology for Church Music and Musical Festivals, in answer to the animadversions of the “Standard” and the “Record,”’ pp. 71, Bristol, 1834. 2. ‘Canticles of the Church,’ compiled New York, 1864. 3. ‘The Te Deum, with Kyrie Chant and Ter Sanctus, in D,’ published after the composer's death by his daughter, London, 1885. 4. According to Grove's ‘Dictionary,’ i. 741, Hodges's ‘Essay on the Cultivation of Church Music,’ was published at New York, 1841. The ‘Trinity Collection of Church Music,’ edited by Tucker, Boston, 1864, contains some psalm and hymn tunes and arrangements by Hodges.

 HODGES, EDWARD RICHMOND (1826–1881), orientalist, born in 1826, became, while a London apprentice, a student of Hebrew, and, after being for a short time a scripture reader, was sent as a missionary by the Society for Promoting Christianity among the Jews, first to Palestine, and afterwards to Algeria, which he quitted in 1856. A few years later he severed his connection with the society, and for some time he acted as a minister of the reformed episcopal church; but he subsequently became a clergyman of the church of England. He died at his house in Tollington Park, London, on 9 May 1881, aged fifty-five, leaving a widow and six children. He was well known as a scholar in oriental languages, and assisted George Smith (1825–1876) [q. v.] in his cuneiform researches. He published, in addition to numerous articles in magazines: 1. ‘Ancient Egypt,’ 1851. 2. An edition of Craik's ‘Principia Hebraica,’ 1863, fol. 3. An edition, with notes, of Cory's ‘Ancient Fragments of the Phœnician … and other Authors,’ 1876, 8vo. He also revised Mickle's translation of the ‘Lusiad’ of Camoens for Bohn's ‘Standard Library,’ 1877, 8vo. Hodges assisted Dr. Gotch in the preparation of his Paragraph Bible, and wrote on American languages in the ‘English Cyclopædia.’ At the time of his death he was engaged upon an English version of the ‘Armenian History’ of Moses of Khorene.

 HODGES, NATHANIEL, M.D. (1629–1688), physician, son of Dr. Thomas Hodges, vicar of Kensington, was born in that parish on 13 Sept. 1629. He was a king's scholar of Westminster School, and obtained a scholarship at Trinity College, Cambridge, in 1646. In 1648 he migrated to Oxford, and was appointed


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 by the parliamentary visitors a student of Christ Church, where he graduated B.A. 1651, M.A. 1654, and M.D. 1659. He was a contributor to the Oxford volume of verse issued in 1654 to celebrate the peace with the Dutch. He then took a house in Walbrook, London, and commenced practice there. He was admitted a candidate or member of the College of Physicians 30 Sept. 1659. When the plague raged in London in 1665, he remained in residence, and attended all who sought his advice. During the Christmas holidays of 1664–5 he saw a few doubtful cases, and in May and June several certain cases; in August and September as many as he could see by working hard all day. He rose early, and took a dose of anti-pestilential electuary as large as a nutmeg. After transacting any household affairs he entered his consulting room. Crowds of patients were always waiting, and for three hours he examined them and prescribed, finding some who were already ill, and others only affected by fear. When he had seen all he breakfasted, and visited patients at their houses. On entering a house he had a disinfectant burnt on hot coals, and if hot or out of breath rested till at his ease, then put a lozenge in his mouth and proceeded to examine the patient. After spending some hours in this way he returned home and drank a glass of sack, dining soon after, usually off roast meat with pickles or other relish, condiments of all kinds being cheap and abundant in the city during the epidemic. He drank more wine at dinner. Afterwards he saw patients at his own house, and paid more visits, returning home between eight and nine o'clock. He spent the evening at home, never smoking tobacco, of which he was a professed enemy, but drinking old sack till he felt thoroughly cheerful. After this he generally slept well. Twice during the epidemic he felt as if the plague had infected him, but after increased draughts of sack he felt well in a few hours, and he escaped without serious illness. In 1666 he published a somewhat pedantic attack on quacks, ‘Vindiciæ Medicinæ et Medicorum, an Apology for the Profession and Professors of Physic.’ In recognition of his services to the citizens during the plague, the authorities of the city granted him a stipend as their authorised physician. In 1671 he completed an account of the plague, which was published in 1672 as ‘Loimologia, sive Pestis nuperæ apud Populum Londinensem grassantis Narratio Historica.’ This book shows Hodges to have been an excellent observer both as to symptoms and the results of treatment. Bezoar, unicorn's horn, and dried toads he tried and found useless, but he recognised the merit of serpentary as a diaphoretic, and of hartshorn as a cardiac stimulant. His cases are clearly related, and he is probably the only writer who has described pericarditis in a case of plague. The College of Physicians recognised the merit of the book, and elected him a fellow 2 April 1672. In 1682 he was censor, and in 1683 delivered the Harveian oration, which has not been printed. When censor he gave the college a fire-engine. His practice did not continue to increase, he became poor, was imprisoned in Ludgate for debt, and there died 10 June 1688. He was buried in Wren's fine church of St. Stephen's, Walbrook, and his bust and inscription are to be seen there. His medical commonplace book, in which little more than the headings are written on most pages, is among the Sloane MSS. in the British Museum. A translation of ‘Loimologia’ by Dr. Quincy was published in 1720.

HODGES, WILLIAM (1645?–1714), London merchant and writer, descended from a Middlesex family, was born about 1645. On 6 June 1611 a complaint was preferred by the citizens of Chester against a William Hodges, merchant, of London, who was perhaps Sir William's father (Harl. MS. 2105, p. 379). Hodges rapidly acquired a large fortune from the Spanish trade, and was in partnership at Cadiz with Christopher Hague, Ellis Terrell, and the Hon. Henry Bertie (see will). On one occasion he accepted a bill for 300,000l., and paid it for the use of the English fleet under the command of Admiral Russell, afterwards Earl of Orford (, Londinium Redivivum, iv. 603). The records of his financial dealings with the government date from 4 Aug. 1697 (Cal. of Treasury Papers, 1697–1701–2 passim, 1702–7 p. 301, cf. pp. 227, 255). Hodges was created a baronet on 31 March 1697. He died on 31 July 1714, and was buried on 6 Aug. at St. Katherine Coleman in Fenchurch Street. Malcolm describes his funeral, which was of unusual grandeur, forty-two noblemen's coaches following the procession (Lond. Red. iv. 603). His will, dated 13 July 1714, was proved in the P.C.C. [Aston, 139]. Hodges resided in 1681 in Mincing Lane, and at the time of his death had a house in Winchester Street, near Austin Friars. He married in 1681 (licence dated 25 April) Sarah, daughter and coheiress of Joseph Hall, merchant, of London and Hampstead, when his age was stated as ‘about thirty-six’ (Harl. Soc. xxx.; Marriage Allega-


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 tions, p. 60). He had an only son, Joseph, who succeeded to the baronetcy, but wasted his estate, and died unmarried in 1722, when the title became extinct (, Extinct Baronetcies, 2nd edit. p. 266). Lady Hodges died in 1717.

Hodges is doubtless the author of the following pamphlets pleading for the relief of British seamen from extortion:
 * 1) ‘An humble Representation of the Seamen's Misery’ [London, 1694], fol.
 * 2) ‘Great Britain's Groans; or an account of the oppression … of the … seamen of England,’ London, 1695, 4to.
 * 3) ‘Humble Proposals for the Relief … of the Seamen of England,’ 1695, 4to.
 * 4) ‘The Groans of the Poor … for the spoiling of our money,’ London, 1696, 4to.
 * 5) ‘Ruin to Ruin … being the distressed state of the seamen of England,’ London, 1699, 4to.

HODGES, WILLIAM (1744–1797), painter and Royal Academician, born in London in 1744, was only child of a smith, who kept a small shop in St. James's Market. He was employed as errand-boy in Shipley's drawing school, where he managed to learn drawing. , R.A. [q. v.], noticed him, and took him to be his assistant and pupil. Hodges made rapid progress. On leaving Wilson he resided in London, and also for a time at Derby, where he painted some scenes for the theatre. In 1766 he exhibited at the Society of Artists a view of London Bridge and another of Speldhurst, Kent, in 1768 two views in Wales, and other views in 1770 and 1771. In 1772 he sent some views on the Rhine and in Switzerland. In the same year he obtained, through the interest of Lord Palmerston, the post of draughtsman to the second expedition to the South Seas under Captain Cook. He returned in 1775, and was employed by the admiralty in finishing his drawings, and superintending the engraving of them (by Woollett and others) for the published account of Captain Cook's voyages. Some of his pictures from the South Seas are still preserved in the admiralty. In 1776 he first exhibited at the Royal Academy, sending a view in Otaheite, and in 1777 some views in New Zealand and elsewhere. In 1778 he went to India under the patronage of Warren Hastings, remained there about six years, and painted a number of views of the most remarkable objects and scenery. On his return to England in 1784 he brought a number of these with him, which were engraved, some on a large scale, by J. Browne and Morris; a set was executed in aquatint by himself, and published in 1786, and smaller copies appear in the ‘European Magazine’ and elsewhere. Humboldt, in his ‘Cosmos,’ says that the sight of Hodges's Indian views was one of the inducements which led him to travel. In 1793 Hodges published an account of his ‘Travels in India’ during the years 1780–3, with plates from his drawings; the book was afterwards translated into French. In 1784 Hodges settled in Queen Street, Mayfair, where he built himself a studio. In 1786 he was elected an associate of the Royal Academy, and an academician in 1789; he continued to exhibit at the Royal Academy up to 1794. Hodges painted several ambitious landscapes, in which he imitated both Wilson's force and negligence; his work suffers from want of accuracy. Figures were introduced into his landscapes by Romney, Gilpin, and others. Some were engraved, such as a scene from the ‘Merchant of Venice’ (by J. Browne), and another from ‘As you like it’ (by S. Middiman), both painted for Boydell's ‘Shakespeare,’ ‘The Retreating Shower’ (aquatint by M. C. Prestel), and a view of ‘Windsor from the Great Park’ (by W. Byrne and J. Schumann). J. Ogborne engraved after Hodges ‘Belisarius’ and ‘The Sleeping Shepherd.’ About 1790 he travelled on the continent, and visited St. Petersburg, of which he painted a view. He painted two large allegorical pictures of the ‘Effects of Peace’ and ‘War,’ which, with some others, he exhibited in Bond Street, with an explanatory catalogue. They, however, failed to attract, and Hodges, on closing the exhibition, retired from his profession, and disposed of his pictures by auction. In 1795 he settled at Dartmouth, and opened a bank. The troubles, however, which affected the financial world at the time proved the ruin of his firm. Hodges died shortly afterwards at Brixham, Devonshire, of gout in the stomach, on 6 March 1797, aged 53.

A profile portrait of Hodges is among the series, preserved at the Royal Academy, drawn by G. Dance; it was engraved by W. Daniell. Another portrait by R. Westall was engraved for the ‘Literary Magazine’ in 1793. Hodges when young etched a plate of Torre del Greco at Naples, after R. Wilson. He painted scenes for the Pantheon, but was not very successful. Two drawings from the South Seas are in the print room at the British Museum, and one of a ruined castle at the South Kensington Museum.

Hodges married, on 11 May 1776, at St. George's, Hanover Square, Miss Martha Nesbit, and settled in Pimlico, but lost his wife in child-bed within a year. On 16 Oct. 1784 he married a second time Miss Lydia


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 Wright, who soon died. Shortly afterwards he married, for a third time, Miss Carr, a lady much beloved and praised by Romney and other friends. His third wife survived him a few months, and died at Tunbridge in May of the same year. By her he had five children, whom he left in great want.

HODGES, WILLIAM (1808–1868), chief justice of the Cape of Good Hope, eldest son of William Hodges of Weymouth, by Sarah, second daughter of William Isaac of the same place, was born at Melcombe Regis, Dorsetshire, on 29 Sept. 1808, and educated at a private school at Salisbury and the university of London. Having attended the lectures of (1790–1859) [q. v.] and [q. v.], on jurisprudence and law, he was called to the bar at the Inner Temple on 3 May 1833. He went the western circuit, practising at first chiefly at quarter sessions. In 1835 he began to report cases in the court of common pleas, then presided over by Sir Nicholas Tindal, from whom he received in 1837 the appointment of revising barrister for Devon and Cornwall. In 1838 he ceased reporting in the common pleas, and began to report in the queen's bench. In 1839 he published ‘Report of the Case of the Queen v. Lumsdaine, with Observations on the Parochial Assessment Act;’ in 1840, jointly with Graham Willmore and F. L. Wollaston, ‘Reports of Cases argued and determined in the Court of Queen's Bench,’ &c., Hilary term to Michaelmas term 1838 (continued, under the title of ‘Term Reports,’ to 1841). In 1842 he published a small treatise on ‘The Law relating to the Assessment of Railways;’ in 1845 ‘The Statute Law relating to Railways in England and Ireland.’ In 1846 he was appointed recorder of Poole, Dorsetshire. In 1847 he published ‘The Law relating to Railways and Railway Companies.’ He also drafted the Public Health Act, 1848, a measure which laid the foundation of subsequent sanitary legislation. He thus acquired some parliamentary and general practice at Westminster. In 1857 he was appointed to the chief justiceship of the supreme court of the Cape of Good Hope, with which was associated the presidency of the legislative council and of the court of admiralty. At the same time he was knighted. He discharged his official duties with energy and efficiency until his death at Sea Point House, Cape Town, 17 Aug. 1868. He was honoured with a public funeral. Hodges married in 1835 Mary Schollar, daughter of James Sanders of Weymouth, by whom he had four sons, since deceased, and four daughters. Hodges's ‘Reports of Cases argued and determined in the Court of Common Pleas’ form a valuable collection of cases from Hilary term 1835 to Michaelmas term 1837, both dates inclusive. His treatise on ‘The Law of Railways’ has passed through seven editions (the last by John M. Lely of the Inner Temple, 1888), and is the standard work on the subject.

HODGKIN, JOHN (1766–1845), grammarian, born at Shipston-on-Stour, 1766, was educated partly at a quakers' school at Worcester, and partly by his uncle, Thomas Hodgkin, a successful private tutor in London, who invited his nephew to enter his own profession. In 1787 he joined [q. v.] in superintending the education of [q. v.] The two tutors seem to have given each other mutual instruction for four years, and tutors and pupil remained warm friends through life.

In 1792 Hodgkin spent some months at Vincennes in order to improve his knowledge of French. Of his recollections of the royal family he has left some record in a manuscript autobiography. When the king took the oath to the constitution, Hodgkin, as a quaker, had a conscientious objection to raise his hand with the multitude swearing fidelity to the compact between king and people, while his plain dress caused him to be continually taken for an abbé. He managed, however, to escape real danger. He describes in graphic language the consternation at Vincennes on 10 Oct. 1792, the day of the massacre of the Swiss guard.

Hodgkin returned to England, and soon became well known as a private tutor. His pupils were chiefly ladies belonging to the families of wealthy citizens in the environs of London. These he instructed in the classics and mathematics, but especially in the art of handwriting, in which he greatly excelled. He resided for some years at Pentonville, London, and then removed to Tottenham, where he died in August 1845. He married in 1793 Elizabeth Rickman of Lewes, a cousin of the architect [q. v.] His sons, [q. v.] (1798–1866) and [q. v.] (1800–1875), are noticed separately.


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Rh How much do I wish that my friends were with me for a moment to enjoy the prospect which now lies before my eyes!

I might have been in Verona this evening: but a magnificent natural phenomenon was in my vicinity,—Lake Garda, a splendid spectacle, which I did not want to miss; and now I am nobly rewarded for taking this circuitous route. After five o'clock I started from Roveredo, up a side valley, which still pours its waters into the Etsch. After ascending this, you come to an immense rocky bar, which you must cross in descending to the lake. Here appeared the finest calcareous rocks for pictorial study. On descending, you come to a little village on the northern end of the lake, with a little port, or rather landing-place, which is called Torbole. On my way up, I was constantly accompanied by fig-trees; and, descending into the rocky atmosphere, I found the first olive-tree full of fruit. Here, also, for the first time, I found as a common fruit those little white figs which the Countess Lanthieri had promised me.

A door opens from the chamber in which I sit into the courtyard below. Before this I have placed my table, and taken a rough sketch of the prospect. The lake may be seen for its whole length, and it is only at the end toward the left that it vanishes from our eyes. The shore, which is enclosed on both sides by hill and mountain, shines with a countless number of little hamlets.

After midnight the wind blows from north to south; and he who wishes to go down the lake must travel at this time, for a few hours before sunset the current of air changes, and moves northward. At this time (the afternoon) it blows strongly against me, and pleasantly qualifies the burning heat of the sun.


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110 Volkmann teaches me that this lake was formerly called "Benacus," and quotes from Virgil a line in which it was mentioned:—

This is the first Latin verse the subject of which ever stood visibly before me; and now, in the present moment, when the wind is blowing more and more strongly, and the lake casts loftier billows against the little harbour, it is just as true as it was hundreds of years ago. Much, indeed, has changed; but the wind still roars about the lake, the aspect of which gains even greater glory from a line of Virgil's.

The above was written in a latitude of 45° 50’.

I went out for a walk in the cool of the evening; and now I really find myself in a new country, surrounded by objects entirely strange. The people lead a careless, sauntering life. In the first place, the doors are without locks; but the host assured me that I might be quite at ease, even though all I had about me consisted of diamonds. In the second place, the windows are covered with oiled paper instead of glass. In the third place, an extremely necessary convenience is wanting, so that one comes pretty close to a state of nature. When I asked the waiter for a certain place, he pointed down into the courtyard: "Qui, abasso puo servirsi!"—"Dove?" asked I. "Da per tutto, dove vuol," was the friendly reply. The greatest carelessness is visible everywhere, but still there is life and bustle enough. During the whole day the women of the neighbourhood are incessantly chattering and shrieking: all have something to do at the same time. I have not yet seen an idle woman.

The host, with Italian emphasis, assured me that he felt great pleasure in being able to serve me with the


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Rh finest trout. They are taken near Torbole, where the stream flows down from the mountains, and the fish seeks a passage upward. The emperor farms this fishery for ten thousand gulden. The fish, which are large (often weighing fifty pounds), and spotted over the whole body to the head, are not trout, properly so called. The flavour, which is between that of trout and salmon, is delicate and excellent.

But my real delight is in the fruit,—in the figs and in the pears, which must, indeed, be excellent, where citrons are already growing.

Evening of Sept. 13.

At three o'clock this morning I started from Torbole with a couple of rowers. At first the wind was so favourable that we put up a sail. The morning was cloudy, but fine, and perfectly calm at daybreak. We passed Limona, the mountain gardens of which—laid out terrace-fashion, and planted with citron-trees—have a neat and rich appearance. The whole garden consists of rows of square white pillars placed at some distance from each other, and rising up the mountain in steps. On these pillars strong beams are laid, that the trees planted between them may be sheltered in the winter. The view of these pleasant objects was favoured by a slow passage; and we had already passed Malsesine when the wind suddenly changed, took the direction usual in the daytime, and blew toward the north. Rowing was of little use against this superior power, and therefore we were forced to land in the harbour of Malsesine. This is the first Venetian spot on the eastern side of the lake. When one has to do with water, we cannot say, "I will be at this or that particular place to-day." I will make my stay here as useful as I can, especially by making a drawing of the castle, which lies close to the water, and is a beautiful object. As I passed along, I took a sketch of it.


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 8th century But the great contribution of the century to the early history of Arabia was the collecting and translating of numerous early Arabian inscriptions (cf. section Antiquities above), which have done service both by their own indication of a great civilization in Arabia for nearly (or more than) a thousand years before the Christian era, and by the new stimulus which they gave to the study and appreciation of the materials in the Assyrian inscriptions, the Old Testament, and the Greek and Roman writers. At the same time the facts that the inscriptions are undated until a late period, that few are historical in their contents, and for the most part yield only names of gods and rulers and domestic and religious details, and that our collection is still very incomplete, have led to much serious disagreement among scholars as to the reconstruction of the history of Arabia in the pre-Christian centuries.

All scholars, however, are agreed that the inscriptions reach as far back as the 9th century (some say to the 16th) and prove the existence of at least four civilized kingdoms during these centuries. These are the kingdoms of Maʽīn (Minaean), of Saba (Sabaean), of Hadramaut (Hadramut) and of Katabania (Katabanū). Of the two latter little is known. That of Hadramut had kings from the time of the Minaeans to about 300, when it was conquered by Ethiopia. The limits of the kingdom of Katabania are not known, but it has its own inscriptions.

As to the Sabaean kingdom there is fair agreement among scholars. The inscriptions go back to 800 or earlier, and the same applies to the kingdom. A queen of this people (the “Queen of Sheba”) is said (1 Kings x.) to have visited Solomon about 950 There is, however, no mention of such a queen in the inscriptions. An Assyrian inscription mentions Ithʽamara the Sabaean who paid tribute to Sargon in 715 At this time the Sabaeans must have been in north Arabia unless the inscription refers to a northern colony of the southern Sabaeans. The former opinion is held by E. Glaser, who thinks that in the 9th and 8th centuries they moved down along the west coast to the south, where they conquered the Minaeans (see below). The Sabaean rule is generally divided into periods indicated by the titles given to their rulers. In the first of these ruled the Makārib, who seem to have been priest-kings. Their first capital was at Ṣirwāḥ. Ten such rulers are mentioned in the inscriptions. Their rule extended from the 9th to the 6th century. The second period begins about 550 The rulers are known as “kings of Saba.” Their capital was Ma’rib. The names of seventeen of these kings are known from the inscriptions. Their sway lasted until about 115, when they were succeeded by the Himyarites. During this period they were engaged in constant strife with the neighbouring kingdoms of Hadramut and Katabania. The great prosperity of south-west Arabia at this time was due in large measure to the fact that the trade from India with Egypt came there by sea and then went by land up the west coast. This trade, however, was lost during this period, as the Ptolemies established an overland route from India to Alexandria. The connexion of Saba with the north, where the (q.v.) had existed from about 200, was now broken. The decay that followed caused a number of Sabaeans to migrate to other parts of Arabia.

The Minaean kingdom extended over the south Arabian Jauf, its chief cities being Karnau, Maʽīn and Yathil. Some twenty-five kings are known from the inscriptions; of these twenty are known to be related to one another. Their history must thus cover several centuries. As inscriptions in the Minaean language are found in al-ʽUlā in north Arabia, it is probable that they had colonies in that district. With regard to their date opinion is very much divided; some, with E. Glaser and F. Hommel, maintaining that their kingdom existed prior to that of Saba, probably from about 1500 or earlier until the Sabaeans came from their home in the north and conquered them in the 9th century. Other scholars think, with D. H. Müller, partly on palaeographical grounds (cf. M. Lidzbarski’s Ephemeris, vol. i. pp. 109 seq., Giessen, 1902), that none of the inscriptions are earlier than about 800 and that the Minaean kingdom existed side by side with the Sabaean. It is curious that the Sabaean inscriptions contain no mention of the Minaeans, though this may be due to the fact that very few of the inscriptions are historical in content.

About 115 the power over south Arabia passed from the Sabaeans to the Himyarites, a people from the extreme south-west of Arabia; and about this time the kingdom of Katabania came to an end. The title taken by the new rulers was “king of Saba and Raidān.” Twenty-six kings of this period are known from the inscriptions, some of which are dated. In this period the Romans made their one attempt at direct interference in the affairs of Arabia. The invasion under Aelius Gallus was an absolute failure, the expedition being betrayed by the guides and lost in the sands of the desert. During the latter part of this time the Abyssinians, who had earlier migrated from Arabia to the opposite coast of Africa, began to flow back to the south of Arabia, where they seem to have settled gradually and increased in importance until about 300, when they became strong enough to overturn the Himyarite kings and establish a dynasty of their own. The title assumed by them was “king of Saba, Raidān, Hadramut and Yemen.” The Himyarites were, however, still active, and after a struggle succeeded in establishing a Jewish Sabaean kingdom, having previously accepted Judaism as their religion. Their best-known king was Dhu Nuwās. The struggle between them and the Abyssinians now became one of Judaism against Christianity. The persecution of the Christians was very severe (see E. Glaser’s Die Abyssinier in Arabien und Afrika, Munich, 1895, and F. M. E. Pereira’s Historia dos Martyres de Nagran, Lisbon, 1899). Apparently for this reason Christian Abyssinia was supported from Byzantium in its attempts to regain power. These attempts were crowned with success in 525. Of the Christian Abyssinian kings in Arabia tradition tells of four, one only of whom is mentioned in inscriptions. The famous expedition of Abraha, the Abyssinian viceroy, against Mecca, took place in 570. Five years later the Persians, who had been called in by the opponents of Christianity, succeeded in taking over the rule and in appointing governors over Yemen. (See further : The Axumite Kingdom.)

Hīra, Ghassān and Kinda.—Before passing to the time of Mahomet it is necessary to take account of three other Arabian powers, those of Hīra, Ghassān and Kinda.

The kingdom of Hira (Ḥīra) was established in the boundary land between the Euphrates and the Arabian desert, a district renowned for its good air and extraordinary fertility. The chief town was Hīra, a few miles south of the site of the later town of Kufa. The inhabitants of this land are said in Ṭabari’s history to have been of three classes:—(1) The Tanukh (Tnuhs), who lived in tents and were made up of Arabs from the Tehama and Nejd, who had united in Bahrein to form a new tribe, and who migrated from there to Hīra, probably at the beginning or middle of the 3rd century, when the Arsacid power was growing weak. The Arabian historians relate their conflict with Zenobia. (2) The ʽIbād or ʽIbādites, who dwelt in the town of Hīra in houses and so led a settled life. These were Christians, whose ecclesiastical language was Syriac, though the language of intercourse was Arabic. A Christian bishop of Hīra is known to have attended a synod in 410. In the 5th century they became Nestorians. (3) Refugees of various tribes, who came into the land but did not belong to the Tanukh or the ʽIbād. There is no trustworthy information as to the earlier chiefs of this people. The dynasty of the Lakhmids, famed in Arabian history and literature, arose towards the end of the 3rd century and lasted until about 602. The names of twenty kings are given by Hishām al-Kalbī in Ṭabari’s history. Although so many of their subjects were Christian, the Lakhmids remained heathen until Nu’mān, the last of the dynasty. The kingdom of Hīra was never really independent, but always stood in a relation of dependence on Persia, probably receiving pay from it and employing Persian soldiers. At the height of its power it was able to render valuable aid to its suzerain. Much of its time was spent in wars with Rome and Ghassān. Its revenues were derived from the Bedouins of the surrounding lands as well as from its own subjects at home. About 602 the Lakhmid dynasty fell, and the Persian Chosroes (Khosrau) II. appointed as governor an Arab of the tribe of Tāi. Shortly after it came into relation with Islam.

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Rh All the leading writers of the city were present, and each one read an original poem written specially for the occasion. With something of the enthusiasm of the time, I recall a charming poem by Juan de Dios Peza. His rich, soft voice is wonderfully effective; its sonorous intonation and smooth inflections, added to the eloquent gestures of the reader, carried his hearers along with rapturous enjoyment.

But Altimirano, Francisco Sosa, Juan Mateos, and others, as they stepped before the audience with dignified and graceful bearing, received an equally hearty greeting.

Our distinguished host read a poem full of dramatic effect, based upon the tales of the pirates of the Gulf. A most weird and peculiar effect was added to this reading by a piano accompaniment composed and dedicated to the author by a señorita, a musician of great celebrity. The voice of the reader and the tones of the piano flowing in admirable accord, now moved the audience to tender sympathy, again aroused soul-thrilling emotions or blood-curdling horror at the will of poet and musician.


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The New York Times/1880/01/16/Thomas A. Edison's Workshop

WHAT A VISITOR SAW AND WAS TOLD THERE - SOME DISCREPANCIES NOTED.

The public has been treated frequently of late to descriptions, of a glowing character, concerning Mr. Thomas A. Edison and his workshops at Menlo Park, Nj.J., and the inventor's promises to demonstrate beyond cavil the practicability of the electric for purposes of general illumination have been spread broadcast over the world by means of "interviews" and other articles in various periodicals. By way of contrast to these assertions, it is perhaps worth calling attention to the experiences of an entirely disinterested gentleman who visited the Edison laboratory, at Menlo Park, yesterday, and subsequently paid a visit to the offices of the Edison Electric Light Company, in this City, both visits being in the interest of Western gentlemen who wished to obtain the refusal of the light for a well-known city in case its practicability should be demonstrated. He expected to find at Menlo Park an extensive laboratory, where a score of Edison's assistants would be seen engaged in experiments under the great electrician's directions. The glowing accounts published suggested visions of numberless bottles, whose labels indexed every chemical known to science, in the manipulation of which the visitor expected to discover every kind of chemical apparatus that would in any way be useful in electrical experiments. Instead of all this, he found a half-dozen small buildings, with but a few of the adjuncts he had imagined. In one building a single assistant was engaged testing telephones of a pattern which he was informed was intended for the English market, and had not yet been introduced here. A young man stood off a few yards, and from the other end of the wire yelled some nonsense about Mary's little lamb, which the obliging assistant informed the visitor was heard in a tone louder than it was spoken. The instrument was an adaptation of the English microphone, and the visitor speedily learned that in place of the supposed laboratory being filled with enthusiastic young men wrestling with science, its occupants were mechanics who attended strictly to the business of manufacturing and testing this kind of telephone. The activity was so fancifully described in the papers was explained. The room which he was told was the scene of the carbon-making appeared deserted, as indeed did every room which was expected to be lively with the work of getting out the electric lamps.

How many lights have you in operation?" he asked the guide.

"Somewhere about 70 or 80," was the reply.

"And how many lamps were lighted at the opening on New Year's night?"

"About the same number, but we are expecting to have 800 very soon."

"What is causing the delay?"

"We are getting them out as fast as possible, but the glass-blower is detaining us. He can't work very fast.  We have advertised for more glass-blowers, but have received no answers yet."

The visitor, at the end of this conversation, reached the building occupied by the glassblower, a young Thuringian, who had been bred to the business from boyhood.

"How long does it take you to blow the glass for one lamp?" asked the visitor.

"I never figured it out, but I will make one for you."

It took him just three minutes by the watch.

"Does this end your part of the work?" was next asked.

"Oh, no; I put in the carbons and seal the lamps."

"Can you make a lamp complete in half an hour?"

"Oh, yes, easily."

"And you work 10 hours a day?"

"Yes."

According to the visitor's figuring there should have been no difficulty in getting out at least 20 lamps a day, or, say since Jan 1, 200. Two hundred and eighty lamps burning, it occurred to him, would have impressed people by this time with a firmer belief in the practicability of the thing.

Another disappointment was experienced. The visitor found three generators instead of one, of four-horse power each, maintaining the lights. Two, he was told, were to regulate the circuit; the third supplied the power in the field. On asked the guide if he was sure there were 80 lights burning, or had been at any time, he admitted that he did not know certainly, but he thought at least there had been 60 lighted at one time. At that rate, a single horse-power would maintain five lights, each equal to 10 candles. The visitor had read that the Brush light in the Cleveland (Ohio) public square maintained 16 lights of 1,200-candle power each with a 12-horse power engine, and ran their large works with it besides. On the cars returning from Menlo Park he fell in with a gentleman who had been there on New Year's night. THis gentleman said that he had counted every electric lamp in operation that night, and that there were but 34 all told, not including a number of coal-oil lamps that helped to dazzle the spectators. At the offices of the Edison Electric Light Company he was told that they were not yet prepared to sell privileges to anybody. They were not through experimenting, and until they had demonstrated the practicability of their light through the construction of a regular system, they did not propose to put it in the market.

A few weeks before New Years, the gentleman whose observations are given above chanced to ask a prominent electrician what he thought of the promised Edison exhibition, just then announced. "I will write it out for you." he replied. It was as follows:

"The Edison Electric Light Company will announce, with a grand flourish of trumpets, that the long-sought for light has been accomplished. A number of lamps will be set to burning, enough to make a showing, and the next day's newspapers will contain sensational accounts of the exhibition.  No more lights were horse power than on the exhibition night will be added after Jan. 1.  One excuse, and then another for deferring it will be given, and after a few more flashes in the pan, we shall hear but a very little more of Edison or his electric lamp.  Every claim he makes has been tested and proved impracticable."

That Mr. Edison's failure to make good his enthusiastic promises speedily is having an effect on the public mind is everywhere admitted. The stock of the company named after the inventor is also feeling the effects of deferred expectations. In illustration of the latter statement the fact may be mentioned that the stock which in consequence of recent sensational publications went up to $3,300 per share on Dec. 30, 1879, was quoted yesterday at $1,500.


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silence of dead centuries That lie entombed on yonder hills Is his. These dreamful poppy seas Wave on; and all their languor fills The land; he lists, as if he heard God speak through some still gorgeous bird.

His babes about; the golden morn Strides godlike down the lofty hill: His wife and daughter grinding corn— "Two women grinding at a mill." Oh, mystery! This sun of old Was god! was god! and ample gold.

His golden hills had flocks of snow, His valley fields had fat increase. He saw his white sails fill and blow By restful isles of flower seas. The wood-dove sang his ceaseless loves— His harshest notes this soft wood dove's.


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400 The Mexican Indian is by inherent custom an agriculturist, and notwithstanding the fact that the conqueror imposed upon him burdensome and distasteful labors—among them that of mining—he at the first opportunity returned to his favorite vocation, to which he still adheres at the present day. He is an uncompromising antagonist to any change of locality, and clings to the place of his nativity with unwavering fidelity. There is but little mirthfulness or merriment in his composition. An intense believer in the supernatural, it cannot be better illustrated than by the fact of Montezuma, in spite of all his splendid resources, yielding with so little resistance to Cortez' small band of four hundred and fifty men; for he must have felt convinced that the Spanish conqueror was the one designated by prophecy and tradition to possess the land.

"According to what you declare," said he, "of the place whence you came, which is toward the rising sun, and of the great Lord who is your King, we must believe that he is our natural Lord."

Without being inventive, they are great imitators and marvelously ingenious in the construction of the infinite variety of curiosities of the country.

Straw, wax, wood, marble, grass, hair and mother earth are all successfully treated by these dexterous brown fingers. True to the


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Rh But, as may be seen in other avenues of business in this land of rest and romance, they work on insignificant articles for days or weeks, seemingly to the exclusion of all else, and then dispose of them for a mere trifle.

The Indian voice is soft and low, almost flute-like in its sweetness, in this quality contrasting with the shrill tones frequently heard in the higher ranks of society. Their step is light, even cat-like, in its softness—a characteristic of all classes, regardless of station.

On dias de santo and other feast-days, outdoor gambling of every description is indulged in by this class, while bullfights and pulque-drinking constitute their principal pleasures.

The love for spectacular display is also a predominating characteristic with them. It is shown in the pleasure taken in sky-rockets and all pyrotechnics, especially if accompanied by a band of music.

Their taste also finds expression in the universal love of flowers. Not only are the humblest homes embellished with such gay and gorgeous flowers as would constitute the choicest treasures of a northern hot-house, but in the streets and markets, edibles and other commodities are exposed for sale side by side with them, and for a tlaco or medio one may buy a lovely bouquet.

They are also great admirers of pictures, and groups may be seen any day in the principal cities, gazing intently on those exhibited


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404 One fact worthy of being chronicled is, that the common people are making a considerable effort toward advancement in learning to read and write, even while employed as servants in families. I saw several at the capital who, unaided, were studying Spanish one day and English the next.

Mexico has a population of about 10,000,000, of which one and a half are pure white—Americans, Germans, French, English and Spaniards—and two and a half mestizos—leaving about 6,000,000 of Indians.

It has been estimated that there are five hundred different dialects in the country. The Indians have, in the main, retained their own race and tribal characteristics. Spanish is the language of many of them, but numerous tribes are to be found who speak purely in their own tongue, and cling to their own traditions, dress, and to some extent, their own peculiar forms of religious worship, seldom intermarrying with others.

In the sixteenth century, according to Mexico á travers de los Siglos the types were classified as follows, and, barring the natural increase of population, they remain about the same to-day:

Occasionally race characteristics, after lying dormant for perhaps generations, crop out unexpectedly in families, causing quite a shock when they appear. A dark, or as is sometimes the case, black child makes its appearance, and this is called Salta atrás (a leap over several generations).

The mestizos are the handsomest, and the zambos must rest


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Rh to him; but, on the other hand, he has a heart and much of the sentimental and romantic instinct which invests him with many of the attractions of the bandit.

The most beautiful and distinctive female type of the common people is the China (Chena), familiarly known as the China poblana. With many added attractions she may be considered the counterpart of the French grisette. But the China has a rich and luxurious tropical order of beauty that is especially her own, with hands, arms, and feet that could not be excelled for artistic elegance by Praxiteles. She has the warmth of nature and faithful devotion which characterize

all Mexican women. Her peculiar costume, now rarely seen, possesses a semi-barbaric charm that interdicts all rivalry; but it will soon be a memory of the past, having given place in great measure to a more modern style.

The common people have, generally, a great dread of having their pictures taken. A sort of superstition haunts them that the process will deprive them of some part of their being, either corporal or spiritual. This dread was realized when the artist took her revenge on a curious crowd who had gathered so closely around us as to almost impede the manipulations of her pencil. I was constantly on the qui vive for some of my former mozos who had left me some years before to go to their families. I was certain on one occasion that I had found one of them, but he had risen from the rank of mozo to a cargador, with all the dignity and equipments of that station. When he entered the house where I was, on an errand, the resemblance to Miguel Rodriguez


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Rh class, which, beyond question in Mexico, as in all other countries, is the most moral and upright.

When legal marriages occur, the parents make every arrangement when the young people have arrived at an age at which they are able to bear the responsibilities of married life. When such a case presents itself, the parents of the lover go to the house of the sweetheart, and take with them a chiquihuite (a certain kind of big basket), containing a turkey, several bottles of native brandy and other drinks, bread, ears of dried corn, and peppers of different kinds. The first time the parents of the lover go to ask for the girl's hand, they organize a sort of procession, composed of some of the relatives and friends of the family and a band of music, which plays without intermission from the house from which they start to the dwelling of the maiden.

Once there, the band and the rest of the procession are profoundly silent, while the petition is being made.

The first request is generally refused by the parents of the girl, until they consult with the relatives and ascertain the will of her who is sought in marriage. If the result is favorable, they appoint the wedding day; if unfavorable, the answer is reduced simply to returning the basket with its contents.

As soon as the news in the affirmative is received, the family of the bridegroom invite all their friends to the fandango which is given on the day of the wedding, in honor of the newly-married couple.


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422 of the original amount. The accompanying plates show how these accounts are kept.

The furnishing of the homes of the common people is necessarily meager; sometimes only mats laid upon the dirt floor serve for beds, or a few rudely made bedsteads and chairs, with pictures of the saints and a quantity of home-manufactured toys, constitute the outfit. They jente ordinario, but their houses are reasonably clean. One corner of the room is generally devoted to an infinite variety of pottery suspended on nails, This is collected from all parts of the country, and is their chief household treasure; even small children can point out the different kinds and tell where each piece was made.

Let one enter when he will, he is sure to be greeted politely, and to have the kindliest hospitality extended to him. I remember one of


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Rh the houses into which I went where a pretty young woman of twenty years sat crocheting, while the baby slept in his petate cradle and the husband lay sick on his humble cot in the corner. She cordially welcomed me, and when I was seated, he, though feeble and trembling, raised himself upon his elbow, tendering me the hospitality of his pobre casa; then asked his wife to prepare for me a cup of coffee or chocolate, which she did.

I condoled with him on his illness and hoped would soon be well. To this he replied he hoped so, but as he had consumption, there was little chance for his recovery; but if it were possible, he would like to get well, "in order to serve me the rest of his life!" I was agreeably surprised to find so many sewing machines, and that the women understand their use quite as well as we do. A machine agent informed me that the women of this class are as prompt to meet their installments as those in any country. But the price of sewing is so very cheap—only one cent a yard—that they must do a great deal to render themselves self-sustaining.

Babies are cared for with great tenderness. They are wrapped as tightly as possible in "swaddling-clothes "until about one month old, when the calzoncillos (little breeches) are substituted, for both


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144. 145. 146. 147. 148. 149. 150. 151. . 153. 154. 155. . PAGE

Introductory. ... ..... 202 Displacement corresponding with plane strain 202 Displacement corresponding with plane stress ... . 204 Generalized plane stress 206 Introduction of nuclei of strain 206 Force operative at a point 207 Force operative at a point of a boundary 208 Case of a straight boundary 209 Additional results : (i) the stress function, (ii) normal tension on a segment of a straight edge, (iii) force at an angle, (iv) pressure on faces of wedge 209 Typical nuclei of strain in two dimensions 211 Transformation of plane strain 213 Inversion 213 Equilibrium of a circular disk under forces in its plane, (i) Two opposed forces at points on the rim. (ii) Any forces applied to the rim. (iii) Heavy disk resting on horizontal plane. . 215 Examples of transformation 217

Appendix to Chapters VIII and IX. Volterea's Theory of Dislocations a. Introductory, (a) Displacement answering to given strain. (6) Discon- tinuity at a barrier, (c) Hollow cylinder deformed by removal of a slice of uniform thickness, {d) Hollow cylinder with radial fissure

Chapter X. Theory of the integration op the equations of equilibrium of an isotropic elastic solid body . Nature of the problem . R&ume of the theory of Potential. . Description of Betti's method of integration. . Formula for the dilatation .... . Calculation of the dilatation from surface data . Formulse for the components of rotation. . Calculation of the rotation from surface data. . Body bounded by plane — Formulae for the dilatation . Body bounded by plane — Given surface displacements . Body bounded by plane — Given surface tractions . Historical Note . Body bounded by plane — Additional results. . Formulse for the displacement and strain . Outlines of various methods of integration 228 230 231 233 234 235 235 237 239 241 242 243 245


text: Dictionary of National Biography, 1885-1900/Hoare, Clement


text: Dictionary of National Biography, 1885-1900/Hoare, Prince


text: Dictionary of National Biography, 1885-1900/Hoare, Richard (1648-1718)


text: Dictionary of National Biography, 1885-1900/Hoare, Richard Colt


text: Dictionary of National Biography, 1885-1900/Hoare, William (1707?-1792)


text: Dictionary of National Biography, 1885-1900/Hoare, William Henry


text: Dictionary of National Biography, 1885-1900/Hobart, George


text: Dictionary of National Biography, 1885-1900/Hobart, Henry


text: Dictionary of National Biography, 1885-1900/Hobart, James


text: Dictionary of National Biography, 1885-1900/Hobart, John (1694?-1756)


text: Dictionary of National Biography, 1885-1900/Hobart, John (1723-1793)


text: Dictionary of National Biography, 1885-1900/Hobart, Miles


text: Dictionary of National Biography, 1885-1900/Hobart, Robert


text: Dictionary of National Biography, 1885-1900/Hobart, Vere Henry


text: Dictionary of National Biography, 1885-1900/Hobart-Hampden, Augustus Charles


text: Dictionary of National Biography, 1885-1900/Hobbes, Robert


text: Talk:The New York Times/1880/01/16/Thomas A. Edison's Workshop


text: Dictionary of National Biography, 1885-1900/Hobbes, Thomas


text: Dictionary of National Biography, 1885-1900/Hobhouse, Benjamin


text: Dictionary of National Biography, 1885-1900/Hobhouse, John Cam


text: Dictionary of National Biography, 1885-1900/Hoblyn, Richard Dennis


text: Dictionary of National Biography, 1885-1900/Hobson, Edward


text: Dictionary of National Biography, 1885-1900/Hobson, Richard


text: Dictionary of National Biography, 1885-1900/Hobson, Thomas


text: Dictionary of National Biography, 1885-1900/Hoccleve, Thomas


text: Dictionary of National Biography, 1885-1900/Hodder, James


text: Dictionary of National Biography, 1885-1900/Hoddesdon, John


text: Dictionary of National Biography, 1885-1900/Hodge, Arthur


text: Dictionary of National Biography, 1885-1900/Hodges, Charles Howard


text: Dictionary of National Biography, 1885-1900/Hodges, Edward (1796-1867)


text: Dictionary of National Biography, 1885-1900/Hodges, Edward Richmond


text: Dictionary of National Biography, 1885-1900/Hodges, Nathaniel


text: Dictionary of National Biography, 1885-1900/Hodges, William (1645?-1714)


text: Dictionary of National Biography, 1885-1900/Hodges, William (1744-1797)


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Page:Essays on the active powers of the human mind; An inquiry into the human mind on the principles of common sense; and An essay on quantity.djvu/612

 ished by subtraction, may be multiplied and divided, and, in a word, may bear any proportion to another quantity of the same kind, that one line or number can bear to another. That this is essential to all mathematical quantity, is evident from the first elements of algebra, which treats of quantity in general, or of those relations and properties which are common to all kinds of quantity. Every algebraical quantity is supposed capable not only of being increased and diminished, but of being exactly doubled, tripled, halved, or of bearing any assignable proportion to another quantity of the same kind. This then is the characteristic of quantity; whatever has this property may adopted into mathematics, and its quantity and relations may be measured with mathematical accuracy and certainty.

Sec. 2. Of proper and improper quantity.
There are some quantities which may be called proper and others improper. This distinction is taken notice of by Aristotle, but it deserves some explanation. I call that proper quantity which is measured by its own kind, or which of its own nature is capable of being doubled or tripled, without taking in any quantity of a different kind as measure of it. Thus a line is measured by known lines, as inches, feet, or miles; and the length of a foot being known, there can be no question about the length of two feet, or of any part or multiple of a foot. And this known length, by being multiplied or divided, is sufficient to give us a distinct idea of any length whatsoever.

Improper quantity is that which cannot be measured by its own kind; but to which we assign a measure by the means of some proper quantity that is related to it. Thus velocity of motion, when we consider it by itself, cannot be measured. We may perceive one body to move faster, another slower; but we can have no distinct idea of a proportion or ratio between their velocities, without taking in some quantity of another kind to measure them by. Having, therefore, observed that by a greater velocity a greater space is passed over in the same time, by a less velocity in a less space, and by an equal velocity in an equal space; we hence learn to measure velocity by the space passed over in a given time, and to reckon it to be in exact proportion to that space. And having once assigned this measure to it, we can then, and not till then, conceive one velocity to be exactly double, or half, or in any other proportion to another; we may then introduce it into mathematical reasoning without danger of confusion or error, and may also use it as a measure of other improper quantities.

All the kinds of proper quantity we know, may, I think, be reduced to these four: extension, duration, number, and proportion. Though proportion be measurable in its own nature, and


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AN ESSAY ON QUANTITY therefore hath proper quantity, yet as things cannot have proportion which have not quantity of some other kind, it follows that whatever has quantity must have it in one or other of these three kinds, extension, duration, or number. These are the measure of themselves, and of all things else that are measurable.

Number is applicable to some things to which it is not commonly applied by the vulgar. Thus, by attentive consideration, lots and chances of various kinds appear to be made up of a determinate number of chances that are allowed to be equal; and by numbering these the values and proportions of those which are compounded of them may be demonstrated.

Velocity, the quantity of motion, density, elasticity, the vis insita, and impressa, the various kinds of centripetal forces, and different orders of fluxions, are all improper quantities, which, therefore, ought not to be admitted into mathematics without having a measure of them assigned. The measure of an improper quantity ought always to be included in the definition of it; for it is the giving it a measure that makes it a proper subject of mathematical reasoning. If all mathematicians had considered this as carefully as Sir Isaac Newton appears to have done, some labour had been saved both to themselves and to their readers. That great man, whose clear and comprehensive understanding appears even in his definitions, having frequent occasion to treat of such improper quantities, never fails to define them, so as to give a measure of them, either in proper quantities, or in such as had a known measure. This may be seen in the definitions prefixed to his "Princip. Phil. Nat. Math."

It is not easy to say how many kinds of improper quantity may in time be introduced into mathematics, or to what new subjects measures may be applied; but this, I think, we may conclude, that there is no foundation in nature for, nor can any valuable end be served by, applying measure to anything but what has these two properties. First, it must admit of degrees of greater and less. Secondly, it must be associated with, or related to something that has proper quantity, so as that when one is increased the other is increased, when one is diminished the other is diminished also; and every degree of the one must have a determinate magnitude or quantity of the other corresponding to it.

It sometimes happens that we have occasion to apply different measures to the same thing. Centripetal force, as defined by Newton, may be measured various ways; he himself gives different measures of it, and distinguishes them by different names, as may be seen in the above-mentioned definitions.

In reality, I conceive that the applying of measures to things that properly have not quantity, is only a fiction or artifice of


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 the mind, for enabling us to conceive more easily and more distinctly to express and demonstrate the properties and relations of those things that have real quantity. The propositions contained in the two first books of Newton's "Principia," might, perhaps, be expressed and demonstrated without those various measures of motion, and of centripetal and impressed forces, which he uses. But this would occasion such intricate and perplexed circumlocutions, and such a tedious length of demonstrations, as would fright any sober person from attempting to read them.

Sec. 3. Corollary First.
From the nature of quantity we may see what it is that gives mathematics such advantage over other sciences in clearness and certainty; namely, that quantity admits of a much greater variety of relations than any other subject of human reasoning; and, at the same time, every relation or proportion of quantities may, by the help of lines and numbers, be so distinctly defined as to be easily distinguished from all others, without any danger of mistake. Hence it is that we are able to trace its relations through a long process of reasoning, and with a perspicuity and accuracy which we in vain expect in subjects not capable of mensuration. Extended quantities, such as lines, surfaces and solids, besides what they have in common with all other quantities, have this peculiar, that their parts have a particular place and disposition among themselves: a line may not only bear any assignable proportion to another, in length or magnitude, but lines of the same length may vary in the disposition of their parts; one may be straight, another may be part of a curve of any kind or dimension, of which there is an endless variety. The like may be said of surfaces and solids. So that extended quantities admit of no less variety with regard to their form than with regard to their magnitude; and as their various forms may be exactly defined and measured, no less than their magnitudes, hence it is that geometry, which treats of extended quantity, leads us into a much greater compass and variety of reasoning than any other branch of mathematics. Long deductions in algebra for the most part are made, not so much by a train of reasoning in the mind, as by an artificial kind of operation, which is built on a few very simple principles: but in geometry, we may build one proposition upon another, a third upon that, and so on, without ever coming to a limit which we cannot exceed. The properties of the more simple figures can hardly be exhausted, much less those of the more complex ones.

Sec. 4. Coroll. 2.
It may I think be deduced from what hath been above said, that mathematical evidence is an evidence sui generis, not competent to any proposition which does not express


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 that seem directly contrary to those of the other. Thereupon, a serious controversy is begun, whether centripetal force be as the velocity, or as the velocity and quantity of matter taken together. Much mathematical and experimental dust is raised; and yet neither party can ever be brought to yield; for they are both in the right, only they have been unlucky in giving the same name to different mathematical conceptions. Had they distinguished these measures of centripetal force as Newton has done, calling the one "vis centripetæ quantitatis acceleratrix," the other, "quantitas motrix," all appearance of contradiction had ceased, and their propositions, which seem so contrary, had exactly tallied.

Tyler & Reed, Printers, Bolt-court, London.


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272 For the career of the Aztec in Mexico we have a respectable historical literature, but for the want of dated sculptures cannot establish so remote a chronology as for the Maya. The tabulated list gives us a few of the most important dates, though all those preceding 1325 A.D. are but crude approximations.

The list of Aztec rulers as given by Sahagun is as follows, the dates being approximate:—

The career of the Aztec rulers appears closely parallel both as to time and extent to that of the Inca in Peru, but both were later than the rise of the Maya. The similar dominance of the rulers of Bogota in Colombia should be noted, though historians have been less successful in projecting their chronology. The three examples we have given, therefore, exhaust the list of historical chronologies for the New World. Among the less cultured tribes there are a few feeble efforts to compile chronologies. The Kiowa and Dakota of the North American Plains have a kind of year count, but this does not reach beyond the period of colonization and so has no significance

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Rh thought, and the rest is but ornament and episode. He is a Christian idealist, and he refuses to regard poetry except in the light of those great ideas which belong to the spirit, and, being nobly and beautifully interpreted, are the substance of the poets who live by their wisdom as well as by charm. The ethical, the philosophical element in a large sense, is to him the engrossing thing; and criticism of this sort, so incited and so aimed, has a reality that does not fall far short of the worth of direct reflection upon the things of the mind, though it deals with them through the medium of literature instead of in life itself.

With Spenser, naturally, he has many affinities. The mediævalism, the sentiment of chivalry, the allegorizing spirit, and not less the Puritan elevation of the first of the Elizabethan poets, exercise a special fascination over a Catholic mind for whom the Ages of Faith, as he likes to call them, have in a peculiar degree the ideality that clothes the past. One no longer looks for original criticism of the father of English verse, who, more than Chaucer, may claim the paternity of great poets in later days; but to remind us of his excellence has become, in


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68 the lapse of time and the decline of poetic taste, almost as desirable an office as it once was to unfold its secret. Spenser is a poet who requires no common critic to speak justly of him. His position was a unique one, and by some infelicity of his stars he failed to rise to the greatness which seems to have been possible to him. Aubrey de Vere remarks that the great romantic poem of the Middle Ages, one that should sum them up on the human as Dante did upon the divine side, was never written; and, looking back, it appears to us that Spenser was the choice spirit that missed this destiny. His pure poetic quality, that sensibility to beauty and delight in it as in his element, was perfect to such a degree that Milton and Keats, who possessed it in something of the same measure, seem almost to have derived it from him, whose poems nourished it in them. The sweetness and noble ease of his expression reveal the presence of a marvelous literary faculty. His responsiveness to the historical and legendary elements in the past, his power of abstracting and idealizing them for poetic use, and his profound interest in human life, were great endowments, and he possessed in a high degree and a pure form


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Rh that moral reason which is the attribute of genius. But by defects as striking as this gift he made his poem less than we fondly think it might have been. The Elizabethan prolixity, the obscure perception of the nature of form in literary work, the artificiality incident to the allegorizing temperament, account for much of what he lost; but, for all that, his poems are marvels of the creative intellect, and it is this intellect that Aubrey de Vere dwells on. Any one can point out Spenser's loveliness, but the great spirit that brooded over his verse is not so easily realized. His aim was "to strengthen man by his own mind," and it is this effort which the critic analyzes, and by so doing tries to show how well he deserved the epithet "grave" as well as "gentle Spenser."

His work, with its intricate allegory, its machinery of faëryland and chivalry, its ideal landscape, is regarded as remote from life; but just as the creations of art, which also have this unreality, are yet the expression, oftentimes, of the most real human feeling and the most substantial thought of the mind, so the figures of his embroidered poem compose a procession of true life. They are conceived and used in accordance


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In the beginning of the 6th century a dynasty known as the Jafnids, enter into the history alike of the Roman and Persian empires. They ruled over the tribe of Ghassān in the extreme north-west of Arabia, east of the Jordan, from near Petra in the south to the neighbourhood of Rosāfa in the north-east. Of their origin little is known except that they came from the south. A part of the same tribe inhabited Yathrib (Medina) at the time of Mahomet. The first certain prince of the Jafnid house was Hārith ibn Jabala, who, according to the chronicle of John Malalas, conquered Mondhir (Mundhir) of Hīra in 528. In the following year, according to Procopius, Justinian perceived the value of the Ghassānids as an outpost of the Roman empire, and as opponents of the Persian dependants of Hīra, and recognized Hārith as king of the Arabs and patrician of the Roman empire. He was thus constantly engaged in battles against Hīra. In 541 he fought under Belisarius in Mesopotamia. After his death about 569 or 570 the friendly relations with the West continued, but about 583 there was a breach. The Ghassānid kingdom split into sections each with its own prince. Some passed under the sway of Persia, others preserved their freedom at the expense of their neighbours. At this point their history ceases to be mentioned in the Western chronicles. There are references to the Ghassānid Nu’mān in the poems of Nābigha. Arabian tradition tells of their prince Jabala ibn Aiham who accepted Islam, after fighting against it, but finding it too democratic, returned to Christianity and exile in the Roman empire. As Islam advanced, some of the Ghassānids retreated to Cappadocia, others accepted the new faith.

In the last decade of the 5th century a new power arose in central Arabia. This was the tribe of Kinda under the sway of the family of Āqil ul Murār, who came from the south. They seem to have stood in much the same relation to the rulers of Yemen, as the people of Hīra to the Persians and the Ghassānids to Rome. Abraha in his invasion of the Hejaz was accompanied by chiefs of Kinda. Details of their history are not known, but they seem to have gained power at one time even over the Lakhmids of Hīra; and to have ruled over Bahrein as well as Yemama until the battle of Shi’b ul Jabala, when they lost this province to Hīra. The poet Amru’ul Qais was a member of the princely family of Kinda.

Outside the territory of the powers mentioned above, Arabia in the 6th century was in a state of political chaos. Bahrein, inhabited chiefly by the Bani’Abd Qais and the Bani Bakr, was largely subject to Persian influence near its coast, and a Persian governor, Sebocht, resided in Hajar, its chief town. In Oman the Arabs, who were chiefly engaged in fishing and seafaring, were Azdites mixed with Persians. The ruling dynasty of Julanda in their capital Suhār lasted on till the Abbasid period. No Persian officials are mentioned in this country; whether Persians exercised authority over it is doubtful. On the west coast of Arabia the influence of the kingdom of Yemen was felt in varying degree according to the strength of the rulers of that land. Apart from this influence the Hejaz was simply a collection of cities each with its own government, while outside the cities the various tribes governed themselves and fought continual battles with one another.

Time of Mahomet.—Thus at the time of Mahomet’s advent the country was peopled by various tribes, some more or less settled under the governments of south Arabia, Kinda, Hīra and Ghassān, these in turn depending on Abyssinia, Persia and Rome (i.e. Byzantium); others as in the Hejaz were ruled in smaller communities by members of leading families, while in various parts of the peninsula were wandering Arabs still maintaining the traditions of old family and tribal rule, forming no state, sometimes passing, as suited them, under the influence and protection of one or another of the greater powers. To these may be added a certain number of Jewish tribes and families deriving their origin partly from migrations from Palestine, partly from converts among the Arabs themselves. Mahomet appealed at once to religion and patriotism, or rather created a feeling for both. For Mahomet as a religious teacher and for the details of his career see. It is enough here to outline his actions in so far as he attempted to create a united, and then a conquering, Arabia. Though the external conquests of the Arabs belong more properly to the period of the caliphate, yet they were the natural outcome of the prophet’s ideas. His idea of Arabia for the Arabians could only be realized by summoning the great kings of the surrounding nations to recognize Islam; otherwise Abyssinia, Persia and Rome (Byzantium) would continue their former endeavours to influence and control the affairs of the peninsula. Tradition tells that a few years before his death he did actually send letters to the emperor Heraclius, to the negus of Abyssinia, the king of Persia, and Cyrus, patriarch of Alexandria, the “Mukaukis” of Egypt, summoning them to accept Islam and threatening them with punishment in case of refusal. But the task of carrying out these threats fell to the lot of his successors; the work of the prophet was to be the subjugating and uniting of Arabia. This work, scarcely begun in Mecca, was really started after the migration to Medina by the formation of a party of men—the Muhājirun (Refugees or Emigrants) and the Ansār (Helpers or Defenders)—who accepted Mahomet as their religious leader. As the necessity of overcoming his enemies became urgent, this party became military. A few successes in battle attracted to him men who were interested in fighting and who were willing to accept his religion as a condition of membership of his party, which soon began to assume a national form. Mahomet early found an excuse for attacking the Jews, who were naturally in the way of his schemes. The Bani Nadīr were expelled, the Bani Quraiza slaughtered. By the time he had successfully stormed the rich Jewish town of Khaibar, he had found that it was better to allow industrious Jews to remain in Arabia as payers of tribute than to expel or kill them: this policy he followed afterwards. The capture of Mecca (630) was not only an evidence of his growing power, which induced Arabs throughout the peninsula to join him, but gave him a valuable centre of pilgrimage, in which he was able by a politic adoption of some of the heathen Arabian ceremonies into his own rites to win men over the more easily to his own cause. At his death in 623 Mahomet left Arabia practically unified. It is true that rival prophets were leading rebellions in various parts of Arabia, that the tax-collectors were not always paid, and that the warriors of the land were much distressed for want of work owing to the brotherhood of Arabs proclaimed by Mahomet. The tribes were a seething mass of restlessness, their old feuds ready to break out again. But they had realized that they had common interests. The power of the foreigner in Arabia was broken. Islam promised rich booty for those who fought and won, paradise for those who fell.

Early Caliphs. I. Conquest.—One task of the early caliphs was to find an outlet for the restless fighting spirit. Abu Bekr (632–634), the first of these caliphs, was a man of simple life and profound faith. He understood the intention of Mahomet as to foreign nations, and set himself resolutely to carry it out in the face of much difficulty. Hence as soon as he assumed office he sent out the army already chosen to advance against the Romans in the north. The successful reduction of the rebels in Arabia enabled him in his first year to send his great general Khālid with his Arab warriors first against Persians, then against Romans. His early death prevented him from seeing the fruits of his policy. Under the second caliph Omar (634–644) the Persians were defeated at Kadesiya (Kadessia), and Irak was completely subdued and the new cities of Kufa and Basra were

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 a relation of things measurable by lines or numbers. All proper quantity may be measured by these, and improper quantities must be measured by those that are proper.

There are many things capable of more and less, which perhaps are not capable of mensuration. Tastes, smells, the sensation of heat and cold, beauty, pleasure, all the affections and appetites of the mind, wisdom, folly, and most kinds of probability, with many other things too tedious to enumerate, admit of degrees, but have not yet been reduced to measure, nor, as I apprehend, ever can be. I say, most kinds of probability, because one kind of it, viz., the probability of chances, is properly measurable by number, as is above observed.

Although attempts have been made to apply mathematical reasoning to some of these things, and the quantity of virtue and merit in actions has been measured by simple and compound ratios; yet I do not think that any real knowledge has been struck out this way: it may perhaps, if discreetly used, be a help to discourse on these subjects, by pleasing the imagination, and illustrating what is already known; but until our affections and appetites shall themselves be reduced to quantity, and exact measures of their various degrees be assigned, in vain shall we essay to measure virtue and merit by them. This is only to ring changes upon words, and to make a show of mathematical reasoning, without advancing one step in real knowledge.

Sec. 5. Coroll. 3.
I apprehend the account that hath been given of the nature of proper and improper quantity, may also throw some light upon the controversy about the force of moving bodies, which long exercised the pens of many mathematicians, and, for what I know, is rather dropped than ended; to the no small scandal of mathematics, which hath always boasted of a degree of evidence, inconsistent with debates that can be brought to no issue.

Though philosophers on both sides agree with one another, and with the vulgar in this, That the force of a moving body is the same while its velocity is the same, is increased when its velocity is increased, and diminished when that is diminished. But this vague notion of force, in which both sides agree, though perhaps sufficient for common discourse, yet is not sufficient to make it a subject of mathematical reasoning. In order to that, it must be more accurately defined, and so defined as to give us a measure of it, that we may understand what is meant by a double or a triple force. The ratio of one force to another cannot be perceived but by a measure; and that measure must be settled not by mathematical reasoning, but by a definition. Let any one consider force without relation to any other quantity, and see whether he can conceive one force exactly double to another; I am sure I cannot, nor shall, till I shall be endowed


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70 with a comprehensive doctrine of the nature of humanity, which Spenser undoubtedly meant to enforce through the medium of the imagination; this doctrine, in fact, is the stuff they are made of.

It is not an easy thing to resolve into its moral elements the creations of a poet who blends many strains of truth. His method is not the consecutive process of logical reflection and explication, but the simultaneous embodiment of what, however arrived at, he presents as intuitive, needing only to be seen, to be acknowledged. In the analysis, the distinctive poetic quality is too apt to be dissipated, and the poet is forgotten in the philosopher. Certain broad aspects may be easily made out. Chivalry, with its crowd of faëry knights, certainly rests, in Spenser's great work, upon the old conception of the Christian life as one militant against the enemies of the soul in the world; and quite as clearly he also represents this life as being, within the breast, ideal peace. Peace within and war without: these are two root-ideas out of which the poem flowers on its great double branches. He teaches specifically how to attain self-control, and how to meet attacks from without; or rather how


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Rh to seek those many forms of error which do mischief in the world, and to overcome them for the world's welfare. This is a bald statement, but it indicates well enough in what way Spenser employed the knightly ideal of succor on the one hand, and the Christian ideal of moral perfection on the other, in order to make a poem which should instruct as well as delight the world. He himself asserts that his aim was so lofty, and to a man such as he was a lower aim, a merely artistic purpose, would have been impossible. It is fortunate that he was not less endowed with the sense of loveliness than with a serious mind; for he thus illustrates not only the possible union of the two principal aims of poetry in all times, but also the truth that to a man whose perception of beauty is most perfect the beauty of holiness is the more impressive and authoritative in its commands. Aubrey de Vere devotes himself especially to the declaration and the proof that Spenser's poetic character was essentially that of a man deeply interested in human life, and he tries to prevent the poet's severely ideal, and sometimes fantastic, method from obscuring, as for many minds it does, the real nature of that


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 with some new faculty; for I know nothing of force but by its effects, and therefore can measure it only by its effects. Till force then is defined, and by that definition a measure of it assigned, we fight in the dark about a vague idea, which is not sufficiently determined to be admitted into any mathematical proposition. And when such a definition is given, the controversy will presently be ended.

Sec. 6. Of the Newtonian measure of force.
You say, the force of a body in motion is as its velocity; either you mean to lay this down as a definition as Newton himself has done; or you mean to affirm it as a proposition capable of proof. If you mean to lay it down as a definition, it is no more than if you should say, I call that a double force which gives a double velocity to the same body, a triple force which gives a triple velocity, and so on in proportion. This I entirely agree to; no mathematical definition of force can be given that is more clear and simple, none that is more agreeable to the common use of the word in language. For since all men agree, that the force of the body being the same, the velocity must also be the same; the force being increased or diminished, the velocity must be so also; what can be more natural or proper than to take the velocity for the measure of the force?

Several other things might be advanced to show, that this definition agrees best with the common popular notion of the word force. If two bodies meet directly with a shock, which mutually destroys their motion without producing any other sensible effect, the vulgar would pronounce, without hesitation, that they met with equal force; and so they do, according to the measure of force above laid down: for we find by experience, that in this case their velocities are reciprocally as their quantities of matter. In mechanics, where by a machine two powers or weights are kept in equilibrio, the vulgar would reckon, that these powers act with equal force; and so by this definition they do. The power of gravity being constant and uniform, any one would expect that it should give equal degrees of force to a body in equal times; and so by this definition it does. So that this definition is not only clear and simple, but it agrees best with the use of the word force in common language, and this, I think, is all that can be desired in a definition.

But if you are not satisfied with laying it down as a definition, that the force of a body is as its velocity, but will needs prove it by demonstration or experiment, I must beg of you, before you take one step in the proof, to let me know what you mean by force, and what by a double or a triple force. This you must do by a definition which contains a measure of force. Some primary measure of force must be taken for granted, or laid down by way of definition; otherwise we can never reason about its


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