434 ON DRAUGHT. 



impeded their revolution; but in practice we cannot aamit of the load 

 revolving with the wheel, and we have no means of suspending it to the 

 wheel, except by means of an axle fixed to the load, and passing through 

 the centre of the wheel. This axle presses upon the lower surface of the 

 hole, and consequently, when the wheel revolves, causes a friction propor- 

 tionate to the load upon the axle. This friction is then the only source 

 of resistance to the motion of a wheel, under the circumstances here sup- 

 posed ; and it is the action of this friction, the degree in which it alfects the 

 draught, and by what means this effect is increased and diminished, that 

 we are now about to consider. 



Let C,fg. 27, be the 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 cen- 

 tre of the wheel, tending to advance it in 

 the direction B, the point D being in 

 contact with the ground, the wheel is 

 compelled to turn or roll, and the force 

 C B in turning the wheel acts with a 

 leverage equal to C D, but the friction between the axle and the wheel is at 

 the point A, and in preventing the turning 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 wheel, 

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

 portion as the diameter of the wheel is increased. 



The exact amount of I'esistance 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, 

 be 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 with 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 ^^ 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 s|)eaking, are the best adapted for this purpose. 

 Owing to their hardness, the friction between tiicm is small, and they 

 will bear without injury a greater pressure, proportionably to the sur- 

 face ; and from their strength, the axle may be of much smaller dimen- 

 sions 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 



