FRICTION IN MECHANICS. 187 



diftance: on the contrary, if the body AB be fixed, 

 and the cylinder turned round about its axis, the fric- 

 tion will be the fame as if the cylinder was fixed, and 

 the body drawn round it by CP, as before : Likewife 

 the friction is the fame, whether the cylinder be fixed, 

 and the body AB moved round the axis MR by a force 

 Oc applied at c ; or whether the point c be fixed with 

 AB fattened to Cc, and the cylinder be revolved in a 

 circle whofe center is c, fo as always to retain its paral- 

 lelifm with refpe6t to any fixt objecl:; and as this laft 

 cafe obtains in the axletrees of carriages, fince every 

 point of the wheel's contaft with the ground may be 

 confidered as the center of motion for that inftant, 

 therefore the effett of the refiftance arifing from the 

 friction of the concave part of the nave upon the axle- 

 tree, is to the effect that would arife from drawing the 

 fame weight over a horizontal plane of the fame kind, as 

 the parts that rub each other, as the radius of the axis 

 to the radius of the wheel. It muft be obferved, that 

 this is not the only fri£tion to which carriages are fub- 

 jecTt ; for there is another part, arifing from the cohefion 

 of the wheel and the ground at their conta6t, which is 

 to be found and allowed for by the three firft Propo- 

 rtions. 



In the above the preffure and friction have been fup- 

 pofed to be as the weight, as it is on a horizontal plane ; 

 but by the Scholium to the fourth Proposition, it is 

 plain that the preffure is greater than the weight, and 

 may be fo in any proportion: however, as it appears by 

 calculation, that the preffure on an arc of ninety de- 

 grees is to that on its chord, only as 1,183 to J * when 

 both the concave and convex parts have exattly the 

 fame curvature, the difference will be fo trifling when 

 the cylinders have different curvatures as ufual, as to 

 require very feldom to be allowed for. 



P 2 This 



