WED 



long, including their narrow bafe, pointed, ferrated, triple- 

 ribbed, light green, roughifh. Flowers yellow, llalked, 

 much fmaller than the foregoing. Calyx broad, extend- 

 ing far beyond the rays. Seeds of the marginal Jlorets 

 large, tumid, each crowned with four, five, or more, irre- 

 gularly placed tubercles, or teeth, not agreeing precifely 

 with the crown of the firft fpecies, but fcarcely affording 

 fufficient reafon to form a generic diftinftion. 



WEDENSCHWEIL, in Geography, a town of Swit- 

 zerland, and principal place of a bailiwick, in the canton of 

 Zurich, on the S.W. coafl of lake Zurich ; 9 miles S. of 

 Zurich. 



WEDGE, CuNEUS, in Mechanics, the laft of the five 

 powers, or fimple machines. 



The wedge is a triangular prifm, whofe bafes are ifofceles 

 acute-angled triangles. 



Authors are divided about the priaciple whence the wedge 

 derives its power. 



Ariftotle confiders it as two levers of the firft kind, in- 

 clined toward each other, and afting oppofite ways. Guido 

 Ubaldus, Merfennus, &c. will have them levers of the fe- 

 cond kind. But Fr. de Lanis fhews, that the wedge can- 

 not be reduced to any lever at all. 



Others refer the wedge to the inclined plane. Others, 

 agam, with De Stair, deny the wedge to have fcarce any 

 force at .ill ; and afcribe much the greateft part to the mal- 

 let that drives it. 



Its doftrine (according to fome writers) is contained in 

 this propofition. " If a power be applied to a wedge, in 

 fuch manner, as that the line of direction C D {Plate XL. 

 Mechanics, fg. 1 . ) perpendicular to A B, is to the refift- 

 ance to be overcome, as A B to C D ; the power will be 

 equal to the refillance." 



Or thus : " If the power direftly applied to the head of 

 the wedge, be to the refiftance to be overcome by the wedge, 

 as the thicknefs of the wedge is to its height ; then the 

 power will be equivalent to its refiftance ; and, if increafed, 

 will overcome it." 



In proof of this propofition, they allege, that the firm- 

 nefs by which the parts of the obftacle, fuppofe wood, ad- 

 here to one another, is .the refiftance to be overcome by the 

 wedge ; and that while the wedge is driven into the wood, 

 the way or length it has gone is B H {Jig. 2.) ; and D C 

 is the way or length gone in the fame time, by the impedi- 

 ment ; that is, the parts C and D of the wood are fo far 

 divided afunder : and according as the wedge is driven down 

 farther and farther along its height ; fo the parts C and D 

 of the wood are divided mere and more, along the thicknefs 

 of the wedge. 



But Dr. Defaguliers has proved, that, when the refiftance 

 afts perpendicularly againft the fides of the wedge, the 

 power is to the whole refiftance as the length of both fides 

 of the wedge, taken together, is to the thicknefs of its 

 back. 



According to the preceding theory, if the thicknefs of 

 the wedge (that is, the way of the impediment, and confe- 

 quently its velocity) be to the height of the wedge (that is, 

 tne way, and confequently the velocity of the power) as 

 the power to the impediment, or refiftance ; then the mo- 

 mentum of the power, and the impediment, will be equal 

 the one to the other : and confequently the power, being in- 

 creafed, will overcome the refiftance. 



Hence, I. The power equivalent to half the refiftance, is 

 to it as A C to D G, {Jig. i.) that is, as the whole fine 

 to the co-tangent of hjilf the angle of the wedge ADC. 

 And 2. As the tangent of a lefs angle is lefs than that of a 

 greater, the power rauft have a greater proportion to half 



01 



WED 



the refiftance, if the angle be greater than if lefs ; confe- 

 quently, the acuter the wedge is, the more does it increafe 

 the power. 



The above proportion is adopted by Wallis, (Op. Math, 

 vol. i. p. 1016.) Keil, (Int. ad Ver. Phyf.) and S'Grave- 

 fande (El. Math. lib. i. cap. 14.); but S'Gravefande, in his 

 Scholium de ligno findendo (ubi fupra), obfcrves, that when 

 the parts of the wood are feparated before the wedge, the 

 force by which it is thruft in is to the refiftance of the wood 

 as a line, drawn from a point in the middle of the bafe to 

 the fide of the wedge, and at right angles with the fide of 

 the feparated wood continued, to the height of the wedge; 

 but when the parts of the wood are feparated no farther 

 than the wedge is driven in, the equihbrium will be, when 

 the power is to the refiftance as the half bafe of the wedge 

 to its fide. 



To this method of eftimating the power of the wedge it 

 has been objefted that, by allowing each part of the weight 

 to have moved through a fpace equal to half the back of the 

 wedge, whilft the power has moved through its height, and 

 the whole weight to have moved through a fpace equal to 

 the whole back, the whole is made to move farther than its 

 parts. 



M. Mufchenbroeck ftates the proportion of the power to 

 the weight in a fimple wedge, or half the wedge {Jig. I.) 

 bifefting it by a plane pafling through C D, as its back is 

 to its length, or in that cafe as A C to C D ; and in a dou- 

 ble wedge or the wedge A B D, as A B to 2 C D. Int. 

 ad Phil. vol. i. p. 132. 



Mr. Fergufon eitimates the power of the wedge, in the 

 two cafes mentioned by S'Gravefande, in the following man- 

 ner. When the wood does not cleave at any diftance before 

 the wedge, there will be an equilibrium (he fays) between 

 the power impelling the wedge downward, and the refiftance! 

 of the wood afting againft the two fides of the wedge, if the 

 power be to the refiftance as half the thicknefs of the wedge 

 at its back is to the length of either of its fides ; and if 

 the power be increafed fo as to overcome the friAion of the 

 wedge, and the refiftance arifing from the cohefion or ftick- 

 age of the wood, the wedge will be drove in, and the wood 

 fplit afunder. 



But when the wood cleaves at any diftance before the 

 wedge (as it generally does), the power impelling the wedge 

 will be to the refiftance of the wood as half its thicknefs is 

 to the length of either fide of the cleft, eftimated from the 

 top or afting part of the wedge : for fuppofing the wedge 

 to be lengthened down to the bottom of the cleft, the 

 power will be to the refiftance as half the thicknefs of the 

 wedge is to the length of either of its fides ; or, which 

 amounts to the fame thing, as the whole thicknefs of the 

 wedge is to the length of both its fides. 



In proof of this proportion we may fuppofe the wedge 

 divided lengthways into two equal part?, and then it will 

 become two equally inclined planes ; one of which, as <2 3 « 

 (j?jT. 3.) may be made ufe of as a half-wedge for fepa- 

 rating the moulding c d from the wainfcot A B. When 

 this has been driven its whole length a c between the wain- 

 fcot and moulding, its fide a c will be at e d, and the mould- 

 ing will be feparated ^o fg from the wainfcot. 



From the property of the inclined plane, it appears, that 

 to have an equilibrium between the power impelling the 

 half-wedjre and the refiftance of the moulding, the former 

 muft be to the latter, is a 5 to a c ; that is, as the thicknefs 

 of the back which receives the ftroke is to the length of the 

 fide againft which the moidding adls. Confequently, Cnce 

 the power upon the half-wedge is to the refiftance againft 

 its fide, as the half back a 6 is to the whole fide a c, it is 



plain, 



