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which, produced, intersect each other and the axis in o.Since, by hypothesis, these three powers directed to the samepoint are in equilibrio, and the three sides of the triangleabc are at right angles to their directions ; therefore, by a■Well-known statical principle, the intensities of these twopowers are as A b, b c, and c A respectively.

Proposition II.—When an impelling power applied tothe head of an isosceles wedge is in equilibrio with theresisting power of a cleft, the angle of which is more acutethan that of the wedge inserted, then, universally,

The impelling power applied to the head,

The action of the wedge on either side of the cleft,

The part thereof which tends to thrust it forward,

And the remaining part, which tends to tear it asunder,Are

As twice the sine of half the vertical angle of the wedge,The radius,

The sine of the angle contained by the sides of the wedgeand cleft,

And the cosine of that angle, respectively; the same radiusbeing common.

Figure 2. —Let abc represent a vertical section of theWedge and cleft, similar in position to that described in Pro-position I. ; also let the two sides of the cleft d n, D H, beequal, and in contact with the sides of the wedge AC, a c, atequal distances, d c, d c, from the vertex c, in which casetlie sides of the wedge make equal angles with those of thecleft. Through either point d, draw d f, at right angles,and equal to a c ; also through d draw b e, at right angles toH, and complete the parallelogram bbfg. Then, by Pro-position I. the line A A represents in quantity the impellingpower applied to the head, and the line d f represents inquantity and direction the whole action of the side of theWedge on that of the clgft, which, by hypothesis, is balancedby its resistance ; but the power dp is resolved into two,represented in quantity and direction by d g, d e, respec-tively: the one, being in the direction of the cleft, tends tothrust it forward; and the other, being at right angles thereto,tends to tear it asunder,

Therefore the powers mentioned in the Proposition are asA a, d f, d G, and d e, respectively ; but as A c = d f, beingradius, these lines are respectively equal to

Twice the sine of half the vertical angle of the wedge,The radius,

The sine of the angle contained by the sides of the wedgeand cleft,

And the cosine of that angle. Hence the proposition isManifest.

WEIGHT, in mechanics, denotes anything to be raised,sustained, or moved, by a machine, as distinguished from thePower, or that by which the machine is put in motion.

Weight, in commerce, denotes a body of a known weight,appointed by law to be the standard of comparison betweendifferent quantities of merchandise of certain descriptions ;^e weight itself being usually of lead, iron, brass, or other•netal.

The great diversity of weights and measures, in all nations,for different kinds of commodities, has always been a Justs,) bject of regret and complaint ; being the cause of variousdisputes and deceptions, which it is almost impossible to avoid^nder present circumstances. And it is therefore much to bewished, though perhaps little to be expected, that one uni-form system of weights should be adopted as applicable tod}l kinds of substances ; an attempt at which was made inFrance during the revolution, but which was afterwards laidas 'de by an imperial decree, in consequence of the repeatedremonstrances of people in trade ; so difficult is it to overcome

prejudices and customs long established, however advanta-geous the change may be when properly understood.

In the reign of king Richard I. it was ordained, that thereshould be only one weight and one measure throughout Eng-land ; and in the Phil. Trans. No. 458, p. 457, we find anaccount of the analogy between English weights and mea-sures drawn up by Mr. Barlow ; in which he states, thatanciently the cubic foot of water was assumed as a generalstandard for all liquids. This cubic foot, of 62^ lb. multipliedby 32, gives 20001b. the weight of a ton ; and hence 8 cubicfeet of water made a hogshead, and 4 hogsheads a tun, or ton,in capacity and denomination, as well as weight.

Dry measures were raised on the same model. A bushelof wheat, assumed as a general standard for all sorts of grain,also weighed 62^lb. Eight of these bushels make a quar-ter ; and 4 quarters, or 32 bushels, a ton. Coals were like-wise sold by the chaldron, supposed to weigh a ton, or2000 lb., though in reality it probably weighs upwards of3000 lb.

This principle, though not sufficiently accurate in somecases, was extremely obvious, and might have been improvedso as to answer all the purposes of commerce ; but unfor-tunately, instead of rendering it more simple, it has beenmade infinitely more complicated by the different weightssince introduced.

Modern European Weights. —1. English weights. Bythe twenty-seventh chapter of Magna Charta , the weightsall over England are to^te the same ; but for different com-modities tliere are two different sorts, viz. Troy weight andAvoirdupois weight. The origin from which they areboth raised is, a grain of wheat gathered in the middle ofthe ear.

In Troy weight, 24 of these grains make 1 pennyweightsterling ; 20 pennyweights make 1 ounce ; and 12 ounces1 pound.

By this weight we weigh gold, silver, jewels, and liquors.The apothecaries also use the Troy pound, ounce, and grain:but they divide the ounce into 8 drachms, the drachm into3 scruples, and the scruple into 20 grains.

In Avoirdupois weight, the pound contains 16 ounces, butthe ounce is less by near one-twelfth than the Troy ounce ;this latter containing 480 grains, and the former only 437^.The ounce contains 16 drachms ; 80 ounces Avoirdupois areonly equal to 73 ounces Troy; and 17 pounds Troy are equalto 14 pounds Avoirdupois.

By Avoirdupois weight are weighed meat, grocery wares,base metals, wool, tallow, hemp, drugs, bread, &c.

Comparison between Troy and Avoirdupois Weight.

175 Troy pounds are equal to 144 Avoirdupois pounds.

175 Troy ounces are equal to 192 Avoirdupois ounces.

1 Troy pound contains 5760 grains.

1 Avoirdupois pound contains 7000 grains.

1 Avoirdupois ounce contains 437-J grains.

1 Avoirdupois drachm contains 27.84375 grains.

1 Troy pound contains 13 ounces, 2.651428576 drachmsAvoirdupois.

1 Avoirdupois pound contains lib. 2 oz. 11 dwts. 16 gr.Troy.

Therefore the Avoirdupois lb. is to-the lb. Troy as 175 to144, and the Avoirdupois oz. is to the Troy oz. as 437^to 480.

Goldsmiths, jewellers, &c., have a particular class ofweights, viz., for gold and precious stones, the carat andgrain ; and for silver, the pennyweight and grain. In themint, they have also a peculiar subdivision of the Troy grain :thus dividing