,324 



REPORT — 1902. 



and the equation of work which equalises the work done by the weights to 

 the work of resistance will be 



PA = RPS 



ov-R = ^ 



Taking the square root of the diameter D of the cylinders, and obtaining 

 the product R n/D, Dupuit found that it always gave a constant number, 

 which proved that the resistance to rolling varies in inverse ratio to the 

 square root of the diameter, and not as the first power, as stated by Morin 

 and Coulomb. 



M. Dupuit concludes from his experiments that on uniform surfaces 

 generally, as macadam : 



(1) The tractive effort is proportional to the load. 



(2) „ „ independent of the width of tyres. 



(3) „ „ inversely proportional to the square root of 



the diameter of the wheels. 



(4) „ ,, independent of the velocity. 



That the tractive effort or horizontal force necessary to move a vehicle 

 on the level is expressed by the formula 



P = weight of vehicle; ^» = a constant which expresses a ratio between the 

 compressibility and elasticity of the surface. 

 The constant p is found from the formula 



^ 8 V.' 



in which e is the instant compression of the ground, and t' the permanent 

 set due to the load. 



On paved roads, Dupuit recognised that the formula had to be modified, 

 for although the force required is always proportional to the load and 

 to the square root of the diameter of the wheels, yet it increases with the 

 speed, and diminishes as the width of tyre diminishes within certain limits, 

 and also that springs diminish the force required, whereas on macadam 

 springs have very little influence. 



