On the Nature and Laws of Friction. 25 



II. The resistance at the circumference of the wheel is directly 

 as the cube root of the fourth power of the weight of the load. 

 That is, representing I 3 ^ 3 g -, g ^.^ 



the weights by J 



the corresponding 1 , 2-5, 4-3,6-35, 8-55, 10-9, 13-4, 16,&c. 



resistances will bej ' ' ' 

 Whence it appears, that a weight of eight tons will produce six- 

 teen times as much resistance at the circumference as a weight 

 of one ton; and consequently, that there is a material advan- 

 tage in carrjing small loads, and increasing the number of car- 

 riages, instead of placing an immense load upon a single pair of 

 wheels. 



III. The resistance at the axis increases directly as the radius 

 of the axis ; or in other words, the resistance of an axis four inches 

 diameter will be twice the resistance of one two inches diameter; 

 and so on. Therefore, the smaller the axis can be made the bet- 

 ter, so that it be of sufficient strength. 



IV. When the direction of the moving power is parallel to the 

 plane or road, the resistance at the axis is inversely as the radius 

 of the wheel. That is, by doubling the radius of the wheel the re- 

 sistance at the axis would be reduced one-half, and so on. 



V. Also, when the direction of the moving power is parallel 

 to the road, the resistance at the circumference of the wheel is 

 inversely as the cube root of the square of the radius of the wheel. 

 That is, representing a series of radii by the numbers 



1,2, 3, 4, '5, 6, 7, 8, &c.; 

 the corresponding ' 1 1 » |_ _i_ _}_ _} J. &c 



resistances will be / ' Tss' ?^' ^-m' ?9 ' s-s' s-ce' 4' 

 From which it it appears that the resistance decreases very rapidly 

 as the height of the wheel increases. But in wheel-carriages 

 drawn bv horses the height of the wheels is limited. In a car- 

 riage moved by steam, the height of the wheels might be much 

 increased ; and it appears to me to be perfectly possible to con- 

 struct such a machine that would move on the common roads. 



VI. The resistance at the axis is inversely as the velocity. That 

 is, a wheel moving with a velocity of three miles an hour will 

 have double the friction at the axis that a wheel moving at the 

 rate of six miles an hour will have. 



VII. The resistance at the circumference of a wheel is as the 

 cube root of the sfjuare of its velocity. Hence, if the velocities be 

 expressed by the series 1, 2, 3, 4,5, 6, 7, 8, &c.; 



the resistance at "j 1 1 1 i 1 1 



the circumference V 1, -^, j:^^, 7:37, 7.^, ITJ, 7^»T' *^''^* 

 will be . , . . J 



Conseciuently, the resistance both at the axis and circumference 

 decreases as the vclocitv increases. Common observation has sa- 

 tisfied 



