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17, ) be a prominent beam, fixed horizontally at the end C, as in awall; and if a weight, proportional to the length of the beam, bedispersed uniformly on all parts of the beam. The stress at anypoint F, will be as DF 2 , the square of the distance from the extre-mity.

Cor. I. Hence the stress at F, by any weight suspended at D,will be double the stress at the same point F, when the sameweight presses uniformly on all the parts between F and I).

Cor. 2. The stress at the end BC, by the weight P, is the sameas the stress upon the middle of a beam of twice the length DC,w ith twice the weight P laid on its middle ; this beam being sup-ported at both ends.

Prop. 3. If there be two beams AC , uc, (fig. IS, 19,)standing aslope, and bearing two weights upon them, either in themiddle, or in any given situation, or equally diffused over the'whole length of the beams: the stress upon them will be directlyas the weights, and the lengths, and the cosines of elevation.

Cor. 1. If the weights and length of the beams be the same, thestress w ill be as the cosine of elevation, and therefore greatest whenit lies horizontal.

Cor. 2. If the beams lie horizontal, or at any equal inclinations,and the weight be as the length, then the stress is as the square ofthe length.

Cor. 3. If the weights are equal on the horizontal beam AB, (fig.

18, ) and the inclined one AC : and BC be perp. to AB: then thestress will be equal upon both.

Cor. 4. But if the weights on the same beams be: as their lengths;then the stress will also be as their lengths, AB and AC .

Car. 5. And universally, the stress upon any point of a slopingbeam, is as the rectangle of the segments, and the weight and cosineof inclination directly, and the length of the beam reciprocally.

Prop. 4. if any beam of timber be to support anv weight, orforce acting laterally upon it; the breadth multiplied by thesquare of the depth, or in similar sections, the cube of Mie diame-ter, in everyplace, ought to be proportional to the length multi-plied by the weight or force acting on it; or as the stress in thatplace, and the same is true of several different pieces of timbercompared together.

Cor. 1. If AEB, (fig. 20,) be a prominent beam fixed at the endAE, and sustaining a weight at the other end B. And if the sec-tions in all places be similar figures; and CD be the diameter inany place C ; then CB will be every where as CD 1 . And if ACBbe a right line, EDB will be a cubic parabola. Therefore two-fifths of such a beam may be cut away without any diminution ofthe strength. But if the beam be bounded by two parallel planes,perpendicular to the horizon; then CB will be as CD 2 , and thenEDB will be the common parabola, whence a third part of abeam may be thus cut away.

Cor. 2. But if a weight press uniformly on every part of AB ;and the sections in all points as C, be similar; then BC 2 ,will be every where as CD 3 ; and EDB a semicubical parabola.But if the bearfi be bounded by parallel planes, perpendicular tothe horizon ; then BC, (fig. 21,) will be as CD, and EDB a rightline; here half a beam may be cut away, without losing anystrength.

TIME, a succession of phenomena in the universe, or a modeof duration marked by certain periods or measures, chiefly by themotion and revolution of the sun. The general idea which timegives in every thing to which it is applied, is that of limited dura-tion. Thns we cannot say of the Deity , that he exists in time;because eternity, whicli lie inhabits, is absolutely uniform, neitheradmitting limitation nor succession. See Metaphysics. Timeis distinguished into absolute and relative. Absolute time, istime considered in itself, and without any relation to bodies, ortheir motions. This flows equally, i. e. never proceeds faster orSlower, but glides on in a constant"equable tenor. Relative time, iis the sensible measure of any duration by means of motion.

1 ime, Astronomical , is that taken purely from the motion ofthe heavenly bodies, without any other regard.

'I ime, Civil, is the former time accommodated to civil uses,and form-'' -and distinguished into years, months, days, &:c.

Time, in music, is an affection of sound, by which it is said tobe long or short, with regard to its continuance in the same toneor degree of tune. Musical tune is distinguished into common orduple time, and triple time. See M osic.

Time-keepers, in a general sense, denote instruments adaptedfor measuring time. See Chronometer . In a more peculiarand definite sense, time-keeper is a term first applied by Mr.John Harrison to his watches constructed for determining fhe lon-gitude at sea, and for which he received, at different times, theparliamentary reward of 20,000 1. Several other artists have sincereceived also considerable sums for their improvements of time-keepers, as Arnold, Mudge, &c. See Longitude . This ap-pellation is now become common among artists, to distinguehsuch watches as are made with extraordinary care and accuracyfor nautical or astronomical observations. The principles of Mr.Harrison ’s time-keeper, as they were communicated by himself tothe commissioners appointed to receive and publish the same inthe year 1,65, are as follow ; “ In this time-keeper there is thegreatest care taken to avoid friction, as much as can he, by thewheels moving on small pivots, and in ruby-holes, and high num-bers in the wheels and pinions. The part which measures timegoes but the eighth-part of a minute without winding up ; so thatpart is very simple, as this winding up is performed at the wheelnext to the balance-wheel, by which means there is always anequal force acting at that wheel, ami all the rest of the work hasno more to do in the measuring of time than the person that windsup once a day. There is a spring in the inside of the fusee, whichi will call a secondary main-spring. This spring is always keptstretched to a certain tension by the main-spring; and during thetime of winding up the lime-keeper, at whicli time the main-springis not suffered to act, this secondary spring supplies its place. Incommon watches, in genera), the wheels have about one-third thedominion over the balance that (he balance-spring has; that is, ifthe power which the balance-spring has over the balance is calledthree, that from the wheel is one; but in this time-keeper thewheels have only about one-eightieth part of the power over thebalance that the balance-spring has; and it must be allowed, theless the wheels have to do with the balance the belter. Thewheels in a common wateli having this great dominion over thebalance, they can, when the watch is wound up, and the balanceat rest, set the watch a going; but when my time-keepci’s balanceis at rest, and the spring is wound up, the force of the wheels canno more set it a going than the wheels of a common regulatorcan, when the weight is wound up, set the pendulum a vibrating;nor will the iorce from the wheels move the balance when at rest,to a greater angle in proportion to the vibration that it is to fetch,than the force of the wheels of a common regulator can move thependulum from the perpendicular, when it is at rest. My time-keeper's balance is more Ilian three times the weight of a large-sized common watch-balance, and three times its diameter; and acommon watch-baiance goes through about six inches of space in asecond, but mine goes through about twenty-four inches in thattime : so that had my time-keeper only these advantages overa common watch, a good performance might be expected from it.But my time-keeper is not affected by the different degrees ofheat and cold, nor agitation of the ship; and the force from thewheels is applied to the balance in such a manner, together withthe shape of the balance-spring, and, if 1 may be allowed the term,an artificial cvcloid, which acts at this spring ; so that from thesecontrivances, let the balance vibrate more or less, all its vibrationsare performed in the same time ; and therefore if it goes at all, itmust go true. So that it is plain from this, that such a time-keeper goes entirely from principle, and not from chance.” AVeiiui-t refer those who may desire to see a minute account of theconstruction of Mr. Harrison ’s time-keeper, to the publication byorder of the commissioners of longitude.

TIM FRYCOTTA, a town ami fortress in (lie Decan of Ilin-doostan, in the province of (Jolconda, 04 miles S. E. of Hydra-bad, and 95 W. Masulipatain. Lon. 79. 26. E. Lat. 15.20. N.

'FIMON, the Sceptic, was a Pldiasian, a disciple of Pyrrho ,and lived in the time of Ptolemy Philadelphus. He toolc littlepains to invite disciples to his school. lie was fond of rural re-tirement ; and was much addicted to wine. The fragments of hissatirical poem Silli, are in the Poesis Pliilosopliica of Stephens.Timou lived to tiie age of 90.

TIN, a metal known to the ancients; the Phoenicians procuredit from Spain and Britain , w ith winch nations they carried on avery extensive and lucrative commerce. This metal has a fi» e

white