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is a thing as certain as it is wonderful. He had contrived for his own use a commodious notation for any large numbers, which he could express on his abacus, or calculat ing table, and with which he could readily perform any arithmetical operations, by the sense of feeling only, for which reason it was called his Palpable Arithmetic.

His calculating table was a smooth thin board, a little more than a foot square, raised upon a small frame, so as to lie hollow, which board was divided into a great number of little squares, by lines intersecting one another perpendicularly, and parallel to the sides of the table, and the parallel ones only one-tenth of an inch from each other; so that every square inch of the table was thus divided into 100 little squares. At every point of intersection the board was perforated by small holes, capable of receiving a pin; for it was by the help of pins stuck up to the head through these holes, that he expressed his numbers. He used two sorts of pins, a large and a smaller sort; at least their heads were different, and might easily be distinguished by feeling. Of these pins he had a large quantity in two boxes, with their points cut off, which always stood ready before him when he calculated. The writer of that account describes particularly the whole process of using the machine, and concludes; "He could place and displace his pins with incredible nimbleness and facility, much to the pleasure and surprise of all the beholders. He could even break off in the middle of a calculation, and resume it when he pleased, and could presently know the condition of it, by only drawing his fingers gently over the table."

SAURURUS, in botany, a genus of the Heptandria Trigynia class and order. Natural order of Piperita. Naiades, Jussieu. Essential character: calyx an ament with one-flowered scales; corolla none; germs four; berries four, one seeded. There is but one species; viz. S. cernuus, lizard's tail, a native of North America.

SAUVAGESIA, in botany, so named in honour of Francois Boissier de Sauvages, professor at Montpellier, a genus of the Pentandria Monogynia class and order. Natural order of Gruinales. Essential character: calyx five-leaved; corolla fivepetalled, fringed; nectary five-leaved, alternate with the petals; capsule one-celled. There is but one species; viz. S. erecta, a native of St. Domingo, Martinico, Jamaica, Surinam, and Guiana.

SAW, an instrument which serves to cut into pieces several solid matters, as wood, stone, ivory, &c. The best saws are of tempered steel ground bright and smooth: those of iron are only hammer-hardened: hence, the first, besides their being stiffer, are likewise found smoother than the last. They are known to be well hammered by the stiff bending of the blade; and to be well and evenly ground, by their bending equally in a bow. The edge in which are the teeth is always thicker than the back, because the back is to follow the edge. The teeth are cut and sharpened with a triangu lar tile, the blade of the saw being first fixed in a whetting block. After they have been filed the teeth are set, that is, turned out of the right line, that they may make the fis sure the wider, that the back may follow the better. The teeth are always set ranker for coarse cheap stuff than for hard and fine, because the ranker the teeth are set the more stuff is lost in the kerf. The saws by which marble and other stones are cut have no teeth: these are generally very large, and are stretched out and held even by a frame. The workmen who make the greatest use of the saw, are the sawyers, carpenters, joiners, cabinet-makers, ebonists, stone-cutters, carvers, sculptors, &c. The lapidaries too have their saw, as well as the workers in mosaic; but these bear little resemblance to the common saw. But of all mechanics, none have so many saws as the joiners; the chief are as follows: the pit saw, which is a large two-handed saw, used to saw timber in pits; this is chiefly used by the sawyers. The whip-saw, which is also two-handed, used in sawing such large pieces of stuff as the hand-saw will not easily reach. The hand-saw, which is made for a single man's use, of which there are various kinds; as the bow or frame saw, which is furnished with cheeks: by the twisted cords which pass from the upper parts of these cheeks, and the tongue in the middle of them, the upper ends are drawn closer together, and the lower set further apart. The tenon-saw, which being very thin, has a back to keep it from bending. The compass-saw, which is very small, and its teeth usually not set: its use is to cut a round, or any other com. pass-kerf: hence the edge is made broad and the back thin, that it may have a compass to turn in.

The surgeons also use a saw to cut off bones; this should be very small and light, in order to be managed with the greater ease and freedom, the blade exceedingly fine,

and the teeth exquisitely sharpened, to make its way more gently, and yet with great expedition, in cutting off legs, arms, &c. Saws are now generally used by butchers in separating the bones of the meat; the divisions by the saw are neater than those by the chopper, and there is a certain saving, as the chopper splinters bones, the parts of which cannot be included in the weight. SAWING, dividing timber, &c. by the application of a saw, either by the hand or mill. The mechanism of a sawing-mill may be reduced to three principal things, the first, that the saw be drawn up and down as long as is necessary, by a motion communicated by water to the wheel: the second, that the piece of timber to be cut into boards be advanced by an uniform motion to receive the strokes of the saw; for here the wood is to meet the saw, and not the saw to follow the wood, therefore the motion of the wood and that of the saw ought immediately to depend the one on the other: the third, that when the saw has cut through the whole length of the piece, the machine stops of itself, and remains immoveable; for fear, lest having no obstacle to surmount, the force of the water, or steam, should turn the wheel with too great rapidity, and break some part of the machine.

In Plate Saw-mill are drawings of a circular saw-mill, used by Mr. George Smart, at his manufactory for hollow-made masts, Westminster Bridge. Fig. 1 is an elevation of the machine; fig. 2, a plan; and fig. 3 and 4, the saw shown separately.

The machine is turned by a horse-wheel, which gives motion to a pinion on a hori zontal shaft; a spur wheel is fixed on this shaft, and turns a pinion on another horizontal shaft, on which the wheel A, (fig. 1) is fixed: this wheel is in the room over the machine, and the bearings for the gudgeons of the shaft are supported on the joists, B, of the floor: by means of an endless strap passing round this wheel, and also round a pulley, N, on the spindle of the circular saw, a rapid motion is given to the saw, which is made of well-tempered steel plate (fig. 8), with teeth on its edge: it is fixed on its spindle, D, (fig. 4) by a shoulder, d, against which it is held by another move. able shoulder, e, pressed against the other by a nut, k, on the end of the spindle which is tapped into a screw to receive it. The saw has a a circular hole through the middle, fitting tight upon the spindle, and a small fillet fitting into the notch, a, (fig. 3) causes them to turn together.

The ends of the spindle are pointed, and that point nearest the saw works in a hole made in the end of a serew screwed in a bench, EFGH, (fig. 1 and 2) made of stout planks, and well braced together; the other turns in a similar screw screwed through a cross beam, K, morticed between two vertical beams, LL, extending from the floor to the ceiling: the cross beam, K, can be raised or lowered in its mortices through the beams, L, by wedges put both above and below its tenons. In order to adjust the plane of the saw perpendicular to the plane of the bench, M M, is a long pa rallel ruler, which can be set at any distance from the saw, and fixed by screws going through circular grooves, g g, cut through the bench. In using the machine, the ruler, M M, is to be set the proper distance from the saw of the piece of wood to be cut, and as the saw turns round, a workman slides the end of a piece of wood to it, keeping its edge against the guide, M M, that it may cut straight.

When the saw requires sharpening, one of the screws at the end of its spindle must be turned back: the spindle and saw can be then removed; and by taking off the nut, k, the saw will be loose, and may be fixed in a common vice to whet it, in the same manner as a common saw: the teeth of the saw are set, that is, bent out of the plane of the saw, one tooth on one side, the next on the other: the outsides, r, (in fig. 3) of the teeth are not filed to leave a surface perpendicular to the plane of the saw, but inclined to it, and in the same direction that each tooth so filed is bent in the setting: by this means the saw, when cutting, first takes away the wood at the two sides of the kerf, leaving an angular ridge in the middle of it, the use of which is to keep the saw steady in a right line, that it may not have so much tendency to get out of the straight in any place where the wood is harder at one side than on the other.

In early periods, the trunks of trees were split with wedges into as many and as thin pieces as possible, and if it were necessary to have them still thinner, they were hewn on both sides to the proper size. This simple and wasteful manner of making boards has been still continued in some places to the present time. Peter the Great of Russia endeavoured to put a stop to it, by forbidding hewn deals to be transported on the river Neva. The saw, however, though so convenient and beneficial, has not been able to banish entirely the

practice of splitting timber used in building, or in making furniture and utensils, for we do not speak here of fire-wood; and, indeed, it must be allowed that this method is attended with peculiar advantages, which that of sawing can never possess. The woodsplitters perform their work more expeditiously than sawyers, and split timber is much stronger than that which has been sawn; for the fissure follows the grain of the wood, and leaves it whole; whereas the saw, which proceeds in the line chalked out for it, divides the fibres, and by these means lessens its cohesion and solidity. · Split timber, indeed, turns out often crooked and warped; but in many purposes to which it is applied this is not prejudicial; and these faults may sometimes be amended. As the fibres, however, retain their natural length and direction, thin boards, particularly, can be bent much better. This is a great advantage in making pipe-staves, or sieve frames, which require still more art, and in forming various implements of the like kind.

The most beneficial and ingenious improvement of this instrument was, without doubt, the invention of saw-mills, which are driven either by water or by the wind. Mills of the first kind were erected so early as the fourth century, in Germany, on the small river Roeur or Ruer: for though Ansonius speaks properly of water-mills for cutting stone, and not timber, it cannot be doubted that these were invented later than mills for manufacturing deals, or that both kinds were erected at the same time. The art, however, of cutting marble with a saw is very old. Pliny conjectures that it was invented at Caria; at least he knew no building incrusted with marble of greater antiquity than the palace of king Mausolus, at Halicarnassus. This edifice is celebrated by Vitruvius for the beauty of its marble; and Pliny gives an account of the different kinds of sand used for cutting it; for it is the sand properly, says he, and not the saw, which produces that effect. The lat ter presses down the former, and rubs it against the marble; and the coarser the sand is, the longer will be the time required to polish the marble which has been cut by it. Stones of the soap-rock kind, which are indeed softer than marble, and which would require less force than wood, were sawn at that period: but it appears that the far harder glassy kinds of stone were sawn then also; for we are told of the discovery of a building which was encrusted with cut agate, corne

lian, lapis lazuli, and amethysts. We have, however, found no account in any of the Greek or Roman writers of a mill for sawing wood; and as the writers of modern times speak of saw-mills as new and uncommon, it would seem that the oldest construction of them has been forgotten, or that some important improvement has made them appear entirely new.

Becher, in his history of inventions, says that saw-mills were invented in the 17th century. In this he erred, for when the infant Henry sent settlers to the island of Madeira, which was discovered in 1420, and caused European fruits of every kind to be carried thither; he ordered saw-mills to be erected also, for the purpose of sawing into deals the various species of excellent timber with which the island abounded, and which were afterwards transported to Portugal. About the year 1427, the City of Breslau had a saw-mill, which produced a yearly rent of three marks; and in 1490, the magistrates of Erfurt purchased a forest in which they caused a saw-mill to be erect. ed, and they rented another mill in the neighbourhood besides.

Norway, which is covered with forests, had the first saw-mill about the year 1530. This mode of manufacturing timber was called the new art; and because the expor tation of deals was by these means increased, that circumstance gave occasion to the deal-tythe, introduced by Christian III. in the year 1545. Soon after the celebrated Henry Canzau caused the first mill of this kind to be built in Holstein. In 1552 there was a saw-mill at Joachimsthal, which, as we are tord, belonged to Jacob Geusen, mathematician. In the year 1555, the bishop of Ely, ambassador from Mary queen of England to the court of Rome, having seen a saw-mill in the neighbourhood of Lyons, the writer of his travels thought it worthy of a particular description. In the sixteenth century, how. ever, there were mills with different sawblades, by which a plank could be cut into several deals at the same time. The first saw-mill was erected in Holland at Saardam, in the year 1596; and the invention of it is ascribed to Cornelius Cornelissen. Perhaps he was the first person who built a saw mill at that place, which is a village of great trade, and has still a great many sawmills, though the number of them is becoming daily less; for within the last half century a hundred have been given up. The first mill of this kind in Sweden was erected

in the year 1653. At present, that king dom possesses the largest perhaps ever constructed in Europe, where a water-wheel, twelve feet broad, drives at the same time seventy-two saws.

In England saw-mills had at first the same fate that printing had in Turkey, the ribbon-loom in the dominious of the church, and the crane at Strasburgh. When at tempts were made to introduce them, they were violently opposed, because it was apprehended that the sawyers would be deprived by them of their means of getting a subsistance. For this reason, it was found necessary to abandon a saw-mill erected by a Dutchman near London, in 1663; and in the year 1700, when one Houghton laid before the nation the advantages of such a mill, he expressed his apprehension that it might excite the rage of the populace. What he dreaded was actually the case in 1767 or 1768, when an opulent timber-merchant, by the desire and approbation of the Society of Arts, caused a saw-mill, driven by wind, to be erected at Limehouse, under the direction of James Stanfield, who had learned, in Holland and Norway, the art of constructing and managing machines of that kind. A mob assembled, and pulled the mill to pieces; but the damage was made good by the nation, and some of the rioters were punished. A new mill was afterwards erected, which was suffered to work without molestation, and which gave occasion to the erection of others. It appears, however, that this was not the only mill of the kind then in Britain; for one driven also by wind had been built at Leith, in Scotland, some years before.

SAXIFRAGA, in botany, saxifrage, a genus of the Decandria Digynia class and order. Natural order of Succulentæ. Saxifragæ, Jussieu. Essential character: calyx five-parted, five-petalled; capsule two-beak ed, one-celled, many-seeded. There are fifty species; of these we shall notice the S. granulata, or white saxifrage, which grows naturally in the meadows in many parts of England. The roots of this plant are like grains of corn, of a reddish colour without: there is a variety of this with double flowers, which is very ornamental. The leaves are tongue-shaped, gathered into heads, rounded at their points, and have cartilaginous and sawed borders. The stalk rises two feet and a half high, branching out near the ground, forming a natural pyramid to the top. The flowers have five white wedge shaped petals, and ten stamina,

placed circularly the length of the tube, terminated by roundish purple summits. When these plants are strong, they produce very large pyramids of flowers. S. umbrosa, commonly called London pride, or none-so-pretty, grows naturally on the Alps, and also in great plenty on a mountain of Ireland, called Mangerton, in the county of Kerry, in that island. The roots of this are perennial. S. oppositifolia grows naturally on the Alps, Pyrenees, and Helvetian mountains: it is also found pretty plentifully growing upon Ingleborough hill, in Yorkshire; Snowdon, in Wales, and some other places. It is a perennial plant, with stalks trailing upon the ground. The flowers are produced at the end of the branches, of a deep blue.

SCABIOSA, in botany, scabious, a genus of the Tetrandria Monogynia class and order. Natural order of Aggregatæ. Dip. sacea, Jussieu. Essential character: ca. lyx common, many-leaved; proper double superior; receptacle chaffy. There are forty-three species. S. arvensis, or meadow scabious, grows naturally in many places of Britain. The flowers are produced upon naked footstalks at the ends of the branches; they are of a purple colour, and have a faint odour. S. succisa, or devil's bit, grows in woods and moist places. This has a short tap-root, the end of which appears as if it was bitten or cut off, whence the plant has taken its name.

SCABRIDE, in botany, the name of the fifty-third order in Linnæus Fragments of a Natural Method, consisting of plants with rough leaves. Among these are the ficus and morus, which yield by incision a milky juice. Another genus is the cannabis, or hemp, from the leaves of which, in the East Indies, an intoxicating liquor is prepared, and from the seeds is drawn an oil useful for lamps.

SCEVOLA, in botany, a genus of the Pentandria Monogynia class and order. Natural order of Campanulaceæ, Jussieu. Essential character: corolla one-petalled, with the tube cloven longitudinally, the border five-cleft and lateral; drupe inferior, containing one two-celled nut. There are three species, natives of the East In dies.

SCHÆFFERA, in botany, a genus of the Dioecia Tetrandria class and order. Essential character: male, calyx four or five-leaved; corolla four-petalled, or none: female, calyx four or five-parted; corolla four-parted, or none; berry two-celled;

seeds solitary. There are two species, viz. S. completa, and S. lateriflora, natives of the West Indies.

SCALE, a mathematical instrument, consisting of several lines drawn on wood, brass, silver, &c. and variously divided, according to the purposes it is intended to serve; whence it acquires various denominations, as the plain scale, diagonal scale, plotting scale, Gunter's scale, &c. See MATHEMATICAL INSTRUMENTS.

SCALE, diagonal, is projected thus: first draw eleven parallel lines at equal distances, the whole length of which being divided into a certain number of equal parts, according to the length of the scale, by perpendicular parallels, let the first division be again subdivided into ten equal parts, both above and below; then drawing the oblique lines from the first perpendicular below to the first subdivision above, and from the first subdivision below to the second subdivision above, &c. the first space shall there. by be exactly divided into one hundred equal parts; for as each of these subdivisions is one tenth part of the whole first space or division, so each parallel above it is one tenth of such subdivision, and consequently one hundredth part of the whole first space; and if there be ten of the larger divisions, one thousandth part of the whole scale. If therefore the larger divisions be accounted units, the first subdivisions will be tenth parts of an unit; and the second subdivisions, marked by the diagonals on the parallels, hundredth parts of an unit.

Again, if the larger divisions be reckoned tens, the first subdivisions will be units, and the second subdivisions tenth parts and if the larger divisions be accounted hundredths, the first subdivisions will be tens, and the second units: and

so on.

SCALE, Gunter's, an instrument, so called from Mr. Gunter, its inventor, is gene. rally made of box: there are two sorts, the long Gunter and the sliding Gunter, having both the same lines, but differently used, the former with the compasses, the latter by sliding. The lines now generally delineated on those instruments are the following, viz. a line of numbers, of sines, tangents, versed sines, sine of the rhumb, tangent of the rhumb, meridional parts, and equal parts; which are constructed after the following manner :

The line of numbers is no other than the logarithmic scale of proportionals, wherein the distance between each division is equal

to the number of mean proportionals contained between the two terms, in such parts as the distance between 1 and 10 is 1000, &c. equal the logarithm of that number. Hence it follows, that if the number of equal parts expressed by the logarithm of any number be taken from the same scale of equal parts, and set off from 1 on the line of numbers, the division will represent the number answering to that logarithm. Thus, if you take .954, &c. (the logarithms of 9) of the same parts, and set it off from 1 towards 10, you will have the division standing against the number 9. In like manner, if you set off .903, &c. .845, &c. .778, &c. (the logarithms of 8, 7, 6) of the same equal parts from 1 towards 10, you will have the divisions answering to the numbers 8, 7, 6. After the same manner may the whole line be constructed.

The line of numbers being thus constructed, if the numbers answering to the natural sines and tangents of any arch, in such parts as the radius is 10,000, &c. be found upon the line of numbers, right against them will stand the respective divisions answering to the respective arches, or which is the same thing, if the distance between the centre and that division of the line of numbers, which expresses the num ber answering to the natural sine or tangent of any arch, be set off on its respective line from its centre towards the left hand, it will give the point answering to the sine or tangent of that arch: thus the natural sine of 30 degrees being 5,000, &c. if the distance between the centre of the line of numbers (which in this case is equal to 10,000, &c. equal the radius) and the division, on the same line representing 5000, &c. be set off from the centre, or 90 degrees, on the line of sines, towards the left hand, it will give the point answering to the sine of 30 degrees. And after the same manner may the whole line of sines, tangents, and versed sines be divided.

The line of sines, tangents, and versed sines being thus constructed, the line sine of the rhumb, and tangent of the rhumb are easily divided; for if the degrees and minutes answering to the angle which every rhumb makes with the meridian, be transferred from its respective line to that which is to be divided, we shall have the several points required: thus if the distance be tween the radius or centre, and sine of 45 degrees equals the fourth rhumb, be set off upon the line sine of the rhumb, we shall have the point answering to the sine of the

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