370 
MINUTES OF PROCEEDINGS OF 
perfect hardness, and want of perfect elasticity. The first defect 
causes obstacles to be presented to the wheel at each instant; the 
second—want of perfect hardness—causes the ground to yield, so that 
the wheel in its onward progress is continually opposed by the materials 
of the road immediately in its front. In the case of a perfectly elastic 
road, this would be of no consequence; for the compressed materials, as 
the wheel passed over them, would expand again just so much as com¬ 
pressed, and in so doing would react upon the wheel in rear with the 
same amount of force as expended by the wheel in compressing them. 
The relations between the forces which act upon the wheel and axle 
are shown in Fig. 1, and may briefly be stated as follows:—• 
W = half weight of axle and load, 
W'z= weight of wheel, 
P =s traction or power, its direction making an angle /3 with the 
horizontal, 
(j) = limiting angle of resistance between the pipe-box and wheel, 
y — angle of slope of the ground. 
Fig. 1. 
