Part 16

_Knotting Yarns_ (fig. 47).--This operation becomes necessary when, a comparatively short piece of junk is to be made into spun-yarn, or large rope into small, which is called twice laid. The end of each yarn is divided, rubbed smooth and married (as for splicing). Two of the divided parts, as _c_, _c_ and _d_, _d_, are passed in opposite directions round all the other parts and knotted. The ends e and f remain passive. The figure is drawn open, but the forks of A and B should be pressed close together, the knot hauled taut and the ends cut off.

[Illustration: FIG. 47.]

[Illustration: FIG. 48.]

_Butt Slings_ (fig. 48).--Made of 4-in. rope, each pair being 26 ft. in length, with an eye spliced in one end, through which the other is rove before being placed over one end of the cask; the rope is then passed round the opposite side of the cask and two half-hitches made with the end, forming another running eye, both of which are beaten down taut as the tackle receives the weight. Slings for smaller casks requiring care should be of this description, though of smaller rope, as the cask cannot possibly slip out. _Bale Slings_ are made by splicing the ends of about 3 fathoms of 3-in. rope together, which then looks like a long strop, similar to the double strop represented in fig. 45--the bights _t_ being placed under the cask or bale and one of the bights _a_, _a_ rove through the other and attached to the whip or tackle.

For a complete treatise on the subject the reader may be referred to _The Book of Knots, being a Complete Treatise on the Art of Cordage, illustrated by 172 Diagrams, showing the Manner of making every Knot, Tie and Splice_, by Tom Bowling (London, 1890).

_Mathematical Theory of Knots._

In the scientific sense a knot is an endless physical line which cannot be deformed into a circle. A physical line is flexible and inextensible, and cannot be cut--so that no lap of it can be drawn through another.

The founder of the theory of knots is undoubtedly Johann Benedict Listing (1808-1882). In his "Vorstudien zur Topologie" (_Göttinger Studien_, 1847), a work in many respects of startling originality, a few pages only are devoted to the subject.[1] He treats knots from the elementary notion of twisting one physical line (or thread) round another, and shows that from the projection of a knot on a surface we can thus obtain a notion of the relative situation of its coils. He distinguishes "reduced" from "reducible" forms, the number of crossings in the reduced knot being the smallest possible. The simplest form of reduced knot is of two species, as in figs. 49 and 50. Listing points out that these are formed, the first by right-handed the second by left-handed twisting. In fact, if three half-twists be given to a long strip of paper, and the ends be then pasted together, the two edges become one line, which is the knot in question. We may free it by slitting the paper along its middle line; and then we have the juggler's trick of putting a knot on an endless unknotted band. One of the above forms cannot be deformed into the other. The one is, in Listing's language, the "perversion" of the other, i.e. its image in a plane mirror. He gives a method of symbolizing reduced knots, but shows that in this method the same knot may, in certain cases, be represented by different symbols. It is clear that the brief notice he published contains a mere sketch of his investigations.

The most extensive dissertation on the properties of knots is that of Peter Guthrie Tait (_Trans. Roy. Soc. Edin._, xxviii. 145, where the substance of a number of papers in the _Proceedings_ of the same society is reproduced). It was for the most part written in ignorance of the work of Listing, and was suggested by an inquiry concerning vortex atoms.

[Illustration: FIG. 49.]

[Illustration: FIG. 50.]

[Illustration: FIG. 51.]

[Illustration: FIG. 52.]

Tait starts with the almost self-evident proposition that, if any plane closed curve have double points only, in passing continuously along the curve from one of these to the same again an even number of double points has been passed through. Hence the crossings may be taken alternately over and under. On this he bases a scheme for the representation of knots of every kind, and employs it to find all the distinct forms of knots which have, in their simplest projections, 3, 4, 5, 6 and 7 crossings only. Their numbers are shown to be 1, 1, 2, 4 and 8. The unique knot of three crossings has been already given as drawn by Listing. The unique knot of four crossings merits a few words, because its properties lead to a very singular conclusion. It can be deformed into any of the four forms--figs. 51 and 52 and their perversions. Knots which can be deformed into their own perversion Tait calls "amphicheiral" (from the Greek [Greek: amphi], on both sides, around, [Greek: cheir], hand), and he has shown that there is at least one knot of this kind for every even number of crossings. He shows also that "links" (in which two endless physical lines are linked together) possess a similar property; and he then points out that there is a third mode of making a complex figure of endless physical lines, without either knotting or linking. This may be called "lacing" or "locking." Its nature is obvious from fig. 53, in which it will be seen that no one of the three lines is knotted, no two are linked, and yet the three are inseparably fastened together.

The rest of Tait's paper deals chiefly with numerical characteristics of knots, such as their "knottiness," "beknottedness" and "knotfulness." He also shows that any knot, however complex, can be fully represented by three closed plane curves, none of which has double points and no two of which intersect. It may be stated here that the notion of beknottedness is founded on a remark of Gauss, who in 1833 considered the problem of the number of inter-linkings of two closed circuits, and expressed it by the electro-dynamic measure of the work required to carry a unit magnetic pole round one of the interlinked curves, while a unit electric current is kept circulating in the other. This original suggestion has been developed at considerable length by Otto Boeddicker (_Erweiterung der Gauss'schen Theorie der Verschlingungen_ (Stuttgart, 1876). This author treats also of the connexion of knots with Riemann's surfaces.

[Illustration: FIG. 53.]

[Illustration: FIG. 54.]

It is to be noticed that, although every knot in which the crossings are alternately over and under is irreducible, the converse is not generally true. This is obvious at once from fig. 54, which is merely the three-crossing knot with a doubled string--what Listing calls "paradromic."

Christian Felix Klein, in the _Mathematische Annalen_, ix. 478, has proved the remarkable proposition that knots cannot exist in space of four dimensions. (P. G. T.)

FOOTNOTE:

[1] See P. G. Tait "On Listing's _Topologie_," _Phil. Mag._, xvii. 30.

KNOUT (from the French transliteration of a Russian word of Scandinavian origin; cf. A.-S. _cnotta_, Eng. knot), the whip used in Russia for flogging criminals and political offenders. It is said to have been introduced under Ivan III. (1462-1505). The knout had different forms. One was a lash of raw hide, 16 in. long, attached to a wooden handle, 9 in. long. The lash ended in a metal ring, to which was attached a second lash as long, ending also in a ring, to which in turn was attached a few inches of hard leather ending in a beak-like hook. Another kind consisted of many thongs of skin plaited and interwoven with wire, ending in loose wired ends, like the cat-o'-nine tails. The victim was tied to a post or on a triangle of wood and stripped, receiving the specified number of strokes on the back. A sentence of 100 or 120 lashes was equivalent to a death sentence; but few lived to receive so many. The executioner was usually a criminal who had to pass through a probation and regular training; being let off his own penalties in return for his services. Peter the Great is traditionally accused of knouting his son Alexis to death, and there is little doubt that the boy was actually beaten till he died, whoever was the executioner. The emperor Nicholas I. abolished the earlier forms of knout and substituted the pleti, a three-thonged lash. Ostensibly the knout has been abolished throughout Russia and reserved for the penal settlements.

KNOWLES, SIR JAMES (1831-1908), English architect and editor, was born in London in 1831, and was educated, with a view to following his father's profession, as an architect at University College and in Italy. His literary tastes also brought him at an early age into the field of authorship. In 1860 he published _The Story of King Arthur_. In 1867 he was introduced to Tennyson, whose house, Aldworth, on Blackdown, he designed; this led to a close friendship, Knowles assisting Tennyson in business matters, and among other things helping to design scenery for _The Cup_, when Irving produced that play in 1880. Knowles became intimate with a number of the most interesting men of the day, and in 1869, with Tennyson's co-operation, he started the Metaphysical Society, the object of which was to attempt some intellectual _rapprochement_ between religion and science by getting the leading representatives of faith and unfaith to meet and exchange views.

The members from first to last were as follows: Dean Stanley, Seeley, Roden Noel, Martineau, W. B. Carpenter, Hinton, Huxley, Pritchard, Hutton, Ward, Bagehot, Froude, Tennyson, Tyndall, Alfred Barry, Lord Arthur Russell, Gladstone, Manning, Knowles, Lord Avebury, Dean Alford, Alex. Grant, Bishop Thirlwall, F. Harrison, Father Dalgairns, Sir G. Grove, Shadworth Hodgson, H. Sidgwick, E. Lushington, Bishop Ellicott, Mark Pattison, duke of Argyll, Ruskin, Robert Lowe, Grant Duff, Greg, A. C. Fraser, Henry Acland, Maurice, Archbishop Thomson, Mozley, Dean Church, Bishop Magee, Croom Robertson, FitzJames Stephen, Sylvester, J. C. Bucknill, Andrew Clark, W. K. Clifford, St George Mivart, M. Boulton, Lord Selborne, John Morley, Leslie Stephen, F. Pollock, Gasquet, C. B. Upton, William Gull, Robert Clarke, A. J. Balfour, James Sully and A. Barratt.

Papers were read and discussed at the various meetings on such subjects as the ultimate grounds of belief in the objective and moral sciences, the immortality of the soul, &c. An interesting description of one of the meetings was given by Magee (then bishop of Peterborough) in a letter of 13th of February 1873:--

"Archbishop Manning in the chair was flanked by two Protestant bishops right and left; on my right was Hutton, editor of the _Spectator_, an Arian; then came Father Dalgairns, a very able Roman Catholic priest; opposite him Lord A. Russell, a Deist; then two Scotch metaphysical writers, Freethinkers; then Knowles, the very broad editor of the _Contemporary_; then, dressed as a layman and looking like a country squire, was Ward, formerly Rev. Ward, and earliest of the perverts to Rome; then Greg, author of _The Creed of Christendom_, a Deist; then Froude, the historian, once a deacon in our Church, now a Deist; then Roden Noel, an actual Atheist and red republican, and looking very like one! Lastly Ruskin, who read a paper on miracles, which we discussed for an hour and a half! Nothing could be calmer, fairer, or even, on the whole, more reverent then the discussion. In my opinion, we, the Christians, had much the best of it. Dalgairns, the priest, was very masterly; Manning, clever and precise and weighty; Froude, very acute, and so was Greg. We only wanted a Jew and a Mahommedan to make our Religious Museum complete" (_Life_, i. 284).

The last meeting of the society was held on 16th May 1880. Huxley said that it died "of too much love"; Tennyson, "because after ten years of strenuous effort no one had succeeded in even defining metaphysics." According to Dean Stanley, "We all meant the same thing if we only knew it." The society formed the nucleus of the distinguished list of contributors who supported Knowles in his capacity as an editor. In 1870 he became editor of the _Contemporary Review_, but left it in 1877 and founded the _Nineteenth Century_ (to the title of which, in 1901, were added the words _And After_). Both periodicals became very influential under him, and formed the type of the new sort of monthly review which came to occupy the place formerly held by the quarterlies. In 1904 he received the honour of knighthood. He died at Brighton on the 13th of February 1908.

KNOWLES, JAMES SHERIDAN (1784-1862), Irish dramatist and actor, was born in Cork, on the 12th of May 1784. His father was the lexicographer, James Knowles (1759-1840), cousin-german of Richard Brinsley Sheridan. The family removed to London in 1793, and at the age of fourteen Knowles published a ballad entitled _The Welsh Harper_, which, set to music, was very popular. The boy's talents secured him the friendship of Hazlitt, who introduced him to Lamb and Coleridge. He served for some time in the Wiltshire and afterwards in the Tower Hamlets militia, leaving the service to become pupil of Dr Robert Willan (1757-1812). He obtained the degree of M.D., and was appointed vaccinator to the Jennerian Society. Although, however, Dr Willan generously offered him a share in his practice, he resolved to forsake medicine for the stage, making his first appearance probably at Bath, and playing Hamlet at the Crow Theatre, Dublin. At Wexford he married, in October 1809, Maria Charteris, an actress from the Edinburgh Theatre. In 1810 he wrote _Leo_, in which Edmund Kean acted with great success; another play, _Brian Boroihme_, written for the Belfast Theatre in the next year, also drew crowded houses, but his earnings were so small that he was obliged to become assistant to his father at the Belfast Academical Institution. In 1817 he removed from Belfast to Glasgow, where, besides conducting a flourishing school, he continued to write for the stage. His first important success was _Caius Gracchus_, produced at Belfast in 1815; and his _Virginius_, written for Edmund Kean, was first performed in 1820 at Covent Garden. In _William Tell_ (1825) Macready found one of his favourite parts. His best-known play, _The Hunchback_, was produced at Covent Garden in 1832; _The Wife_ was brought out at the same theatre in 1833; and _The Love Chase_ in 1837. In his later years he forsook the stage for the pulpit, and as a Baptist preacher attracted large audiences at Exeter Hall and elsewhere. He published two polemical works--the _Rock of Rome_ and the _Idol Demolished by its own Priests_--in both of which he combated the special doctrines of the Roman Catholic Church. Knowles was for some years in the receipt of an annual pension of £200, bestowed by Sir Robert Peel. He died at Torquay on the 30th of November 1862.

A full list of the works of Knowles and of the various notices of him will be found in the _Life_ (1872), privately printed by his son, Richard Brinsley Knowles (1820-1882), who was well known as a journalist.

KNOW NOTHING (or AMERICAN) PARTY, in United States history, a political party of great importance in the decade before 1860. Its principle was political proscription of naturalized citizens and of Roman Catholics. Distrust of alien immigrants, because of presumptive attachment to European institutions, has always been more or less widely diffused, and race antagonisms have been recurrently of political moment; while anti-Catholic sentiment went back to colonial sectarianism. These were the elements of the political "nativism"--i.e. hostility to foreign influence in politics--of 1830-1860. In these years Irish immigration became increasingly preponderant; and that of Catholics was even more so. The geographical segregation and the clannishness of foreign voters in the cities gave them a power that Whigs and Democrats alike (the latter more successfully) strove to control, to the great aggravation of naturalization and election frauds. "No one can deny that ignorant foreign suffrage had grown to be an evil of immense proportions" (J. F. Rhodes). In labour disputes, political feuds and social clannishness, the alien elements--especially the Irish and German--displayed their power, and at times gave offence by their hostile criticism of American institutions.[1] In immigration centres like Boston, Philadelphia and New York, the Catholic Church, very largely foreign in membership and proclaiming a foreign allegiance of disputed extent, was really "the symbol and strength of foreign influence" (Scisco); many regarded it as a transplanted foreign institution, un-American in organization and ideas.[2] Thus it became involved in politics. The decade 1830-1840 was marked by anti-Catholic (anti-Irish) riots in various cities and by party organization of nativists in many places in local elections. Thus arose the American-Republican (later the Native-American) Party, whose national career begun practically in 1845, and which in Louisiana in 1841 first received a state organization. New York City in 1844 and Boston in 1845 were carried by the nativists, but their success was due to Whig support, which was not continued,[3] and the national organization was by 1847--in which year it endorsed the Whig nominee for the presidency--practically dead. Though some Whig leaders had strong nativist leanings, and though the party secured a few representatives in Congress, it accomplished little at this time in national politics. In the early 'fifties nativism was revivified by an unparalleled inflow of aliens. Catholics, moreover, had combated the Native-Americans defiantly. In 1852 both Whigs and Democrats were forced to defend their presidential nominees against charges of anti-Catholic sentiment. In 1853-1854 there was a wide-spread "anti-popery" propaganda and riots against Catholics in various cities. Meanwhile the Know Nothing Party had sprung from nativist secret societies, whose relations remain obscure.[4] Its organization was secret; and hence its name--for a member, when interrogated, always answered that he knew nothing about it. Selecting candidates secretly from among those nominated by the other parties, and giving them no public endorsement, the Know Nothings, as soon as they gained the balance of power, could shatter at will Whig and Democratic calculations. Their power was evident by 1852--from which time, accordingly, "Know Nothingism" is most properly dated. The charges they brought against naturalization abuses were only too well founded; and those against election frauds not less so--though, unfortunately, the Know Nothings themselves followed scandalous election methods in some cities. The proposed proscription of the foreign-born knew no exceptions: many wished never to concede to them all the rights of natives, nor to their children unless educated in the public schools. As for Catholics, the real animus of Know Nothingism was against _political_ Romanism; therefore, secondarily, against papal allegiance and episcopal church administration (in place of administration by lay trustees, as was earlier common practice in the United States); and, primarily, against public aid to Catholic schools, and the alleged greed (i.e. the power and success) of the Irish in politics. The times were propitious for the success of an aggressive third party; for the Whigs were broken by the death of Clay and Webster and the crushing defeat of 1852, and both the Whig and Democratic parties were disintegrating on the slavery issue. But the Know Nothings lacked aggression. In entering national politics the party abandoned its mysteries, without making compensatory gains; when it was compelled to publish a platform of principles, factions arose in its ranks; moreover, to draw recruits the faster from Whigs and Democrats, it "straddled" the slavery question, and this, although a temporary success, ultimately meant ruin. In 1854, however, Know Nothing gains were remarkable.[5] Thereafter the organization spread like wildfire in the South, in which section there were almost no aliens, and the Whig dissolution was far advanced. The Virginia election of May 1855 proved conclusively, however, that Know Nothingism was no stronger against the Democrats than was the Whig party it had absorbed; it was the same organization under a new name. In the North it was even clearer that slavery must be faced. Know Nothing evasion probably helped the South,[6] but neither Republicans nor Democrats would endure the evasion; Douglas and Seward, and later (1855-1856) their parties, denounced it. In the North-West the Know Nothings were swept into the anti-slavery movement in 1854 without retaining their organization. In the state campaigns of 1855 professions were measured to the latitude. The national platform of 1856 (adopted by a secret grand council), besides including anti-alien and anti-Catholic planks, offered sops to the North, the South and the "doughfaces" on the slavery issue. Millard Fillmore was nominated for the presidency. The anti-slavery delegates of eight Northern states bolted the convention, and eight months later the Republican wave swept the Know Nothings out of the North.[7] The national field being thus lost, the state councils became supreme, and local opportunism fostered variation and weakness. By 1859 the party was confined almost entirely to the border states. The Constitutional Union--the "Do Nothing"--Party of 1860 was mainly composed of Know Nothing remnants.[8] The year 1860 practically marked, also, the disappearance of the party as a local power.[9]

Except in city politics nativism had no vitality; in state and national politics it really had no excuse. Race antipathies gave it local cohesive power in the North; various causes, already mentioned, advanced it in the South; and as a device to win offices it was of wide-spread attraction. Its only real contribution to government was the proof that nativism is not Americanism. Public opinion has never accepted its estimate of the alien nor of Catholic citizens. Some of its anti-Church principles, however--as the non-support of denominational schools--have been generally accepted; others--as the refusal to exclude the (Protestant) Bible from public schools--have been generally rejected; others--as the taxation of all Church property--remain disputed.

See L. D. Scisco, _Political Nativism in New York State_ (doctoral thesis, Columbia University, New York, 1901); L. F. Schmeckebier, _Know Nothing Party in Maryland_ (Johns Hopkins University, Baltimore, 1899); G. H. Haynes, "A Know Nothing Legislature" (Mass., 1855), in _American Historical Assoc. Report_, pt. 1 (1896); J. B. McMaster, _With the Fathers_, including "The Riotous Career of the Know Nothings" (New York, 1896); H. F. Desmond, _The Know Nothing Party_ (Washington, 1905).

FOOTNOTES:

[1] E.g. for some extraordinary "reform" programmes among German immigrants see Schmeckebier (as below), pp. 48-50.

[2] "The actual offence of the Catholic Church was its non-conformity to American methods of church administration and popular education" (Scisco).

[3] The Whigs bargained aid in New York city for "American" support in the state, and charged that the latter was not given. Millard Fillmore attributed the Whig loss of the state (see LIBERTY PARTY) to the disaffection of Catholic Whigs angered by the alliance with the nativists.

[4] The Order of United Americans and the Order of the Star Spangled Banner, established in New York respectively in 1845 and 1850, were the most important sources of its membership.

[5] This year "American Party" became the official name. Its strength in Congress was almost thirty-fold that of 1852. It elected governors, legislatures, or both, in four New England states, and in Maryland, Kentucky and California; minor officers elsewhere; and almost won six Southern states.

[6] For it delayed anti-slavery organization in the North, and presumably discouraged immigration, which was a source of strength to the North rather than to the South.

[7] They carried only Maryland. The popular vote in the North was under one-seventh, in the South above three-sevenths, of the total vote cast.

[8] Note the presidential vote. Seward's loss of the Republican nomination was partly due to Know Nothing hostility.

[9] Its firmest hold was in Maryland. Its rule in Baltimore (1854-1860) was marked by disgraceful riots and abuses.