712 
there may be some other advantages attending a devi- ; 
ation from this form, which will be afterwards examin- 
Fig. 1 ed. Thus A B, Fig. 1, would 
Oh likely be among the more early 
modes of constructing the axle, 
having shoulders at C and D, 
and iron bars called linch-pins 
B at Eand F, to keep the wheels 
G H and I K (having their 
planes perpendicular to their 
axis, and rendering their mo- 
tion of rotation by that means the easiest possible), 
steady in their proper position; the parts E C and 
D F, round which they revolve, being equal cylin- 
ders of the same diameter. In this mode, however, 
it would be found from experience, that the wheels 
would with difficulty, or at least Jess easily, be re- 
moved’ and replaced, more especially before the in- 
las 
ig 
vention of a machine for raising the:wheel from the 
ground, as is now usual, at least for gentlemen’s 
carriages. This would suggest the propriety of giv- 
ing the axle a slight taper towards its axis at the 
extremities, in order to remove the inconvenience. 
At the same time, the wheel may be prevented from 
becoming loose by wearing, by pressing the nave to- 
wards the shoulder, and tightening it by the linch-pin. 
The axle would then have the shape of a b, Fig. 2, 
Fig. 2. 
tapering all around regu- 
larly from ¢ toa, and from 
d to 6b, and the planes of 
the wheels gh, 7k, would 
i still be at right angles to 
the axis, rendering their 
circular motion the most 
i favourable for ease and 
simplicity. One bad property would result from this 
structure, namely a tendency of the wheels to slide 
off at the end of each axle, thus producing a consid- 
erable pressure on the linch-pins, at e and f, which 
would be both inconvenient and injurious, from the 
severe friction of the bushes in the naves against 
them. The upper parts of the wheels would, in 
both the preceding methods, be liable to rub or chafe 
the carriage, or the load when it projected over the 
sides of the cart; while in wet weather the mud car- 
ried up by them would partly be thrown into the 
cart, and would partly fall upon the axle and nave, 
and work in between the axle and bush, causing a 
considerable wear in both in a short time. 
To obviate these inconveniences, it would next be 
requisite to render the lower surface of the tapering 
and working part of the axle called the arm perfectly, 
or at least nearly, horizontal, so that the pressure on 
it should have no tendency to force off the wheel, 
and make it press unnecessarily on the linch-pins, 
while the upper parts of the wheels by this means 
would be thrown outwards from the load, and would 
move quite free of it. Indeed, it seems to be sanc- 
tioned by experience, that the axle should be slightly 
bent at the shoulder, in order to give the wheel a 
tendency to press upon the axle rather than on the 
linch-pin. By this we get free of one or two diffi- 
a) Ff 
culties, though others of a different kind are intro- 
Fig. 3. 
duced. 
Let AB, Fig. 3, be the axle, having its under side 
nearly a straight line, the extremities PA, AB, ta- 
pering within the naves; then the planes of the wheels 
become oblique to the horizon: the exterior surface 
W HEEL-CARRIAGE. 
of the felloes must be bevelled so as to become a 
small frustrum of a cone, the vertices of which are 
about @ and X, thus introducing oblique action in 
motion, and an unfavourable position of the spokes 
of the wheels, with regard to strength, since they 
must be strongest when perpendicular to the level 
plane @HOX. This last evil may be corrected by 
dishing the wheels, as it is called, while the oblique 
motion of the wheels arising from their necessarily 
conical shape, produces less injury in ordinary cir- 
cumstances than that derived from the pressure of 
the nave against the linch-pins in equally tapering 
axles. Hence, if the under surface of the axle be 
straight, the quantity or amount of the dishing ought 
to depend upon the angle of taper of the axle, the 
one being exactly equal to the other. For let AB, 
fig. 4, be a horizontal line, Fig. 4- 
and CD a vertical line at right B a 
angles to it. Also, let EF be 
a part of the axis, or central 
line of the tapering axle, and ib 
GH a perpendicular to it, B 
passing through O as before. — 
Then the angles AOD, EOH 
are right angles. From each 
take away the common angle Z HE 
EOD, and there remains the angle AOE equal to 
DOH; that is, to bring the under part OH of the 
oblique wheel GH into the vertical position OD, it 
must decline from the plane of the oblique wheel GH 
at an angle of dishing HOD, equal to AOE, which 
the oblique central line of the axle makes with the 
horizontal line AB. If this principle be attended to, 
the spokes will, on a road nearly level, be truly ver- 
tical, or in the strongest position, as in this situation 
they ought to be. ’ 
In the case of iron axles, the taper is in general 
small, and perhaps would not, in many cases, be suf- 
ficient for the required quantity of dishing, which 
should be about one-twelfth of the diameter of the 
wheel; whence this easy practical rule,—the diame- 
ter of the wheel in feet gives the dishing in inches. 
Then a moderate bend in the axle will be requisite 
to bring them nearly to an equality, though the dish- 
ing should be properly a little more, not exceeding 
an inch or two, taking the direction OI; so that, 
when the carriage is inclined in a small degree, the 
under spokes are truly vertical. On these princi- 
ples, let « e, Fig. 5, be the central line or axis of the 
cylindrical portion of the axle within the naves, to 
which x is perpendicular, similarly to EH, Fg. 3, 
and ¢ ~ perpendicular to the under surface of the axle; 
then, as has just been demonstrated in last article, 
ica 
V1 
W 
Fig. 4, itis obvious, that the angle 1 ¢ 4 is equal to the 
inclination of ze to the sole of the axle. ‘The taper 
consequently ought to regulate the amount of the 
dishing when properly executed, so that the spokes, 
in ordinary circumstances, may be nearly perpendi- 
cular to the plane of the road. Whence ¢ ¢% and éo. 
give the dished shape of the wheels; and, to make 
the dishing moderate, the taper of the extremities of 
the axle, combined with the bend, should not, taken. 
together, be great. Hence also the stability of the 
carriage is not injured by this mode of dishing, be- 
cause the centre of gravity is in as favourable a situ- 
ation as if the wheels were actually vertical, since 
the spokes in the under part of the wheels are nearly 
vertical, however different the distance between the 
