176 HINTS RELATIVE TO 



to be fufpended, as in the cafe of land-ties, the beft angle 

 (on the foregoing fuppoiition) muft be i8°.26' below 

 the plane. 



SCHOLIUM. 



In thofe propofitions the fri£lion is eftimated accord- 

 ing to the moft generally received opinion, that the re- 

 fiftance isproportional to the whole preffure compound- 

 ed of the weight of the body, and the additional force 

 neceffary to overcome the fritlion ; but it has been 

 afferted, that there may be cafes where the friction is 

 not proportional to the whole preffure, but to that 

 which would arife if the body was fuftained in a given 

 direction, exclufive of fri&ion ; and that there might 

 alfo be cafes, where the refiftance, arifing from tenacity 

 orcohefion, might be as the relative preffure againfl the 

 plane, and the force to overcome it the fame in every 

 direction ; fomething fimilar to a globe ftuck faft in 

 wet tenacious clay : I fhall therefore give folutions to 

 both cafes. 



In the firft cafe,* the force requifite to fuftain the 

 body in direction RV, exclufive of friftion, is Rn j and 

 as Rn is equivalent to RD and Dn, therefore Pn is the 

 preffure, exclufive of friclion ; and as the fri&ion is the 

 n part of the preflure, the force a£ting parallel to AB 

 to overcome it, is the n part of Pn; but the force which 

 afting in direction Rn will be equivalent to the n part 

 of Pn in the direction Rn, is a fourth proportional to n 

 times RD, Pn, and Rn ; but becaufe DQ is the n part 

 of DP, therefore fn is the n part of Pn, and the fourth 

 proportional aforefaid will be nz ; confequently the 

 fum or difference of Rn and nz muft be a given quan- 

 tity, or the leafl poflible : the Problem therefore is 

 reduced t to drawing a line Rn from the given point 

 R, meeting the two lines PD and PQ given in pofi- 



tion 



* Fig. 3. Fig. 4. 



