428 



ON DRAUGHT. 



Fig. 16 



Fig. 17. 



But in practice no such material can be 

 obtained, and rollers, on the contrary, are f^e- 

 nerally made of wood, and when loaded they 

 must yield until the surface A B,fig. 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 orio'inal 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, fig. 1 7, equal to, and exactly similar, but 

 opposite to C B, and would consequently 

 balance 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 

 C D considerable yielding, — provided this yield- 



ing:, 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.Jig. 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 GD the diameter. The 

 weight upon the roller pressing it down, 

 acts with a lever equal to E F ; but E F 

 is equal to V ^f F, X aJFT) ; 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 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 — — — 



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



1 

 equal to 



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 



