199-] FRICTION. IIC> 



contact with different points or areas of the other. In the case 

 of rolling friction, the points that come successively in contact 

 .are different for both bodies. 



Let us examine the simplest case, viz. that of a cylinder roll- 

 ing over a horizontal plane. If both cylinder and plane were 

 perfectly rigid, there could be no resistance to rolling. This 



Fig. 64. 



resistance is due to the compression both of the lower part of 

 the cylinder and of the plane. Experiments made with a heavy 

 roller on india-rubber have shown that the supporting surface 

 when elastic is not only compressed under the roller but bulges 

 out in front and behind, as indicated in Fig. 64. Thus, the area 

 of contact is considerably increased, and as the roller advances, 

 the portion AB of its surface rubs over the surface of the sup- 

 port, while the elastic material of the support in trying to regain 

 its horizontal surface causes friction over the area B 1 A also. 



The experiments indicate for the value Fof. rolling friction an 

 expression of the form 



where W is the weight, r the radius of the cylinder, and ^ a 

 constant depending on the nature of the materials in contact. 

 For hard surfaces, this constant of rolling friction p' is very 

 much smaller than the constant of sliding friction /z. 



199. On the subject of plane statics the student may consult in par- 

 ticular the recent work : E. J. ROUTH, A treatise on analytical statics^ 



