FRICTION IN MECHANICS. 1 89 



a force juft fufficient to prevent M from descending ; 

 then the weight upon d in the fir ft figure will be 

 M+N — w; in the fecond figure, the weight will be 

 M — N-f-w ; and in the third figure, N — M — w ; and 

 by proceeding as before, the values of w in the Append- 

 ing forces are dn (M, J rN)'. (n.Bd-\-dn) : dn (M — N) : 

 (n.Bd—dn), and'*/?* ( N— M) : (n.Bd+dn,) in thefirft, 

 fecond and third figures reflectively. 



Becaufe Bd : d A : : M : N, therefore if this value of N 

 be fubftituted in each of the above expreflions for the 

 friclion, the whole force capable of fuftaining the fric- 

 tion and weight M will be had. Thus, for example, the 

 moving force to overcome the friction and weight M in 

 the fir ft figure, will be M (n.dA-\-dn) : (n.Bd — dnj' 

 and the fufpending force^M (n.dA — dn) : (n.Bd-\-dnj) 

 in the fecond figure the moving force will be M (n.dA 

 -\-dn) : (n.Bd-{-dn,) and the fufpending force M (n.dA — 

 dn) : (n.Bd — dn ;) and in the third figure, the moving 

 force will be M (n.dA — dn) : (n.Bd — dnj and the fuf- 

 pending force will be M (n.dA-\-dn) : (n.Bd-\-dn.) 



The method of finding n from each of the above 

 equations is evident, and confequently the ratio of the 

 friction to the preffure by experiments. 



OF FRICTION IN THE WEDGE. 



Let AC* be the force neceffary to fuftain the wedge 

 QPB in the direction aB perpendicular to QP, friclion 

 included ; and let AB be the force exclufive of friction : 

 draw AN and AH perpendicular to the BQ and BP ; 

 CG parallel to AN, and CF parallel to AH : Now GA 

 and AF, the forces of the wood againft the fides of the 



wcdge 4 



» Pig. 15, 



