ON DRAUGHT. 



551 



Fig. 16. 



from the use of rollers, viz. the unevenness of the surfaces, or the yielding 

 ^of the material, which amounts to nearly the same thing. 



A circle resting iipon a straight line can only 

 touch it in a single point, and the contact of a 

 cylinder ^^th a plane is mei-ely a line : conse- 

 quently, if the material of the roller, and the 

 surface on which it rolled, were perfectly hard 

 and inelastic, such woiild be their contact, what- 

 ever weight might be placed upon the roller. 



But in practice no such material can be ob- 

 tained, and rollers, on the contrary, are gene- 

 rally made of wood, and, when loaded, they must 

 yield until the surface A B, fig. 16, is propor- 

 tionate to the pressure. Still, if the substance 

 were perfectly elastic ; that is to say, if it would 

 return to its original form with the same force 

 and velocity which were required to distort it, 

 this alteration would not cause any resistance ; 

 the elasticity at E would tend to raise the back 

 of the roller with a force D %fig. 17, equal to, 

 and exactly similar, but opposite to C B, and 

 would consequently balance it. 



Althouo-h perfect elasticity is unattainable, yet most hard substances 

 possess this quality to some extent ; consequently, when the load is not 

 sufficient to crush the materials, the resistance is not much increased by 

 even a considerable yielding, provided this yielding, as we before said, 

 arises from elasticity. Thus if a bladder be filled with air and used as a 

 roller, the resistance will hot be greater than if a perfect and hard cylinder 

 were 'employed, although the bladder may be nearly flattened under the 

 weight ; but the permanent compression of the roller, and the crushing 

 of dust or other extraneous substances lying in the way, are the great 

 impediments to its movements ; these constitute a resistance in the direc- 

 tion B C, which is not counterbalanced by any force arising frpm elasticity 

 on the opposite side. The effect of this resistance is dependent upon the 

 diameter of the roller, diminishing when the latter is increased, though 

 not in so rapid a proportion. 



If to a circle a horizontal force P be applied at G, fig. 18 ; if an obstacle 

 be placed at E, the force P will tend to push 

 the roller over the obstacle, and will act 

 Avith a lever equal to G F, and for all small 

 obstacles G F may be considered equal to G D 

 the diameter, the weight upon the roller 

 pressing it down, acts wit h a le ver eq ual to 

 E F ; but E F is equal v G F X VF D ; 

 therefore E r, which is equal to F D, remain- 

 ing constant, and the diameter being in- 

 creased, E F increases only as the square root 

 of diameter, and consequently, the force ne- 

 cessary to advance the roller is inversely as 

 the square root of the diameter ; that is to 

 say, if a roller be increased four times in diameter, the resistance arising 



from the causes now under consideration will be reduced to —j^ or -^^ 



and if increased nine times in diameter, the resistance will be only equal 



to or 4. 



V9 ^ 



