THE ROYAL ARTILLERY INSTITUTION, 
141 
Let h =5 tlie height of the obstacle; then 
sin c (= Z B'C'B) = 
\/n . C'B — h* 
C'B 
(C) 
which determines the value of c. 
Every road, no matter how apparently good, has its imperfections— 
namely, in its want of perfect smoothness and hardness; and every 
wheel, no matter how apparently true, in the same manner, has its irre¬ 
gularities of form. These defects oppose the motion of the wheel—-in 
fact, place an obstacle of more or less magnitude continually in its 
path tantamount to an incline of more or less slope; so that whether 
on the level or on sloping ground, there is always an angle e to be 
taken into account. 
Suppose the wheel to be on a level road, and the direction of the 
traction to be parallel to the ground, then in the equation for P the 
angle /?==<?, y = o, and y = e; so that the equation becomes 
AC . fx VCB 3 (1 + /x 3 ) ( W 3 + sin 3 c . W'* + 2 sin 3 e . WW‘) -AC*. ,x* . W* 
CB 3 (1 + \j*) — AC'* . [x* 
CB* (1 + fx*) cos e . sin c . {JF -{- W) 
CB* (1 + fx*) — AC*.[x* . 
Imagine now, under the same circumstances, the road to be most 
favourable for traction (more so than ever practically met with), 
opposing but a very slight obstacle to the wheel—one of so small 
height as only sufficient to call into play the maximum resistance of 
friction between the pipe-box and the axletree-arm; then the equation 
approximates to 
P= AC.jx.W ^ 
VCB*{l+fx*)-AC*.fx* . V ; 
From which it appears that on a hard level road the traction or 
amount of power necessary to put a wheel in motion is directly propor¬ 
tional to the radius of the pipe-box, the co-efficient of friction between 
the pipe-box and axle, and the weight of and upon the axle, while it is 
approximately inversely proportional to the radius of the wheel. 
It is evident that this equation (or any former one for P), though 
deduced from consideration of a single wheel, requires no modification 
to make it suitable for the traction of any two-wheeled carriage, or 
four-wheeled carriage with fore and hind wheels of equal height. It is 
simply necessary to give W its proper value—namely, the weight of the 
carriage body and its load. If, however, it is required to ascertain the 
traction of a “ lock-under ” wagon, in which the fore wheels are of 
smaller diameter than the hind, it is obvious that the traction of the 
fore and hind carriage must be calculated separately, JF being given in 
each case an appropriate value—namely, that proportion of the weight 
of the carriage body and load borne by the particular pair of wheels; 
the total traction being then taken as the sum of that of the parts. 
Applying, in this manner, the formula for P to wagons, one or two 
inferences may be drawn from it. 
