1 30 Statics. 



As there are no bodies which have not a certain degree of flex- 

 ibility, the parts of the cleft in contact with the faces of the 

 wedge may be separated further from each other without the 

 extremity Z of the cleft shifting its place; so that a part of the 

 force applied at the back DE of the wedge is employed in 

 simply bending the two branches which form the cleft ; and the 

 other is exerted in distending the fibres of the part that has not 

 yet yielded. 



222. As this resistance depends upon causes so numerous and 

 so variable at the same time, it is not to be expected that the 

 nature and operation of the wedge, considered physically, will 

 ever be reduced to a clear and satisfactory theory. In a math- 

 ematical point of view, the following explanation seems to be 

 unexceptionable. 



Fi.i23. 223. We suppose the direction of the power />, to be perpen- 

 dicular to the back of the wedge, since if it is not, it may always 

 be decomposed into two others, one perpendicular, and the 

 45. other parallel to the back, of which the latter is incapable of 

 35. urging the wedge backward or forward. This perpendicular 

 force, therefore, may be considered as keeping the wedge ABC 

 in equilibrium, while pressed at 7, K, by the parts of a body that 

 tend to unite. The theory of the inclined plane is accordingly 

 211. applicable to this case, and the resistance exerted at 7, K, can- 

 not destroy the action of the power p, except while this power 

 admits of being decomposed into two others q, r, passing through 

 these points, and directed perpendicularly to the faces BC, AC, of 

 the wedge. Therefore, the forces/?, q, r, must meet in the same 

 point E, be in the same plane ABC, and have the following pro- 

 portion to each other, namely, 



p : q : r :: sin q E r : sin p Er : sin p E q, 



reom or ' s ^ nce ^6 sines of the angles q E r, p E r, p E q, are equal res- 

 so pectively to the sines of their supplements C, A, B, 



Trig. 13. 



p : q : r : : sin C : sin A : sin B, 



:: AB : BC : AC, 



that is, the three forces p, q, r, are to each other as the three 

 sides of the triangle to which their directions are perpendicular. 



