•14 LECTURE XVIII. 



for in this manner tlie weight may be supported on an axis ending in 

 a very small surface, and the effect of the friction on this surface will be 

 about one third less than if it acted at the circumference. The velocity of 

 the parts sliding on each other may be still more reduced, by placing each 

 extremity of the axis on another wheel, or between two wheels, on which 

 the axis rolls as they turn, round, so that the friction is transferred to the 

 axis of these wheels, of which the motion is very slow. But when a 

 great weight is to be supported, ft is necessary that the friction wheels be 

 very strong, and very accurately formed; for if their surface were irregu- 

 lar, they might stand still, and their use would be destroyed. (Plate 

 XVIII. Fig. 224.) 



Perrault attempted to avoid all friction by supporting the axis of a wheel 

 in the coil of a rope, which allowed it to turn while the whole wheel ascended 

 and descended; but the stiffness of a rope occasions in general even a greater 

 resistance than the friction for which it is substituted. 



The wheels.of carriages oweagreat part of their utility to the diminution of 

 friction, which is as much less in a carriage than in a dray, as the diameter 

 of the axle is less than that of the wheel, even supposing the dray to slide on 

 a greased surface of iron. The wheels also assist us in drawing the carriage 

 over an obstacle, for the path which the axis of the wheel describes, is always 

 smoother and less abrupt than the surface of a rough road on which the wheel 

 rolls. It is obvious that both these advantages are more completely attained 

 by large wheels than by smaller ones ; the dimensions of the axis not being in- 

 creased in the same proportion with those of the wheel, and the path of the axis, 

 to which that of the centre of gravity is similar, consisting of portions of larger 

 circles, and consequently being less curved; and if the wheels are elastic, and 

 rebound from an obstacle, the difference is still increased. It is, however, barely 

 possible, that the cui"vature of the obstacle to be overcome may be intermediate 

 between those of a larger and of a smaller wheel; and in this case the higher 

 wheel will touch a remoter part of the obstacle, so that the path of the axis 

 will form an abrupt angle, while the smaller wheel follows the curve, and 

 produces a more equable motion; this, however, is a case of rare occurrence, and 

 an advantage of little importance. (Plate XVIlt. Fig. 225, 226.) 



