On the Mechanical Power of the Wedge. 317 



thofe conclufions have refulted from falfe opinions concern- 

 ing the directions of the refilling powers. 



It is evident, that when wood or other fubftance is fplit by 

 a wedge which does not fill the cleft, that is, when the angle 

 of the cleft is more acute than that of the wedge, the power 

 or action of each fide of the wedge, equal and oppofite to the 

 refiftance of the cleft, muft be refolved into two ; the one in 

 the direction of the fide of the clefr, which tends to thruft it 

 forward ; and the other perpendicular to that direction, 

 which tends to tear it afunder. It is by not attending to the 

 above refolution that writers on this fubject have been led 

 into miftakes ; for, inftead of confidering the powers which 

 act in thofe two directions, they have imagined a fingle 

 power only as acting obliquely on each fide. But if the fides 

 of the wedge are perfectly polifhed, as we muft here confider 

 them, no fingle permanent power can be applied to impel 

 any one of them, unlefs its direction be perpendicular to the 

 plane of the fide to which it is applied : therefore two ob- 

 lique powers, applied on oppofite fides of the fame point, are 

 at lead necefiary to fuftain each other and the action of the 

 plane ; and in the cafe of the wedge above mentioned, the 

 directions of thofe two oblique powers will always be per- 

 pendicular to each other, as will appear obvious from the 

 two following propofitions. 



Prop. I. Let ABC (Fig. 3, Plate X.) be a vertical fec- 

 tion patting through the centre and at right angles to the 

 head and fides of any ifofceles wedge ; alfo in the plane of 

 this fection, and at right angles to its fides AB, BC, and C A, 

 let three powers be applied, fuch, that their directions may 

 all mutually interfect in the axis, and their efforts fuftain the 

 wedge in equilibrio ; I fay, that thefe three powers are as 

 AB, BC, and CA refpectively. 



Let LM, KI, ED be the directions of thefe three powers, 

 which produced, interfect each other and the axis in O. 

 Since, by hypothefis, thefe three powers directed to the fame 

 point are in equilibrio, and the three fides of the triangle 

 ABC are at right angles to their directions j therefore, by a 



well 



