164 LECTURE XVIII. 



be wholly removed, whatever may be the magnitude of the rollers. 

 (Plate XVII. Fig. 222, 223.) 



The effect of friction in any machine being always diminished, in pro- 

 portion as the velocity of the parts sliding on each other is diminished, it 

 is obvious that by reducing the dimensions of the axis of a wheel as much 

 as possible, we also reduce the friction. When the pressure on the axis is 

 derived principally from the weight of the wheel itself, the friction may 

 be lessened by placing the wheel in a horizontal position and making the 

 axis vertical ; for in this manner the 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, it is necessary that the friction 

 wheels be very strong and very accurately formed ; for if their surface 

 were irregular 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 owe a great part of their utility to the diminu- 

 tion 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 increased 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 conse- 

 quently 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 curvature 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 XVIII. 

 Fig. 225, 226.) 



The greater part of the resistance to the motion of a carriage very 

 frequently arises from the continual displacement of a portion of the 

 materials of the road, which do not react on the wheels with perfect elasfi- 



* Machines approuve*es par 1' Academic, i. 13. Leupold, Th. Mach. t. xiv. xv. 

 Desaguliers Ph. Tr. xxxvi. 222. 



