31 8 On the Mechanical Power of the Wedge. 



well known ftatical principle, the intenfities of thefe powers, 

 are as AB, BC, and CA refpectively. 



Prop. II. When an impelling power applied to the head 

 of an ifofceles wedge is in equilibrio with the refilling power 

 of a cleft, the angle of which is more acute than that of the' 

 wedge inferted, then universally, 



The impelling power applied to the head, 



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



The part thereof which tends to thruft it forward, 



And the remaining part, which tends to tear it afunder, 

 Are 



As twice the fine of half the vertical angle of the wedge,' 



The radius, 



The fine of the angle contained by the fides of the wedge 

 and cleft, 



And the co-fine of that angle reflectively, the fame 

 radius being common. 



Let Fig. 2, Plate X. reprefent a vertical fection of the 

 wedge and cleft, fimilar in pofition to that defcribed in Pro- 

 pofition i ; alio let the two fides of the cleft DH, DH be 

 equal, and in contact with the fides of the wedge AC, AC at 

 equal diftances DC, DC from the vertex C, in which cafe 

 the fides of the wedge make equal angles with thofe of the 

 cleft. Through either point D, draw DF at right angles, 

 and equal to AC ; alfo through D, draw DE, at right angles 

 to DH, and complete the parallelogram DEFG. Then by 

 Propofition I, thelin£ A A represents in quantity rhe impel- 

 ling power applied to the head, and the line DFreprefents in 

 quantityand direction the whole action of the fide o£ the wedge 

 on that of the cleft, which byhypothefis is balanced by its refin- 

 ance ; but the power DF is refolved into two, reprefented in 

 quantityand direction by D G", DE refpectively : the one, being 

 in the direction of the cleft, tends to thruft it forward ; and the 

 other, being at right angles thereto, tends to tear it afunder. 

 Therefore the powers mentioned in the Propofition are as 

 A A, DF, DG and DE refpeaively •, but AC = DF being 



Radius, thefe lines are refpe&ively equal to 



Twic« 



