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port the principal Rafters of the Roof. No Houfe has lefs than two of thefe Sea ms, viz. one at each Head: Into thefe the Girders of the Garret-Floor are alio framed ; and, if the Building be Timber, the Teazle Tenons of the Polls. The Proportions of Beams near London, are fix'd by Statute, as follows: A Beam 15 Foot long, mult be feven Inches on one fide its Square, and five on the other ; If it be 16 Foot long,one fide mull be eight Inches,the other fix : If 17 Foot long, one fide mull be 10 Inches, the other fix : In the Country they ufually make 'em ftronger. Sir H. Wotton advifes thefe to be of the ftrongeft and molt durable Timber. Herrera tells us, that in Fer. Cortc-zs Palace, hi Mexico, there were 7000 Beams of Cedar: But he mutt certainly ufe the Word Seam in a greater^ Lati- tude than what we do. In effect, the French, under Poutrc, 'Beam, take in not only the Pieces which fupport the Raf- ters, but alfo thole which fuftain the Joilfs for the Cielings. Some of their belt Authors have confider'd the Force or Strength of Seams, and brought their Refinance to a pre- eife Calculation 5 particularly M. F'ar/gjion, and M.'Parciit-y the Syftem of the latter is as follows.

When, in a Beam breaking Parallel to its Bafe, which is fuppoied to be a Parallelogram, two Plans of Fibres, which were before contiguous, are feparated, there is nothing to be confider'd in thofc Fibres, but their Number, Bigneis, Tenfion before they broke, and the Lever by which they act; all thefe together making the Refinance of the Bca?n to be broke. Suppofe then another Beam of the fame Wood, where the Bale is Iikcwife a Parallelogram, and of any Bignefs, with regard to the other, at Pleafure ; the Height of each of thefe, when laid Horizontal, being divided into an indefinite Number of equal Parts, and their Breadth into the fame Number, in each of their Bafes will be found an equal Number of little quadrangular Cells, pro- portional to the Bafes whereof they are Parts : Thefe then will reprefent ljttle Bafes, or which is the fame thing, the Thickneffes of the Fibres to be feparated for the Fracture of each "Beam ; and fince the Number of Cells is equal in each, the Ratio of the Bafes of both Beams will be that of the Refiftance of their Fibres, both with regard to Num- ber and Thicknels. Now, the two Beams being fuppoied of the fame Wood, the Fibres, the molt remote from the Points of Support, which arc thofc which break the firft, muft be equally ftretch'd when they break. Thus the Fi- bres, v.g. of the 10th Divifion, are equally ftretch'd in each Cafe, when the firfl: breaks ; and in whatever Pro- portion the Tenfion be fuppoied, 'twill ftill be the fame in both Cafes ; fb that the Doctrine is entirely free, and un- imbarrafs'd with any Syftem of Phyficks. Laftly, 'tis evi- dent the Levers whereby the Fibres of the two Beams aft, are reprefented by the Height of their Bafes ; and of Con- sequence, the whole Refinance of each Beam is the Pro- duct of its Bafe by its Height ; or, which is the fame thing, the Square of the Height multiplied by the Breadth : Which holds, not only in cafe of Parallclogram- matick, but alfo of Eiliptick Bafes.

Hence, if the Bafes of twoBeams be equal, tho both their Heights and Breadths be unequal, their Refinance will be as the Heights alone 5 and by Confequence, one and the fame Beam laid on the fmalleft fide of its Bafe, will refill more than when laid flat, in proportion as the firft Situa- tion gives it a greater Height than the fecond : and thus an Eiliptick Bafe will rcfift more, when laid on its greateft Axis, than on its fmalleft.

Since in Beams equally long, 'tis the Bafes that deter- mine the Proportion of their Weights or Solidities; and fince their Bafes being equal, their Heights may be diffe- rent, two Beams of the fame Weight may have Refif- ftances differing to Infinity : Thus, if in the one the Height of the Bale be conceiv'd infinitely great, and the Breadth infinitely fmall, while in the other the Dimenfions of the Bafe are finite; the Rcfiftan.ee of the firfl will be infinite- ly greater than that of the fecond, tho their Solidity and Weight be the fame. If therefore all required in Architec- ture were to have Beams, capable of fupporting vait Loads, and at the fame time have the leaft Weights poflible, 'tis plain they muft be cut thin as Laths, and laid edge-wife.

If the Bales of the two Beams be fuppos'd unequal, but the Sum of the Sides of the two Bafes equal, -v. g. if they be either 12 and 12, or 11 and 13, or 10 and 14, &c. fo that they always make 24; and further, if they be fup- pos'd to be laid edge-wife ; purfuing the Series, it will ap- pear, that in the Beam of 12 and 12 the Refinance will he 1728, and the Solidity or Weight 144; and that in the lafr, or 1 and 23, the Refinance will be 529, and the Weight 23 : The firft therefore, which is fquare, will have lefs than half the Strength of the laft, with regard to its Weight. Hence M. Parent remarks, that the common Practice of cutting the Beams out of Trees as fquare as poflible, is ill Husbandry : He hence takes occafion to deter- mine geometrically, what Dimenfions the Bafe of a Beam, to b* cut out of any Tree propos'd, /hall have, in order tg

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its having the grcateft poflible Refiftancc ; -or, which is the fame thing, a Circular Bafe being given, he determines the Rectangle of the greateft Refinance that can be inferibed, and finds that the Side's muft be nearly as 7 to. 5, which agrees with Obfervation.

Hitherto the Length of the Beams has been fuppofed e- qual; if it be unequal, the Bafes will refill: fo much the lefs, as the j9(-,!7;;zj- are longer. To this it may be added, that a Beam fuftained at each End, breaking by a Weight fuipended from its middle, does not only break at the mid- dle, but alfo at each Extreme ; or, if it does not actually break there, at leaft immediately before the Moment of the Fracture, which is that of the ^Equilibrium between the Refinance and the Weight, its Fibres are as much ftretch'd at the Extremes us in the Middle : So that of the Weight iuftain'd by the middle there is but one third Part which acts at the middle, to make the Fracture; the other two only acting to induce a Fracture in the two Extremes. A Beam may either be fuppofed loaden only with its own Weight, or with other foreign Weights applied at any dis- tance, or only with thofe foreign Weights ; fince according to M. Parent the Weight ot^Bcam is not ordinarily above yl- part of the Load given it to fuftain, 'tis evident that in considering fcveral Weights they muft be all reduced by the common Rules to one common Centre of Gravity. M. Parent has calculated Tables of the Weights that will be fuftained by the middle, in Beams of various Bafes and Lengths, fitted at. each End into Walls, on a Suppofition that a Piece of Oak of an Inch fquare and a Foot long, retain'd horizontally by the two Extremes, will fuftain 315 lib. in its middle before it breaks, which 'tis found by Ex- perience it will. Sec Mem. French Academy, An. 1708.

Beam-Comi- asses, an Inftrument made in Wood or Brafs, with Hiding Sockets, or Curfors, ferving to carry fe- vcral fluffing Points, in order 10 draw and divide Circles with very long Radii. They are of ufe in large Projections for drawing the Furniture, on Wall-Dials, He. See Com- passes.

Beam-Filling in Building, the filling up the vacant Space between the Raifon and Roof, with Stones, or Bricks, laid between the Rafters on the Raifon, and plaifter'd on with Loom ; frequent where the Garrets are not pargeted, or plaifter'd.

Beam, among Hunters, that Part of the Head of a Deer, which bears the Antlers, Royals, and Tops; the little Streaks wherein are called Circles. From the Saxon Beam, a Tree; becaufc they grow out of the Head, as Branches out of a Tree. .

Beams or" a Ship are the large, main, crois Timbers, which hold the Sides of a Ship from falling together, and which alfo fupport the Decks and Orlops. The main Beam is next the Main-Maft; and from it they are reckoned by Firft, Second, and Third. The great Beam of all is called the Midjbip-Beam..

BEAR, in Aftronomy, a Name given to two Conftella- tions; called the Greater and the Le (fer Bear ; or Urfa- Major, and Minor • The Pole-Star is faid to be in the Tail of the Lejfcr ; becaufe that Star is never above two De- grees diftant from the North-Pole of the World. Sec Ursa Major £f? Minor.

Bear is alfo a Term ufed in Heraldry : Thus, he than hath a Coat of Arms, is faid to bear in it the feveral Charges or Ordinaries which are in his Efcutcheon ; as, if there are three Lions Rampant in it, he is faid to bear three Lions Rampant. See Charge, &c.

At Sea, when a Ship fails towards the Shore, Ibe is faid to bear in -ivith the Land ; when a Ship that was to Wind- ward comes under another Ship's Stern, and fo gives her the Wind, fhc is faid to bear under her Lee ; if a Ship fails into an Harbour with the Wind large, or before the Wind, flic is faid to bear in ivith the Harbour, &c. In Conding they fay, bear tip the Helm, that is, let the Ship go more large before the Wind; and b ear up round, that is, let the Ship go between her two Sheets, directly before the Wind. There is Hkewife another Ufe of the Word, in reference to the Burden of a Ship, (which Word is derived from hence ; ) for, they fay a Ship bears, when having too Ilen- dcr a Quarter fhe will fink too deep into the Water wirfi an over-light Freight, and thereby can carry but a fmall Quantity of Goods.

BEARD. See Hair, and Tonsure.

Beard of a Comet, the Rays which the Comet emits towards that part of the Heavens to which its proper Mo- tion feems to direct it ; in which the Beard of- the Comet is diftinguifhed from xkeTail, which is underftood of the Rays emitted towards that part whence its Motion feems to carry it. 'Tis called Beard, from fome fancied Refcnl- blancc it bears to the Beard of a Man. See Comet.

BEARER, in Architeaure, a Poft, or Brick- WaN, trim- med up between the two Ends of a Piece of Timber to /horten its Bearing, or to prevent its bearing with the whole Weight a,t the Ends only,

B b Bearsr.