ON DRAUGHT. 547 



First let us examine the theory of it, and suppose it acting on a level plain. 

 The wheel being a circle, the centre will remain always at the same height, 

 and consequently will move parallel to the plane in a perfectly level line : if 

 any weight be attached to or suspended from its centre, this will also move in a 

 continued straight line without rising or falling, and consequently when once put 

 in movement, there is nothing to check its progress (neglecting for the moment 

 the slight resistance of the air), and it will require no force to keep it in motion 

 oo long as the wheels continue to turn. 



We have, therefore, in this case only to examine into the force necessary to 

 turn the wheels. The wheels, if left to themselves, would roll on with perfect 

 freedom, whatever might be their weight, or whatever weight might be attached 

 to them, provided nothing in the mode of attaching that weight impeded their 

 revolution ; but in practice we cannot admit 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 proportionate 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 supposed ; and it is the action of this friction, the 

 degree in which this affects the draught, and by what means this effect is increased 

 and diminished, that we are now about to consider. 



Let C, fig. 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 centre ol 

 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 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 asC A, 

 the force CB 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 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 proportionate 

 dimensions of the wheel and axle. 



The friction between polished surfaces bears a certain proportion to the 

 pressure : if the pressure is doubled, the fraction 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 -fo 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 pressure, proportionably to the surface ; and, from their strength, 



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