On the Nature and Laws of Friction. 



21 



Of that Part of the Resistance of a Wheel-carriage that arises 

 from Friction at the Axis. 



B. — If a wheel, of which the radius of the axis is CA (fig. A) 



XZ>^ 



and the radius of the wheel C B, be put in motion over a hori- 

 zontal plane D E, and the wheel slides ; then, the friction at the 

 axis multiplied into the radius of the axis, is greater than the fric- 

 tion at the circumference of the wheel multiplied into its radius. 



For the weight of the load acts in a vertical direction ; and when 

 the wheel is devoid of friction both at the axis and circumference, 

 a very small force in the horizontal direction C F would cause it 

 to roll forward. Again ; suppose there to be friction at the axis 

 only, then the horizontal force would cause the wheel to slide in 

 the same manner as if the wheel and axis were one bodv; be- 

 cause in that case friction at the circumference would be neces- 

 sary to destroy the effect of the friction at the axis, and to cause 

 the wheel to move round it. Now consider C as the centre of 

 motion; then the friction at the circumference acts with a lever- 

 age equal to the radius of the wheel, that at the axis with a lever- 

 age equal to the radius of the axis. Let R be the radius of the 

 wheel, and F the friction at the circumference, r the radius of 

 the axis, and f the friction of the axis. By the property of the 

 lever, we have R x F = r x /in the case of equilibrium. And 

 when R X F is less than r xf, the difference places the wheel in 

 the same state as when there is a friction ecpial to that difference 

 at the axis only, consetiuently the wheel would slide. 



Cor.— Hence it appears that in practical cases a wheel will al- 

 ways roll, as the conditions necessary to produce a sliding motion 

 are scarcely within the limits of possibility. For if the rubbing sur- 

 faces at the circumference had only the friction of polished glass, 

 while those at the axis had the friction of wood, the wheel would 

 roll when the radius of the wheel exceeded three times the radius 

 of the axis. 



B 3 C— The 



