316 REPORT— 1902. 



The work of resistance consists of : — 



(i.) That absorbed by the play of the springs, usually negligible. 



(ii.) That due to the action of the wheels upon the road. 



(iii.) Axle friction. 



(iv.) That absorbed by hills, 



(v.) That due to the variation of the momentum, which may be 

 neglected during a day's run, as the vehicle passes in a short time from 

 a state of rest to its normal velocity. 



Coriolis states that the tractive effort required is practically propor- 

 tional to the work due to the action of the wheels upon the road and 

 axle friction, the other quantities being negligible. 



That axle friction is a sliding friction constant in value and inde- 

 pendent of the extent of surface in contact, and can be reduced by altering 

 the arc of contact, which is limited by practical considerations. 



That the reaction of the road upon the wheel would be nil if the 

 ground were infinitely soft, and equal to the load if incompressible. 

 Neither case appears in practice, but the reaction is variable and increases 

 with the compression. 



Ii p = reaction of the ground, h =■ compression of the road, then work 



of resistance = «c?A = ^ _ . dp. 

 J J (^P 



The more rigid the ground the more will p increase with h ; . " , - 



dp 



will diminish with p, and the work will be less for a given value of p. 



That the reaction depends not only on the nature of the road, but also 

 on the diameter of the wheels and width of the tyres. 



That on a homogeneous surface the resistance due to reaotiou 



_ a^\/p* J 



V'LVR''^ 



a =■ coefficient that varies inversely as the hardness of the road ; p = 

 total load ; L = width of tyre ; R = radius of the wheel. 

 Coriolis drew the following conclusions : — 



That to reduce the work due to resistance the road ought to have as 

 great a rigidity as possible, and that the springs should be as flexible as 

 possible. 



IV. Experiments and Conclusions of General Morin (1837-42). 



These experiments were made by General Morin, 1837-42, by order 

 of the Ministers of War and Public "Works, being carried out with the 

 greatest care and under the most varied conditions. The results have 

 been collected together into a large treatise, from which the following is 

 taken : — 



A R4sumi of General Morin s Work on Rolling Friction. 



(a) There is the simple turning of one curve upon another when the 

 two curved surfaces are always in contact, and when the arcs passed 

 through in a given time are of equal length. 



' This formula is midway between General Morin'a and Dupuit's, 



