CH. X ROLLING 'FRICTION 1 49 



the surface of the road is at all loose or soft, as in 

 newly stoned roads, or in roads wet, and partly 

 disintegrated by hauling over them, the resistance 

 to rolling will be measured not only by the effort 

 required to surmount the obstacle, but also by the 

 force expended in pushing, in front of the wheel, the 

 loose stones or particles which oppose its motion. 



If a wheel rolling on ice meets a stone, it is more 

 likely to push the stone before it, sliding it on the 

 ice, than to mount over it ; and in a loose road 

 some of this sliding, with the consequent friction 

 between the particles of the road, takes place. Into 

 such a road a narrow wheel will sink deeper than a 

 wide one, or will, in other words, form a rut, and 

 will have to push a portion of the material forward 

 before surmounting it. On soft ground, therefore, 

 increased width of tire is an advantage, and Morin's 

 experiments indicate, that up to six inches of width 

 the draught diminished, but that no advantage was 

 gained by a further increase. On good roads 



in proportion to the square root of the diameter, while Morin's ex- 

 periments seem to show that it changes directly as the diameter. 



Accurately, the relation between the resistance and the diameter 

 depends on the relation of the sine and the cosine of the angle at the 

 centre of the wheel, included between the vertical radius CA, and 

 the radius CB which ends at the point of contact of the rim with 

 the obstacle (Fig. 73). On ordinary roads the relation is measured 

 closely enough by the diameter, but on rough, stony roads it is 

 measured more nearly by the square root of the diameter, and the 

 advantage of the larger diameter, compared with that of the smaller 

 one, diminishes. 



