113 



FLEXURE, CONTRARY. 



FLOOR-CLOTH. 



114 



hardness than an independent property of matter. If iron, steel, 

 brass, and copper, be heated and suddenly cooled in cold water, they 

 become brittle, but if after being heated they are buried in hot 

 sand, and allowed to cool slowly, they lose their brittleness and 

 become flexible. 



The deflexions of beams or bars in vertical and in horizontal positions, 

 when strained by weights, will be noticed under MATERIALS, STRENGTH 

 OF ; and the employment of the fibres of hemp and of iron or copper 

 wire in the formation of ropes will be explained under ROPES. Ropes 

 made of metal are said to be even more flexible than those made of 

 hemp, the capabilities of suspending weights being equal, and the 

 former being, of course, less in circumference than the latter. 



The mathematical theory for the vibrations which may take place in 

 a thread which is perfectly flexible, when small forces are applied to all 

 its points ; and the investigation of formula: for determining the 

 position and velocities of the points at the end of a given time, may be 

 seen in Poisson's ' Traitd de M&anique,' No. 482, &c., edit. 1833. 



FLEXURE, CONTRARY. A point of contrary flexure in a curve 

 is that at which the branch of the curve ceases to present convexity to 

 a straight line without it, and begins to present concavity, or vice 

 versa. [CuuvE.] But when a straight line passes throut/h a point of 

 contrary flexure, the curve presents either convexity on both sides or 

 concavity on both sides. 



The algebraical test of a point of contrary flexure is a change of 

 sign in the second differential coefficient of either of the two, abscissa 

 or ordinate, with respect to the other. It is frequently stated, in 

 works on the differential calculus, that the sole test of such a point is 



-J-T.= O, where x and y are the abscissa and ordinate. This is not 



correct ; the above equation may be true when there is no contrary 

 flexure, and there may be contrary flexures when the above is not true. 



(Fy 

 It is necessary and sufficient for a point of contrary flexure that ^p 



should change its sign, which cannot be except when it is nothing or 

 infinite. Examine therefore all the roots of the two equations, 



<Py 

 5 = 



and 



= 



dx> 



IMT 



and such of them as are accompanied by change of sign give points of 

 contrary flexure. 



For instance, let the equation of the curve be 



y = 3i- 20z 4 +50z J - 

 <% 



then jT3= when z = 1 and when z = 2 : but there is only a point of 



contrary flexure when z = 2, for when z = 1 there is no change of 

 sign. 



FLEXURE OF COLUMNS. [MATERIALS, STRENGTH OF.] 

 FLIBUSTIER. [BUCCANEERS J 

 FLINT-GLASS. [GLASS.] 



FLINTS, LIQUOR OF, is a solution of flint or silica in the alkali 

 potash ; it U prepared by fusing together a mixture of four parts of 

 hydrate of potash and one part of powdered flint or fine sand. When 

 a part of the fluid compound is poured out of the crucible, crystals are 

 formed in the residual portion, which, according to Berzelius, are com- 

 posed of one equivalent of each of its constituents. This compound, 

 sometimes called silicate of potash, silica being regarded as an acid, is 

 soluble in water, and when sulphuric, nitric, or other powerful acids 

 are added to it, hydrate of silica is precipitated. 

 FLOOR. [AXCHOB.] 



FLOOR-CLOTH is made partly of hemp and partly of flax, the former 

 being the cheaper of the two, but the latter better fitted to retain the 

 oil and paint on the surface. As a means of avoiding the necessity for 

 seams of joinings in the cloth, looms are constructed expressly for the 

 weaving of the canvas, of the greatest width likely to be required. As 

 brought to the floor-cloth factories, the pieces of canvas have generally 

 one of three scales of dimensions : 100 yards long by 6 wide, 108 yards 

 by 7, 113 yards by 8. The flax and hemp are spun, and the canvas 

 woven, almost entirely in Scotland, chiefly at Dundee ; and the degree 

 of fineness is generally such as to present about 16 or 18 threads to the 

 linear inch. 



The canvas, throughout the subsequent operations, retains the same 

 width as was given to it in the loom ; but it is cut into pieces varying 

 from 60 to 100 feet long : each of these pieces has to be stretched over 

 a frame in a vertical position ; and in most of the factories there is a 

 large number of such frames, some 100 feet long by 18 or 20 high, 

 others 60 feet long by 24 high. As a means of transferring the canvas 

 to these frames, it is, when the bales are opened, cut to the proper 

 length, laid down on the floor of a large room, and coiled round a long 

 wooden roller about 5 inches in diameter ; this roller is then lifted up 

 vertically and removed close to the frame ; one edge of the canvas is 

 nailed or hooked to one edge of the frame, and the roller is made to 

 travel onwards and to revolve in such a manner as to give off the can- 

 vas as fast as the latter can be hooked to the upper horizontal bar of 



ARTS AND SCI. DIV. VOL. IV. 



the frame ; when all is uncoiled and the canvas hooked on all four of 

 its edges, the sides of the frame are so drawn by winches and levers as 

 to stretch the canvas to a degree of tightness nearly equal to that of a 

 drum, notwithstanding the extent of the surface (from 1500 to 1800 

 square feet). Here the canvas remains many weeks, during most of 

 the processes. 



Before the imprinting of the pattern which forms the most con- 

 spicuous feature in floor-cloth, the surface of the canvas requires a 

 great deal of preparation, to render it smooth and durable. The pat- 

 tern is applied on one surface only ; but both surfaces are painted and 

 prepared, the back before the front. A wash of melted size is applied 

 by means of a brush to each surface ; and, while this is yet wet, tho 

 surface is well rubbed with a flat piece of pumice-stone, whereby the 

 little irregularities of the canvas are worn down, and a foundation is 

 laid for the oil and colour afterwards to be applied. To work over so 

 large an extent of surface, the workmen are provided with narrow 

 scaffoldings, built up in front of, but not in contact with, the surface 

 of the canvas : one scaffold being in front and another behind the 

 canvas. 



When the size-preparation is dried, the painting begins. The paint 

 employed consists of the same mineral colours as those used in house- 

 painting, and, like them, mixed with linseed oil ; but it is much 

 thicker or stiffer in consistence, and has very little turpentine added to 

 it. The first layer of paint is applied with a trowel ; or rather, the 

 paint is dabbed on in large masses here and there, by means of a brush, 

 and then levelled and spread by means of a kind of trowel 12 or 14 

 inches in length. Ten or twelve days are required for this thick 

 coating to dry ; and at the expiration of this time a second coating is 

 laid on, thinner than the former, and applied with a brush instead of a 

 trowel. These two layers of paint are all which the back or hinder 

 surface of the canvas receives ; but the front or face receives a greater 

 thickness, and undergoes a greater number of processes. For instance, 

 after the sizing, the surface is rubbed down with pumice-stone ; then 

 comes the trowel-colour, followed by a second rubbing with pumice ; 

 and then two, three, or more layers of colour, applied with a brush, 

 each coating being followed by a rubbing with pumice before the next 

 one is applied. The surface has by this time acquired a great degree 

 of smoothness, and the general substance suppleness and pliability. 



The prepared canvas is next removed from its vertical position in 

 the frame, and wrapped round a roller, which is so placed as to allow 

 the canvas to be uncoiled and spread out on a table to be printed. 

 The printing of floor-cloth is conducted much on the same principle 

 as that of paper-hangings for rooms. [PAPER-HANGINGS.] Both are 

 examples of colour-printing ; that is, the successive application of two 

 or more blocks or engraved surfaces, each one giving a different part 

 of the device from the others, and being supplied with paint of a 

 different colour. In the infancy of this art the pattern was given by 

 means of stencil-plates; thin plates of metal or of pasteboard were pierced 

 with holes at the parts intended to form the pattern, and the paint was 

 so applied as to fall through these holes upon the surface of the canvas 

 spread out beneath. It was about a century ago that the use of wood 

 blocks superseded that of stencil-plates for this purpose. The first 

 block so employed was about 15 inches square, and had a simple device 

 of zigzag lines cut upon its surface ; when this was pressed face down- 

 wards on a cushion coated with wet paint, it took up a layer on all the 

 raised parts of the device, and was then in a fit state to impart its 

 impress to the canvas. The increased complexity arising from the 

 employment of several colours was a feature of later introduction. 



As at present conducted, the printing of floor-cloth with several 

 colours requires much care on the part of the designer before the 

 painter enters on his department. In the first place, the device is 

 carefully drawn on the full scale on a stiff sheet of paper, and is 

 coloured fully in every part according to the exact appearance which it 

 is intended to present on the canvas. A second piece of paper is 

 placed under this, and with a pin or pricker a series of holes is made 

 through both papers, following the outlines of the pattern so far as 

 regards one colour, which we may suppose to be green ; another blank 

 paper is placed under the pattern in lieu of the former, and the out- 

 lines of another coloured portion of the device are marked through 

 both papers with the pricker ; and so on as many times as there are 

 colours, the outline of each colour being transferred to a paper distinct 

 from the others. An equal number of blocks of wood are then pre- 

 pared ; these consist of two thicknesses of white deal and one of pear- 

 tree wood, ranged at right angles with respect to the grain, to prevent 

 warping ; they are about fifteen inches square, by two and a half in 

 thickness, and the pear-tree surface is the one on which the engraving 

 U to be executed. One of the pricked papers is laid down on a 

 prepared block, and a little bag containing pounce or pounded charcoal 

 is daubed all over it ; the powder enters the pin-holes, and leaves upon 

 the surface of the wood a series of dots sufficient to guide the carver 

 in working out the design, which he does by cutting away all the 

 surface except where the lines of device are marked. All the other 

 blocks are treated in the same way ; and it is easy to see that each 

 one is left uncut at those parts which are cut away in all the others, 

 so as to avoid confusion of colours. 



The blocks (which we will suppose to be four for one pattern, red, 

 yellow, blue, and green) being ready, and the prepared canvas spread 

 out on a flat table, the printing commences. The paint (say red) is 



