On the Theory of the Wedge. 



235 



ialned in Article 163 of his Mechanics asserts, that " when a 

 resisting body is sustained against the face of a wedge, by a 

 force acting at right angles to its direction, in the case of equi- 

 librium, the power is to the resistance, as the sine of the semi- 

 angle of the wedge, to the sine of the angle which the direction 

 •of the resistance makes with the face of the wedge." 



Dr. Gregory proves, that, with respect to the rectangular 

 wedge ah c^ when it slides 

 freely along the plane w/, 

 and the resisting body is sus- 

 tained against its face h c, the 

 power is to the resistance as 

 the sine of the angle a c 6 to 

 the sine of the angle which 

 the direction of the resistance 

 makes with b c, and thence 

 infers, that " if the wedge be 

 isosceles, or composed of two 

 rectangular wedges, the force, 

 wliich in the former case was 

 counteracted by the plane, will 

 now be counteracted by the 

 other half of the wedge ; and the power, resistance, and sustain- 

 ing force, will remain in the same ratio as before.!' 



The latter part of this inference appears to me to be absurd. 

 It necessarily supposes the resistance to be equal to the 

 ■sum of iwo forces^ acting in a similar manner against the op- 

 posite sides of the wedge ; which is contrary to the terms of the 

 proposition. And moreover, when two bodies are to be sepa- 

 rated, by forcing a wedge betwixt them, the resistance of the 

 body which gives way is alone the force requisite to be overcome ; 

 the other body merely serves as a fulcrum to the wedge. If the 

 wedge be isosceles, or composed of two rectangular wedges, as 

 •bch^ and be supposed to slide freely along the plane mr, the 

 force, which in the former case was counteracted by the plane n /, . 

 will now be counteracted by the other half, a c A, of the wedge ; 

 jand as action and re-actiou are always equal, the power requisite 



