Part 16

_Double Strop_ (fig. 45).--Made with one piece of rope, the splice being brought as usual to the crown of the block _t_, the bights fitting into scores some inches apart, converging to the upper part, above which the thimble receives the bights _a_, _a_; and the four parts of the strop are secured at _s_, _s_ by a round seizing doubly crossed. If the block be not then on the right slew (the shell horizontal or vertical) a union thimble is used with another strop, which produces the desired effect; thus the fore and main brace-blocks, being very large and thin, are required (for appearance) to lie horizontally; a single strop round the yard vertically has a union thimble between it and the double strop round the block. The double strop is used for large blocks; it gives more support to the shell than the single strop and admits of smaller rope being used. Wire rope is much used for block-strops; the fitting is similar. Metal blocks are also used in fixed positions; durability is their chief recommendation. Great care should be taken that they do not chafe the ropes which pass by them as well as those which reeve through.

_Selvagee Strop._--Twine, rope-yarn or rope is warped round two or more pegs placed at the desired distance apart, till it assumes the requisite size and strength; the two ends are then knotted or spliced. Temporary firm seizings are applied in several places to bind the parts together before the rope or twine is removed from the pegs, after which it is marled with suitable material. A large strop should be warped round four or six pegs in order to give it the shape in which it is to be used. This description of strop is much stronger and more supple than rope of similar size. Twine strops (covered with duck) are used for boats' blocks and in similar places requiring neatness. Rope-yarn and spun-yarn strops are used for attaching luff-tackles to shrouds and for many similar purposes. To bring to a shroud or hawser, the centre of the strop is passed round the rope and each part crossed three or four times before hooking the "luff"; a spun-yarn stop above the centre will prevent slipping and is very necessary with wire rope. As an instance of a large selvagee block-strop being used--when the "Melville" was hove down at Chusan (China), the main-purchase-block was double stropped with a selvagee containing 28 parts of 3-in. rope; that would produce 112 parts in the neck, equal to a breaking strain of 280 tons, which is more than four parts of a 19-in cable. The estimated strain it bore was 80 tons.

_Stoppers_ for ordinary running ropes are made by splicing a piece of rope to a bolt or to a hook and thimble, unlaying 3 or 4 ft., tapering it by cutting away some of the yarns, and marling it down securely, with a good whipping also on the end. It is used by taking a half-hitch round the rope which is to be hauled upon, dogging the end up in the lay and holding it by hand. The rope can come through it when hauled, but cannot go back.

_Whipping and Pointing._--The end of every working rope should at least be whipped to prevent it fagging out; in ships of war and yachts they are invariably pointed. Whipping is done by placing the end of a piece of twine or knittle-stuff on a rope about an inch from the end, taking three or four turns taut over it (working towards the end); the twine is then laid on the rope again lengthways contrary to the first, leaving a slack bight of twine; and taut turns are repeatedly passed round the rope, over the first end and over the bight, till there are in all six to ten turns; then haul the bight taut through between the turns and cut it close. To point a rope, place a good whipping a few inches from the end, according to size; open out the end entirely; select all the outer yarns and twist them into knittles either singly or two or three together; scrape down and taper the central part, marling it firmly. Turn every alternate knittle and secure the remainder down by a turn of twine or a smooth yarn hitched close up, which acts as the weft in weaving. The knittles are then reversed and another turn of the weft taken, and this is continued till far enough to look well. At the last turn the ends of the knittles which are laid back are led forward over and under the weft and hauled through tightly, making it present a circle of small bights, level with which the core is cut off smoothly. Hawsers and large ropes have a becket formed in their ends during the process of pointing. A piece of 1 to 1½ in. rope about 1½ to 2 ft. long is spliced into the core by each end while it is open: from four to seven yarns (equal to a strand) are taken at a time and twisted up; open the ends of the becket only sufficient to marry them close in; turn in the twisted yarns between the strands (as splicing) three times, and stop it above and below. Both ends are treated alike; when the pointing is completed a loop a few inches in length will protrude from the end of the rope, which is very useful for reeving it. A hauling line or reeving line should only be rove through the becket as a fair lead. _Grafting_ is very similar to pointing, and frequently done the whole length of a rope, as a side-rope. Pieces of white line more than double the length of the rope, sufficient in number to encircle it, are made up in hanks called foxes; the centre of each is made fast by twine and the weaving process continued as in pointing. Block-strops are sometimes so covered; but, as it causes decay, a small wove mat which can be taken off occasionally is preferable.

_Sheep-Shank_ (fig. 46).--Formed by making a long bight in a topgallant back-stay, or any rope which it is desirable to shorten, and taking a half-hitch near each bend, as at _a_, _a_. Rope-yarn stops at _b_, _b_ are desirable to keep it in place till the strain is brought on it. Wire rope cannot be so treated, and it is injurious to hemp rope that is large and stiff.

_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.

_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.

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.

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.