1824.] 
For the Monthly Magazine. 
On the Necessity of applying Mathema- 
tical Principles in the Construction of 
Four-Wuecr CarriaceEs. 
YT AHNHOUGH none of the operative 
arts have received more encou- 
ragement from the opulent classes of 
society than coach-building, it must be 
evident that there is yet ample room 
for improving that art ;. the Greeks 
and Romans, were acquainted with a 
better principle than those now in use 
for giving action-to four-wheel carriages, 
though their mode of using that prin- 
ciple has not been transmitted to us, 
and must have been lost, like the art 
of making malleable glass, and other 
practical processes. 
The chief defects of the four-wheel 
carriages now in use are, first, their in- 
ability to turn as quick as the horses ; 2d. 
their liability to overset ; 3d. their heavi- 
ness n draft. ‘The first-mentioned de- 
fect is the chief cause of the» second, 
and both of them originate from two 
errors of construction, which shall be 
demonstrated presently; one is, that 
the centre of action is in a wrong 
place, viz., at the perch bolt of the fore 
carriage, and not where it ought to be, 
viz., half way between the two axles, at 
or under the centre of gravity, when the 
carriage is in a horizontal position ; and 
the other error is, that the hind axle or 
wheels have no lateral or spinning ac- 
tion like the fore ‘axle and wheels, the 
hind axle being fixed at right angles 
with the perch or longitudinal section 
of the body, and with the axis of both 
the bind wheels in the same right line. 
Here itis necessary, though unseason- 
able, to interrupt: this statement, in 
order to anticipate an exception which 
might be made to the plan above as- 
signed for the centre of action, because, 
when a carriage is turned short, without 
any progressive motion, the centre of 
action then appears to be in the hind 
axle, as one of the hind wheels then 
revolves backwards and the other for- 
wards, at which time the centre of ac- 
tion appears to be in the middle of the 
hind axle, or else the hind wheel of the 
side to which the carriage turns spins 
without revolving on the lowest part of 
its circumference, and the other hind 
wheel encireles the former which is idle, 
‘until it:obtains rotatory motion by get- 
ting into the line of draft: during which 
suspension of its rotatory motion, the 
centre of: action appears to be in that 
arm of the hind axle which is the axis 
On the Construction of Four-Wheel Carriages. 
301 
of the idle wheel. But it should be con- 
sidered, that the centre of action alluded 
to in this exception is the centre of the 
action or’ movement of the whole car- 
riage relatively to surrounding objects, 
but is not the centre of that action or 
movement which enables the carriage 
so to change its position without pro- 
gressive motion, for the latter is cer- 
tainly the true action of the carriage 
itself, and is at the perch bolt, and 
therefore it can at most be asserted, 
that the action of the carriage is thus 
divided between the fore and hind car- 
riage. But even if the exception be valid 
to the extent above stated, it only proves 
that the centre of action is occasionally 
in the hind axle, and consequently not 
at or under the centre of gravity, which 
is the right place. 
All the’ before-mentioned causes 
concur in oversetting a common car- 
riage when it makes a rapid turn on 
a descending road; and the danger 
is not a little increased by the dispro- 
portionate lowness of the fore-wheels, 
because the centre of gravity is by the 
descent thrown towards or over the 
fore-carriage, at the very moment when, 
by the turning of the fore axle and 
wheels, the slope of the road, and the 
change of the line of draft, the centre 
of gravity is left without adequate sup- 
port; and when the impetus which it 
acquired from the descent, sways the 
body of the carriage in the original di- 
rection, at that moment the hind wheels, 
instead of supplying the support which 
is wanted, are too slow in getting into 
the line of draft, and therefore contri- 
bute to make the catastrophe certain. 
The cause of another defect, viz. 
heaviness in draft, remains to be ex- 
plained; but the disproportionately small 
or low fore-wheels of common carriages 
has been so fully proved to be the chief 
cause of their heaviness in draft by wri- 
ters upon the subject, that it is needless 
here to enlarge further upon their solid 
arguments, than to say, that the small- 
ness or lowness of the fore-wheels is a 
direct and immediate consequence of 
misplacing the centre of action at the 
perch-bolt of the fore-carriage, because 
with that centre of action the fore- 
wheels must be small or low, to lock in 
near enough to the perch, and under the 
body of the carriage, to allow the fore 
axle to attain to an angle of at least 
45° with the fore transom. 
There are, however, several other 
causes of heaviness in draft inherent in 
common carriages; one is the necessity 
of 
