ON DRAUGHT. 435 



about the proportion in a large two-wheeled cart, the whole resistance 

 arising from friction at the axle will be equal to i of -j^, or of ^V' ^hich is 

 equal to -i- and ^lo respectively. So that to move one ton would not, 

 in the latteV case, require a force of traction greater than IS^lbs. ; and 

 havlno' overcome this resistance, the force of traction required remains 

 nearly* the same at all velocities; that is to say, friction is not materially 

 affected by velocity: therefore the resistance arising- from it is not sensibly 

 augmented by a considerable increase in the speed. In practice, how- 

 ever, the friciion at the axle is far from being the greatest impediment to 

 the motion of a carriage. We have hitherto, for the purpose of considering 

 friction alone, supposed the surface upon which the wheel moved as 

 perfectly hard, smooth, level, and plane : we need hardly say that such can 

 never be the case in a road. The friction, however, remains, practically 

 speaking, the same, and the laws which govern the amount and the effects 

 of it remain unaltered ; and we have only to ascertain what is the addi- 

 tional resistance, arising from other sources, to obtain the whole draught 

 of the carriage. We have already stated, when pointing out the difference 

 between the roller and the wheel, that the movement of the latter was 

 attended with two sources of resistance, viz., friction at the centre, which 

 we have considered, and another, which is common both to the wheel and 

 the roller, arising from impediments in the road, or the yielding of the 

 materials. 



The laws which affect the amount of this latter are, of course, the same 

 in a wheel as in a roller. 



We have found that the power required to overcome it is inversely as 

 the square root of the diameter; therefore, by increasing the diameter of 

 the wheel, the effect of friction, which is inversely as the diameter, dimi- 

 nishes much more rapidly than that caused by impediments in the roads ; 

 and on ordinary roads, with common carts, the amount of the latter is about 

 three times as great as that of the former, and when the roads are at all 

 injured by weather or by neglect, or if they are naturally heavy or sandy, 

 it bears a much greater proportion. A light four-wheeled cart, weigh- 

 ing, with its load, lOOOlbs*, was repeatedly drawn upon different sorts of 

 roads, the average of a number of experiments gave the following results : 



Force of Traction requiied 

 Description of Road. to move the Carriage. 



Turnpike roadj — hard, dry . . . SO^lbs. 



Ditto dirty . . . .39 



Hard, compact loam . . * . 53 



Ordinary by-road . * . ,106 



Tmnpike road — new gravelled * * 143 



Loose, sandy road . . ' • 204 



The friction at the axles, which were of wood, was, of course, nearly 

 constant, and probably absorbed at least gV of the weight, or 12jlbs. of 

 the force of traction, leaving, therefore, for the resistance caused by the 

 road in the different cases, as under — 



_, . . <.„ 1 Force of Traction required to move the 



Description ot Koad, Carriage, independent of the Friction at the Axles » 



Turnpike road — hard, dry, about » . 18 lbs. 



Ditto dirty . . . .26^ 



Ditto new gravelled . . 130^ 



Loose, sandy road .... 191:^ 



SO that in the last case, one by no means of rare occurrence in many parts of 



* The experiment was not made with a load of exactly lOOOlbs., but the proportions 

 of the results are calculated to this standard. The public are indebted to Mr. Bevan for 

 these as well as a great number of other highly useful and practical experiments itpou 

 the effects of power in various cases. 



2F2 



