mathematics, such as have relation to length only; such is a number which represents one side of a plain figure. If the plain figure be a square, the linear figure is called a root.

Linear Problem; that which may be solved geometrically by the intersection of two right lines. This is called a simple problem, and is capable but of one solution.

Linens, in commerce, a well-known kind of cloth chiefly made of flax. The linen manufacture was probably introduced into Britain with the first settlements of the Romans. The flax was certainly first planted by that nation in the British soil. The plant itself indeed appears to have been originally a native of the east. The woollen drapery would naturally be prior in its origin to the linen; and the fibrous plants from which the threads of the latter are produced, seems to have been first noticed and worked by the inhabitants of Egypt. In Egypt, indeed, the linen manufacture appears to have been very early: for even in Joseph's time it had risen to a considerable height. From the Egyptians the knowledge of it proceeded probably to the Greeks, and from them to the Romans. Even at this day the flax is imported among us from the Eastern nations; the western kind being merely a degenerate species of it.

In order to succeed in the linen manufacture, one set of people should be confined to the ploughing and preparing the soil, sowing and covering the seed, to the weeding, pulling, rippling, and taking care of the new seed, and watering and dressing the flax till it is lodged at home: others should be concerned in the drying, breaking, scutching, and heckling the flax, to fit it for the spinners; and others in spinning and reeling it, to fit it for the weaver; others should be concerned in taking due care of the weaving, bleaching, heeling, and finishing the cloth for the market. It is reasonable to believe, that if these several branches of the manufacture were carried on by distinct dealers in Scotland and Ireland, where our home-made linens are manufactured, the several parts would be better executed, and the whole would be afforded cheaper, and with greater profit.

Staining of Linen. Linen receives a black colour with much more difficulty than woollen or cotton. The black streak on linen with common vitriol and galls, or logwood, is very perishable, and soon washes out. Instead of the vitriol, a solution of iron in four strong beer is to be made use of. This is well known to all the calico-printers; and by the use of this, which they call their iron liquor, and madder-root, are the blacks and purples made which we see on the common printed linens. The method of making this iron-liquor is as follows: A quantity of iron is put into the four strong beers, and, to promote the dissolution of the metal, the whole is occasionally well stirred, the liquor occasionally drawn off, and the rust beat from the iron, after which the liquor is poured on again. A length of time is required to make the impregnation perfect; the solution being reckoned unfit for use till it has stood at least a twelvemonth. This solution stains the linen of a yellow, and different shades of buff colour; and is the only known substance by which these colours can be fixed on linen. The cloth stained deep with the iron liquor, and afterwards boiled with madder, without any other addition, becomes of the dark colour which we see on printed linens and cottons; which, if not a perfect black, has a very near resemblance to it. Others are stained paler with the same liquor diluted with water, and come out purple.