ox DRAUGHT. 557 



Let C, Hq. 27, be tlie centre of a wheel, of which C D is the radius, and 

 C A that* of the axle passing through the wheel, and which being fixed 

 to the load does not revolve with the 

 wheel. 



If a force C B be applied to the centre of 

 the wheel, tending to advance it in the direc- 

 tion B, the point D being in contact with 

 the ground, the wheel is compelled to turn g" 

 or roll, and the force C B in turning the 

 wheel acts with a leverage equal to C D, 

 biTt the friction between the axle and the 

 Avheel is at the point A, and in preventing 

 the t^^rning of the wheel it acts only at the 

 extremity of the lever C A ; consequently if C D be ten times as great 

 as C A, the force C B need only be equal to one-tenth of the amount of 

 the friction, and, as a general rule, the radius of the axle and the friction 

 remaining the same, the force necessary to overcome the resistance arising 

 from this friction will be inversely as the radius or the diameter of the 

 vlieel, or, in other words, the draught will, in this case, diminish exactly 

 in proportion as the diameter of the wheel is increased. 



The exact amount of resistance occasioned by friction will depend upon 

 the nature of the substances in contact at the axle, as well as upon the pro- 

 portionate dimensions of the wheel and axle. 



The friction between polished surfaces bears a certain proportion to the 

 pressure : if the pressure is doubled, the friction will, within certain limits, 

 he also doubled ; but the proportion between the friction and the pressure 

 is only constant so long as the same substances are employed : it varies 

 very much v»dth different substances. Thus with soft wood sliding upon 

 soft wood, the friction amounts to one-fourth or one-third of the pressure ; 

 while between hard brass and iron, the surfaces smooth and oiled, the 

 resistance may be as low as ^L of the pressure. The relative advantages, 

 therefore, of different materials, as applied to the axle and box of a wheel, 

 is a point of much consequence. 



Metals, generally speaking, are the best adapted for this purpose. Owing 

 to their hardness, 'the friction between them is small, and they will bear 

 without injury a greater press'ire, proportionably to the surface ; and, from 

 their strength, 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 ^V' or of 4o, which is equal to ^^ and yj „ 

 respectively. So that to move one ton would not, in the latter case, require 

 a force of traction greater than 18-^ lbs. ; and having overcome this resist- 

 ance, the force of traction required remains nearly the same at all velo- 

 cities ; 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 iii the speed. In practice, however, the friction at 

 the axle is far from being the greatest impediment to the motion of a car- 

 riao-e. We have hitherto, for the purpose of considering friction alone, 

 supposed the surface upon Avhicli the wheel moved as perfectly hard, 



