170

l'RHITION OF CARRIAGES

to the progressive motion of the body. Onthe contrary, if the body be cylindrical, andbe rolled along the plane, no part of it issubjected to the action of attrition, the oidyresistance being that produced by the rollingmotion of the periphery upon the plane;which, when the surfaces are smooth and hard,is very trifling.

Suppose now a cylinder, instead of beinguniformly solid, to be composed of a numberof concentric circles or cylinders, one withinanother; if this body be rolled along theplane, upon the periphery of the exterior orouter cylinder, the velocities of the peri-pheries of the respective cylinders, around thecentres, will be in the ratio of their diameters.Let the interior cylinder, or that nearest thecentre of motion, be of finite diameter; then,if we cause the cylinder to roll along theplane upon the periphery of the exterior cylin-der, and place the body or carriage to bemoved upon the periphery of the innercylinder, the velocity of the rubbing surface,or extent of attrition, compared with theextent of rolling surface, or progressive mo-tion of the body, will be in the ratio of thediameter of the inner to that of the exteriorcylinder. In all wheel-carriages, therefore,the interior cylinder represents the axles, and