140 
MINUTES OF PROCEEDINGS OF 
If now the wheel meet an obstacle, the effect, when the wheel is on 
the point of surmounting it, is to change the point of contact with the 
ground from B to B '; or, in other words, ,to increase for the instant 
the slope of the ground by an angle equal to that subtended by the 
height of the obstacle at the point in which the tangent to the wheel, at 
the new point of contact, meets the line of the slope of the ground. 
Thus, in Fig. 1, the wheel meeting an obstacle whose height equals 
Fig. l. 
c' 
B'F, is tantamount to the slope of the ground being increased by the 
angle B'GF, B’l being drawn tangential to the wheel at B 1 ; for 
Z G1K = z IGH (= P'GP 1 ) -f Z GUI ; 
or, denoting the angle due to the obstacle by e, and the increased 
angle of the slope of the ground by y, 
and 
P = 
/ = c* + y, 
AC . ii 
. CC'B\ 1 + fB){ cos 3 /?. W 2 + sin 2 /.# 7 ' 2 + 
(sin 2 / + cos 2 0 - cos 2 (P -7) mV'\ - AC 2 . ^. cos 2 P . 7F 2 
CB 2 (1 + /x 2 ) cos Q8 - /) sin / (7F+ W) - AC* . . sin p . TV ( 
+ <7'P 2 Q 4- a 2 ) cos 2 (B — y'f — AC 2 . n 2 * 
* In the case of the wheel moving down an incline and meeting an obstacle, € is negative* 
