429 



ON DRAUGHT. 



Fi^i'lQ 



But in practice no such material can be 

 obtained, and rollers, on the contrary, are gen- 

 erally made of wood, and, when loaded, the}' 

 must yield until the surface A B,fg. 16, is pro- 

 portionate to the pressure. Still, if the sub- 

 stance 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 E, fg. 17, equal to and exactly similar, but 

 opposite to C B, and would consequently bal- 

 ance it. 



Although 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 not 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 

 movement; these constitute a resistance in the direction B C, which is not 

 counterbalanced by any force arising from 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 A B C be a circle, let 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 with 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 with a lever equa. to E Fj but E F 

 is equal to V G F, X V F D ; therefore 

 E r, which is equal to F D, remaining con- 

 stant, and the diameter being increased, 

 E F increases only as the square root of 

 diameter, and consequently the force neces- 

 sary 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 



1 



arising from the causes now under consideration will be reduced to 



V4 

 or -1, and if increased nine times in diameter, the resistance will be only 

 1 



equal to or i 



V9. 



This being the only source of resistance to the action of a roller, it will 



easily be conceived that, in practice, by laying a plank, or any other plane 



surface upon the ground, and preparing in like manner the lower surface 



of the body to be moved, and interposing rollers between the two, a very 



