THE ROYAL ARTILLERY INSTITUTION. 
413 
Let W — the whole pressure communicated by the wheel to the ground, 
/x = co-efficient of friction between the surfaces of the tire and road, 
l = the length of the transverse section of the tire parallel to the axis. 
Ax = n n n any laminal disc. 
Then, 
At?? a • . 
W . = weight borne by any laminal disc, 
b 
W . —- . — = that fraction of the weight thus borne which at each 
Is 
instant is referable to friction, 
A x 
1 . -A = tangential friction exerted continuously upon the 
1 4 disc.(1) 
This applies equally to the discs on either side of the rolling line. 
Let OS (Fig. 1) = x, ST = y, AB = l, OB = n, FB = m } and let 
b = radius of the rolling disc. The cone, constrained to move in a straight 
line, is supposed to roll through an angle </>. Then the distance which has 
been travelled by the wheel is the distance which the rolling disc has rolled. 
. •. s — bf/)~ distance passed by every disc. 
And the disc at SI must have revolved a distance ST . </> = y $; therefore, being 
larger than the rolling disc, it must have rubbed a distance <j> ( y—b ) = s v 
Therefore for each disc larger than the rolling disc, 
£i y- b . 
s “ b 3 
and for each of those smaller than the rolling disc, by similar reasoning, 
£i b—y 
s b * 
•Si .. 
Substituting for -j its values in equation (1), 
Tangential friction = on one side, 
and 
= . — 7 -ff . At??, on the other side. 
i b 
Taking first a disc Tt on the larger side, the moment of its friction about 
the axis at S is the tangential friction multiplied by y 
Now, 
= ^ • O — %A*. 
A y y a — b 
Ax x n 
*•. Aa? = —~- . A y. 
a — b 
