THE KOYAL AKTILLEKY INSTITUTION. 
871 
Let C and C be the centres respectively of the axle and wheel, A 
the point of contact between the axle and pipe-box, B the point of 
contact between the wheel and ground; also, let the direction of the 
power meet the vertical through the centre of the axle in E. The 
forces acting upon the axle are P, W, and the resistance of the pipe- 
box. P and W have a certain resultant; let it be B, and let the angle 
its direction makes with the vertical be 0. Supposing the axle to be 
in a state of equilibrium, the resistance opposed by the bearing of the 
pipe-box must be equal and opposite to B; and further, supposing the 
axle to be just on the point of motion, the direction of the resistance 
must make an angle 0 with the normal to the point of contact. Hence, 
we have the angle EAC = 0, and the following relations, viz.:—- 
P cos /3 = R sin 0, . (1) 
P sin £ + B cos 0 = JF. . (2) 
The forces acting upon the wheel, are the pressure on the pipe-box, 
the weight of the wheel, and the resistance of the ground. Supposing 
the wheel to be in a state of equilibrium, the resultant of the first two 
must pass through B —the point of contact between the wheel and the 
ground. Calling the resultant B', and denoting the angle its direction 
makes with the vertical by O ', we have the following relations, viz.:— 
Also, 
and 
therefore, 
R sin 0 = B! sin O', ...(3) 
R cos 0 + W' — R! cos O' ... .....(4) 
sin 0 = sin f . 
AC _ AC _ AC CB _ AO sin & 
CE~ CD ~ OB' CD ~ OB' sin {6'-y)’ 
sin O' . sin 0 
sin {O' — y) 
(5) 
In order that the wheel may roll, it is only necessary that the 
direction of B! should fall to the left of the point P, instead of passing 
through it. 
If the wheel meet an obstacle, as at B the effect, when the wheel is 
on the point of surmounting it, is merely to change the point of contact 
from B to B', and increase the angle O' by an angle BBB'. 
V/heels in the service are classed according to the size of the pipe- 
box—viz., first (or siege), second (or field), third (or transport), and 
special. The scantling of the material for each particular part of a 
wheel is fixed for the class, the dimensions determined upon in each 
case being the results of experience. 
Passing on now to consider the component parts of the wheel in 
detail, and commencing with the nave, we see, from what has been said 
about friction, that the more play there is allowed between the pipe-box 
and the axletree-arm (that is, the greater the difference of their radii), 
