Page:Encyclopædia Britannica, Ninth Edition, v. 14.djvu/139

K N I K N 127

KNITTING is the art of forming looped fabrics or tex tures with the use of needles or wires and a single con tinuous thread. Crochet is au analogous art, differing from knitting in the fact that the separate loops are thrown off and finished successively, whereas in knitting the whole series of loops which go to form one length or round of the fabric are retained on one or more needles while a new series is being formed from them on a separate needle. The origin and history of the art of knitting are referred to under the heading HOSIERY, vol. xii. p. 299. The wires, needles, or pins used are of different lengths and gauges, according to the work for which they are intended, and are made either of steel, ivory, bone, or wood. Some are headed, to prevent loops from slipping over their ends, but on these can be woven only flat pieces of work; others are pointed at both ends, and with the use of three or more of these circular webs can be made. The materials used in knitting are specially twisted for the purpose, and consist of twines, threads, cotton, silk, wools, and worsteds, the latter being the most important and largely used substance. Ordinary stockings and socks, which are the staple hand-knit articles, are worked in "lambswool," "fingering," and "wheeling" worsteds respectively, these differing in size and fineness of quality; and for other articles of under clothing and fancy knitting the worsteds most commonly used are "fleecy," "Berlin," and "Lady Betty" wool. Shetland wool is a thin hairy undyed and very tenacious and strong worsted, spun in the Shetland Islands from the wool of the native sheep, and very extensively used in the knitting of fine shawls, veils, scarfs, and small articles by the islanders, among whom the industry is of much local consequence. "Crewels" are closely twisted coloured worsteds of the same size as Shetland wool, and capable consequently of being knit into the same fabric. Much spun silk is also knit into patterns and articles similar in form and appearance to Shetland wool goods. In Ayrshire the hand-knitting of Scotch caps is extensively prosecuted as a domestic industry, the knit work being collected and "waulked" or felted and otherwise finished in factories. The methods by which, with plain knitting, "purling," "slipping" loops, "taking up" and "casting off," &c., materials can be shaped and worked into varied and variegated forms are endless, and patterns and directions for working arc to be found in all magazines and papers devoted to ladies work, as well as in numerous special cheap publications.

Standard works, from which many of the patterns and directions in smaller manuals are copied, are Mrs Gaugain's Knitting and Crochet Work, and Esther Copley's Comprehensive Knitting Book, London, 1849.

KNOLLES, Richard (c. 1545-1610), author of the History of the Turks, was a native of Northamptonshire, and was born about 1545. In 1560 he entered Lincoln's College, Oxford, of which four years later he was elected fellow. After graduating M.A. he left Oxford to become master of the free school at Sandwich in Kent, where he died in 1610.

In 1603 Knolles published A General History of the Turks, a second edition of which appeared in 1610. The work was continued up to date in several editions subsequently published, the best known being that by Sir Paul Rycaut, 1687-1700, who gives a continuation to 1699. The history of Knolles was highly praised by Dr Johnson, and, though now entirely superseded, it has for the time in which it was written considerable merits at least as regards style and arrangement. Knolles also published a translation of Bodin's Respublica in 1606, but the Grammaticæ Latinæ, Græcæ, et Hebraicæ Compendium, and the Rudiments of Hebrew Grammar, attributed to him by Anthony Wood and in most works of reference, were, as is shown in the Athenæum of August 6th, 1881, the works of the Rev. Hanserd Knollys, a Baptist minister.

KNOT. 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 Listing. 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. 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. 1 and 2. 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 has published contains a mere sketch of his investigations.

Fig. 1. Fig. 2. Fig. 3. Fig. 4. Fig. 5.

The most extensive dissertation on the properties of knots is that of Tait (Trans. Roy. Soc. Edin., 1876-7). It was for the most part written in ignorance of the work of Listing, and was suggested by an inquiry concerning vortex atoms (see ATOM). 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. 3 and 4 and their perversions. Knots which can be deformed into their own perversion Tait calls "amphicheiral," 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. 5, in which it will be seen that no one of the three lines is knotted, no