ON THE RESISTANCE OF ROAD VEHICLES TO TRACTION. 323 



Below is General Moriu's table for the maximum load that can be 

 drawn on a level road. 



General Morin's experiments decided for the time being the dimen- 

 sions of the wheels and the maximum loads that vehicles should be allowed 

 to carry. He strongly recommended the erection of weighing machines 

 on all the principal thoroughfares. 



V. The Researches of M. Dupuit. 



General Morin's experiments were fully accepted by the scientific 

 world ; they were, however, fiercely attacked by a civil engineer, M. 

 Dupuit, who, after much experimenting, arrived at formula? which differed 

 considerably from those of Morin. 



]\I. Dupuit pointed out a number of errors in the calculations given in 

 Morin's tables, and leads us to suppose that these suggest many others in 

 Morin's preliminary calculations, of which the results only are shown in 

 the tables. 



He states that the figures obtained differ considerably from those that 

 give the proportion of the load to the diameter of the wheel ; that General 

 Morin commits a serious error in his value for axle friction, i.e.,/. = 0-05, 

 which is too small and ought to be 0-12. That the distance travelled per 

 revolution ought to be calculated from the diameter of the interior of the 

 nave, as there is considerable play between the axle and the nave. That 

 for the proportion of the tractive effort to the diameter of the wheel 

 Morin compares experiments taken under various conditions, which re- 

 moves all certainty from his results. That in Morin's experiments on the 

 width of tyres, the pressure and width of tyre are varied at the same time, 

 so that it is impossible to distinguish the part played by each in the 

 experiments. 



After pointing out these errors in General Morin's experiments, 

 Dupuit proceeded to conduct experiments exactly similar, but with his 

 own apparatus, which was attached to a special car and had the advantage 

 that experiments could be performed more quickly, as the vehicles to be 

 tested had only to be attached to the dynamometer coupling on the special 

 car. 



Dupuit experimented on the resistance to rolling of cylinders, by 

 placing at the top of an inclined plane wheels which were allowed to roll 

 down and run along the level until they were brought to a state of rest 

 by the frictional resistance. 



If h = height of incline ; P = weight of wheel ; S = distance travelled 

 along incline and level ; R = resistance to rolling, then resistance offered 

 to the weight P will be PR. The work due to resistance will be PRS, 



t2 



