THE KOYAL AltTILLEKY INSTITUTION. 
369 
PRINCIPLES 
CONSTRUCTION OF WHEELS AND AILETREES. 
CAPTAIN W. KEMMIS, R.A. 
The “ object” of using wheels is to lessen the resistance to the 
movement of a carriage over the ground, by converting that resistance 
from one of “ sliding ” friction, or the friction of a surface of contact, 
to one of “ rolling” friction, or the friction of a line of contact. 
When wheels are used, rolling friction is developed not only between 
them and the carriage body—that is, between their pipe-boxes and the 
axletree-arms—but also between them and the ground; the first men¬ 
tioned portion of the friction alone resists the movement of the carriage, 
the second prevents the wheel from sliding. 
The wheel, in carrying out its object, attains, from its form, some 
minor advantages, thus :—Suppose, for simplicity, the carriage standing 
on the level, and power applied to move it at the axis of the axletree 
in a direction perpendicular to the latter and parallel to the ground; 
then, the friction between the pipe-box and axle, which tends to 
prevent the wheel turning, acts with a leverage equal to the radius of 
the pipe-box, while the power making the wheel to roll acts with a 
leverage equal to the radius of the wheel; thus the power has an ad¬ 
vantage over the friction in the proportion of the radius of the wheel 
to that of the axle. Again, if the wheel meets a small obstacle in its 
path, the power, with regard to that obstacle, has a greater leverage, 
measured by the perpendicular let fall from the point of contact upon 
its direction, than the resistance of the weight, measured in a similar 
manner. This gain is true, as stated, with regard to small obstacles 
only; when the height of an obstacle exceeds a certain limit, it is 
manifest that the gain no longer holds good. If the obstacle, instead of 
being raised, be in the form of a transverse rut, the wheel gives a 
further advantage, proportional to its radius, in spanning the rut. 
Setting aside special obstacles in a road to the motion of a wheel, 
certain what may be called imperfections exist in every road, which, as 
well as irregularity of form in the wheel itself, oppose some resistance 
to rolling. Such imperfections are: unevenness of surface, want of 
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