FRICTION IN MECHANICS. l8l 



Example. Let AB, BC, and AC, be 5, 3, and 4, 



reflectively, and let the inclination of the fides be 45 ; 

 the weight of a ton and the friclion one third of the 

 prefTure ; then 3648 pounds is the moving, and 499 

 the fufpending force. 



SCHOLIUM. 



In this propofition, thofe parts of the plane on which 

 the body moves are fuppofed rectilineal, as moftly hap- 

 pens in practice; but the friclion is eafily eitimated in 

 curvilinear furfaces, and may be found generally as 

 follows : 



Let AMP * be half the feclion perpendicular to the 

 horizon, and to the axis of the folid which forms the 

 curvilineal plane on which the body is moved; AP the 

 axis; PM the ordinate, and MS a tangent to the curve 

 at the point M ; alfo let RM reprefent the weight or 

 preffure in a direction perpendicular to the horizon 

 at the point M ; and let RF be perpendicular to MS 

 meeting MP in F; alfo let PN be taken equal to MR, 

 and PQ equal to RF ; and fuppofe the fame conftruc- 

 lion to be made for every point of the curve, and let 

 HN be the locus of all the points N, and GQ the locus 

 of ail the points Q ; then will the friclion, when drawn 

 along the horizontal plane, be to the friclion of the 

 fame body when drawn along the curvilinear plane in 

 the fame direction, as the area APNH to the area 

 APQG. 



For the friclion on the horizontal plane being as the 

 fum of the preffures, is as the fum of all the elementary 

 lines MR or PN; that is, as the area AHNP; and the 

 friction on the curvilinear plane is for the fame reafon as 



the 



* Fig. a. 



