54 B ON DRAUGHT. 



the axle may be of much smaller dimensions than if made of wood ; and we have 

 proved that a reduction in the diameter of the axle causes a proportionate 

 reduction in the resistance caused by friction. In consequence of these advantages, 

 iron or steel axles, working in iron boxes, are now almost universally adopted. 

 The friction in this case, when the parts are in proper order, greased, and the 

 pressure upon them not excessive, amounts to about one-eighth, or, at the most, 

 one-fifth of the pressure or weight ; suppose it one-sixth, and if the diameter of 

 the wheel is to that of the axle as 18 or 20 to 1, which is about the proportion 

 in a large two- wheeled cart, the whole resistance arising from friction at the axle 

 will be equal to ^ of -^g-, or of -^j, which is equal to T ^ and y-|^ respectively. 

 So that to move one ton would not, in the latter case, require a force of traction 

 greater than IS^lbs. ; and having 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 friction at the axle is far from being the greatest impediment to tho 

 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 additional 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, diminishes 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 propor- 

 tion. A light four-wheeled cart, weighing, with its load, lOOOlbs.,* was repeat- 

 edly drawn upon different sorts of roads ; the average of a number of experiments 

 gave the following results : 



Turnpike road, hard, dry . . f . 30|lbs. 



Ditto dirty . . . '? .*.-- 39 



Hard, compact loam .'* . ,<< 53 



Ordinary by-road . . . . >v . ^ 106 



Turnpike 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 fa of the weight, or 12^1bs. of the force of 

 traction, leaving, therefore, for the resistance caused by the road in the different 

 cases, as under 



* 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 those as 

 well as for a great number of other highly useful and practical experiments upon the effects of 

 power in various cases. 



