MECHANICS. 105 



If a, P and W are given, p can only be lessened by 

 diminishing r, or increasing n, that is, by diminish- 

 ing the radius of the axle, or polishing its sur- 

 face. 



For the application of a like correction to the other 

 mechanical powers, see PRONY, Arch. Hyd. Sect. v. 

 BOSSUT, Mech. 261, to 283. VAN SWINDEN, Po- 

 sitiones Phys. 312325. 



174. The stiffness of ropes, or their resist* 

 ance to bending, has a great analogy to friction. 

 In different ropes, the forces requisite to bend 

 them, are in the direct ratio of their diameters 

 and their tensions jointly, and in the inverse ratio 

 of the radii of the cylinders round which they are 

 bent. 



Van SWINDEN, Pos. Pkys. 339. COULOMB, whose ex- 

 periments ought to have great weight, holds the 

 stiffness to follow the ratio of the section of the rope, 

 that is, of the square, not of the simple power of its 

 diameter. The decision of the question requires new 

 experiments. 



175. The friction of a rope wound round a 

 cylinder, increases in geometrical progression, while 

 the number of turns increases in arithmetical pro- 

 gression. 



If the turns be represented by the numbers, 0, 1, 2, 

 3, 4, &c. ; the resistance made by the rope may be 

 represented by the numbers 1, 2, 4, 8, 16, &c. 



Hence 



