156 Slatics. 



We learn at the same time from this experiment, that the 

 phenomenon in question requires (1.) That the point should be 

 small compared with the distance of the parts of the top from the 

 axis jVZ) ; and (2.) That these parts should turn avith consider- 

 able rapidity ; and the success will be more or less complete, as 

 these conditions are more or less perfectly fulfilled. 



It will be seen, moreover, that upon an inclined plane the top 

 must have a tendency not to a vertical but to a perpendicular 

 to the plane. But as it must at the same time slide along the 

 plane, and as this motion would cause a great vacillation in 

 passing over the inequalities of the plane, it will not so easily 

 preserve its perpendicular position as if the plane were hori- 

 zontal. 



Of the Stiffness of Cords. 



Pig.HO. 253. The stiffness of ropes and cords, or the difficulty with 

 which they are bent into a given curve, is also one of the causes 

 which diminish the effect of forces applied to machines. 



In order to understand in what manner this stiffness impairs 

 the effect of forces, let us suppose the wheel or pulley ABC to be 

 moveable about the axle /, without friction. The two weights p 

 and q being equal, if we make a very small addition to one of them, 

 as <?, for example, no motion will follow, unless the cord p ABC q 

 be perfectly flexible. Indeed, if we imagine that this cord, 

 instead of being perfectly flexible, is perfectly inflexible, so that 

 the parts Ap, C q, are stiff rods firmly fixed to the body of the 

 pulley ; it is evident that the pulley being moved by an external 

 force in the direction ABC, the two weights p and q will take the 

 situations p' and q' ; but they will tend to return to their first 

 position, and can be prevented only by the constant exertion 

 of a particular force. If, then, the cord is neither perfectly in- 

 flexible, nor perfectly flexible, the effect of this imperfect flexi- 

 bility will be, that the point A passing to A', and the point C to 

 C', the parts A' p*, O q', will be a little bent, and in such a man- 

 ner that the weight p' will be farther from /, and the weight q' 

 nearer to it, than they would be if the cord were perfectly flexi- 



