542 



ON DRAUGHT. 



siderable 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 resist- 

 ance 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 per- 

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

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

 he roller over the obstacle, and will act 

 twith 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 equal to EF; 

 but E F is equal v'GF, x a/F D ; therefore 

 Er, which is equal to FD, remaining constant, 

 and the diameter being increased, EF increases 

 only as the square root of diameter, and con- 

 sequently, the force necessary 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-j, and if increased nine times in diameter, the resistance will be 



V 

 only equal to 



v/9 



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 great weight 

 may be moved with comparatively small power ; but, on the other hand, there 

 is a serious practical inconvenience attending the use of the roller, which pre- 

 vents its adoption except in very particular cases. 



A weight moved upon rollers proceeds at twice the rate of the roller ; for if 



Fig. 19. C,fig. 19, be the centre of the roller, D the point of 



contact with the ground, and E that with the weight 



to be moved, and W the weight, if this weight be put 



in motion, the point D is for an instant stationary, since 



it is in close contact with the ground. The diameter 



ECD moves, therefore, round the point D as a centre, 



and, consequently, E being as twice as far from D as C 



is, describes E e twice as great a distance as C c ; fresh 



points are now brought to the summit and in contact 



with the ground, and again the latter is stationary, 



while the former moves twice the distance which the 



point C does. The summit, therefore, or that point 



which is in immediate contact with the weight, always 



moves with twice the velocity of the centre of the roller ; but the velocity of 



the centre is, of course, that of the roller, and the velocity of the point E which 



is in contact with, and is moved by, the weight, is the same as that of the 



