328 REPORT— 1902. 



He retuElrks that the deductions of M. Mofin are in perfect accordance 

 Avith the previous theoretical investigations, and alludes to the Second 

 Report of the Select Committee of the House of Lords (1833) upon Turn- 

 pike Road Trusts, where Mr. Macneill has given the following empirical 

 formula for the draught on common roads : — 



■"O* 



where W is the weight of waggon, to is the load, V the velocity in feet 

 per second, and c a constant, wJiich depends on the surface over which 

 the waggon is drawn. 



Mr. Macneill ascertained the value of c for different surfaces as 

 folloAvs : — 



r= 2 for a timber surface. 



c = 2 for a paved surface. 



<;= 5 for a well-made broken slone road in a dry state. 



c= 8 for the like surface covered with dust. , 



c=- 10 for the .same wet, and covered with mud. 



c^ 13 for a gravel or flint road when wet. 



c = 32 for the fsame, very wet and covered with mud. 



Leahy then compares the theoretical investigation with experiment, 

 showing in the first place that both agree tliat springs do not diminish 

 the draught when the motion is so slow as to permit the body of the 

 vehicle to be elevated and depressed just as much as the axle. The fact 

 that the draught over an even, soft surface is not affected by the velocity 

 corresponds with the experiments of M. Morin, but is at variance with 

 the views of Mr. Macneill. 



By equation (4) he shows that oVer hard, irregular surfaces tlie varia- 

 tion of the draught is as the square of the velocity, and remarks that 

 there is a seeming discrepancy between this conclusion and the results of 

 experiments made under apparently analogous hypotheses; which would 

 regulate the increments of traction by proportional increments of 

 velocity. 



It must be remembered, however, that the experiments of M. Morin 

 and others were made upon roads said to be hard, yet not so in fact, and 

 with elastic machines, whereas had the experiments been conducted upon 

 a perfectly unyielding surface and with a rigid and inelastic machine 

 there is no doubt that the draught would vary as the square of the 

 velocity, and therefore the conclusion is arrived at that according as the 

 machine and rough roadway approach a state of inelasticity the more 

 nearly will the draught correspond with this law of variation. Every 

 road presents a different descrii^tion of surface, and if upon one the 

 draught was not at all affected by the velocity, or varied as Vowing to 

 its softness and regularity, and upon another it varied as V- owing to its 

 hardness and roughness, surely as there are many intermediate descrip- 

 tions of surface between these extremes, so also must the draught upon 

 them vary, as some intermediate power, between and 2 of the velocity. 

 Therefore, in general, the resistance to rolling must vary as V", in which 

 71 is the constant suitable to each particular surface, and always lying 

 between and 2 ; and any accurate empirical expression for the draught 

 upon roads must have V" as one of its terms. 



