FRICTION IN MECHANICS. lQX 



or equal to (2Ba.BA) : (n.QP — 2Ba), an 1 therefore 

 AC =(n.QP.AB) : (n.OP — 2Ba;) and by following 

 the fame method for the fu {'pending force, we findBC= 

 (2Ba.AB):(n.QP-f 2Ba,)andconfequentlv AC is equal 

 to (n.QP.AB) : (n.QP-f 2Ba.) 



SCHOLIUM. 



By proceeding in a fimilar method, the forces of the 

 arch-ftones of bridges may be determined; for let ObbP 

 be a (tone fuftained by the parts of the arch prefling 

 againft Pb and Qb, and let A be its center of gravity, 

 and AB perpendicular to the horizon; alfo let AB and 

 AC be the fame as before; then becaufe the body is in 

 equilibrio, the force in dircftion AC will be equivalent 

 to the force in a contrary direction, arifing from the 

 preffures againft the body in the directions GAandKA, 

 together with the force of friction; and becaufe the 

 prelfures are AG and AK, if Be (the n part of AG) be 

 drawn parallel to PB ; and Bn (the n part of AK) be 

 drawn parallel to QB; and the parallelogram Bnme be 

 compleated, and Cm joined; Bm will be the force arif- 

 ing from friction, and the angle BmC a right angle. 

 The adjacent figure * is for the moving force ; but the 

 method is fimilar for the fu fpen five force ; and it is 

 evident that the one construction is of ufe to determine 

 the force which tends to break an arch by prcfling it 

 downwards, and the other the force that tends to break 

 it upwards. 



Eut as that excellent mathematician P. Friji, in his 

 Ihfliiitziohi 6i Ai eccamca^ has objected to thedivihonof 

 the force AB into the forces AN and AH, and thence 

 concluded Behdorand Couplet to have been miftakenon 

 that account in their writing upon bridges ; I fhall, 



therefore, 



* Fig. IS. 



