174 HINTS RELATIVE TO 



force 747 pounds, and the force excluding fritlion 1680 

 pounds; nearly. 



PROBLEM II. 



Given the weight of the body, the inclination of the 

 plane, and the ratio of the friction to the preffure; to 

 find the direction fo that the fuftaining force may be a 

 given quantity, or the leaft poffible. 



Draw DQ and QP as before, and let PR be to Rm as 

 the weight to the given force; then from the center R, 

 with a diftance equal to Rm, interfeft FO in m; then 

 Rm is the required direction when the force it- given ; 

 but to have it the leaft poffible, draw Rm at right angles 

 to PQ, then Rm is the direclion required. 



Corollary 1. An expreflion for the fuftaining force 

 when the leaft poffible, may be found as follows: In the 

 triangles PDQ, RQm, the angle Q is common, there- 

 fore FQ: PD:: RQ: Rm; lut PD is a forth propor- 

 tional to AB, AC, and PR, and DO is to PD as 1 ton, 

 fuppofing this the given ratio; alfo RD is a fourth pro- 

 portional to AB, BC, and PR, consequently RQisequal 

 to 1)Q either added to or fubtracted from DR, as it is 

 the firft or lecond cafe; and becauie PQ: PDxv' 

 (vn+i); n : : RO: Rm, therefore Rm=PR (n. BC 

 Bte r AC) : AIV (nn+ 1) or (nfr**c) W : (Vnn + i) 

 by fubltituting 5 and c for the natural fine and coline 

 of the plane's elevation, and ufing the negative or af- 

 firmative fign as the force required^ is the moving or 

 fufpending one refpettively. 



Example* 



