76 Royal Society: — 



causes the one surface to slide over the other ; and this sliding is 

 accomplished against friction. In this way we should expect to 

 find the resistance to rolling greatest under those circumstances in 

 which the sliding is greatest, i. e. where the indentation is greatest ; 

 and so far it is in accordance with Coulomb's laws. In the case 

 of india-rubber, we find the slipping is very large ; and hence we 

 should expect the resistance to rolling to be large also ; and ac- 

 cordingly we find it so, for it is more than ten times as great as 

 when the roller is on an iron plane. This very great resistance 

 which india-rubber causes to rolling appears not to have previously 

 caught attention; and yet it is the natural explanation of the 

 invariable failure which has attended the numerous endeavours 

 which have been made to use this material for the tires of wheels. 

 This idea, that the resistance to rolling is due to the friction 

 between the surfaces sliding at the point of contact, naturally leads 

 to the conclusion that it must depend on the coefficient of friction 

 between these surfaces, and that we might expect to diminish the 

 resistance by using oil or any other means of reducing the coefficient 

 of friction. This was the author's first impression. Experiments, 

 however, showed that the effect of oiling the surface, although it 

 did generally reduce the resistance, was very small ; and sometimes 

 it appeared to act in the reverse manner, and increase the resistance. 

 This conclusion or surmise was therefore wrong ; and the cause of 

 the error Mas not far to seek. It consisted in having overlooked 

 the fact that friction not only opposes the sliding of the one surface 

 over the other, but also prevents it to a considerable extent, and 

 thus modifies the deformation which would otherwise take place ; 

 so that any diminution in the coefficient of friction is attended 

 with an increase in the extent of slipping, which tends to balance 

 the advantage gained by the reduced coefficient. 



The truth of this view derives independent support from a cir- 

 cumstance remotely connected with rolling-friction, of which it 

 furnishes an explanation. When the roller rests on a horizontal 

 surface and is very slightly disturbed, it does not move off, but 

 oscillates backwards and forwards. This happens on all kinds of 

 elastic surfaces ; on soft india-rubber the oscillations are both large 

 and continue "o: some time. Now if the deformation in the surface 

 of the ruo )er were complete, there would be no tendency to bring 

 the roller back ; but since, owing to friction, the india-rubber, under 

 the advancing side of the roller, is prevented from extending while 

 that under the other side is prevented from contracting, there will 

 exist a state of constraint from which the surface is endeavouring 

 to free itself by forcing the roller back. 



Besides the relative softness of the materials, the curvature of 

 the roller will affect the lateral extension both of the roller and 

 the plare at the point of contact, so that if the roller and the plane 

 were of the same material there would still be slipping. This 

 would not be the case, however, between two wheels of the same 

 diameter and material rolling in contact. 



Such is a short sketch of the subject of the paper, a considerable 



