WHEEL WORK. 
not be admissible for us to give the whole of 
the reasonings of that correspondent as 
contained ii;i various numbers ; but from 
that vvliich we have particularized we have 
the pleasure to furnish the following extract ; 
or, at least, the sense of it. 
“ If the fore-wheel be four feet four 
inches in height, and the line of traction 
(draught) be drawn at an elevation of 
twelve degrees from the centre of its axle, 
' the point where that line cuts the circum- 
ference of the wheel in its front, gives that 
height from the plane on which the carriage 
stands, that will determine the radius of the 
hinder w'heel. In this instance the hind- 
wheel would have a radius of two feet nine 
inches, giving of course live feet six inches 
for its diameter.” 
A view of the plate given in that work, 
not only will illustrate the above explana- 
tion, hut will satisfy a person respecting 
the justness of the proportions above de- 
tailed ; when tempered by the following 
cautions, we consider the instruction given 
to be admirable. “ The fore-wheel ought 
to be as nearly level witli the point of 
draught, that is, where the shaft is suspend- 
ed by the gear, as may be convenient ; ob- 
serving, that an angle of twelve degrees is 
to be given on account of the dilference be- 
tween the horse’s height as he stands at rest, 
and the real-altitude of the point of draught 
from the ground, when he is in a state of 
exertion. During great efforts, horses lose 
very considerably of their standard, and 
thus bring the shaft to nearly a parallel 
with the plane on which they move. Atten- 
tion must be paid to keeping the wheel 
within such limits as may not trespass on 
other matters, often of more consequence 
even than ease of draught; loading, turn- 
ing, weight, expense, &c. must always form 
a part of the calculation.” 
\V HEEL work. Of all the modes of com- 
municating motion, the most extensively 
useful is the employment of wheel-work, 
which is capable of varying its direction and 
its velocity without any limit. 
Wheels are sometimes turned by simple 
contact with each other ; sometimes by the 
intervention of cords, straps, or chains, 
passing over them ; and in these cases the 
minute protuberance of the surfaces, or 
whatever else may be the cause of friction, 
prevents their sliding on each other. Where 
a broad strap runs on a wheel, it is usually 
confined to its situation, not by causing the 
margin of tlie wheel to project, but, on the 
contrary, by making the middle prominent ; 
the reason of this may be understood by 
exarnining the manner in which a tight strap 
running on a cone would tend to run to- 
wards its thickest part. Sometimes also 
pins are fixed in the wheels, and admitted 
into perforations in the straps ; a mode only 
practicable where the motion is slow and 
steady. As raooth motion may also be ob- 
tained, with considerable force, by forming 
the surfaces of the wheels into brushes of 
hair. More commonly, however, the cir- 
cumferences of the contiguous wheels are 
formed into teeth, impelling each other, as 
W'ith the extremities of so many levers, ci- 
ther exactly or nearly in the common direc- 
tion of the circumferences ; and sometimes 
an endless screw is substituted for one of 
the H’heels. In forming the teeth of wheels, 
it is of consequence to determine the curva- 
ture which will procure an equable commu- 
nication of motion, with the least possible 
friction. For the equable communication 
of motion, two methods have been recom- 
mended ; one, that the lower part of the 
face of each tooth should be a straight line 
in the direction of the radius, and the upper 
a portion of an epicycloid, that is, of a curve 
described by a point of a circle rolling on 
the wheel, of which the diameter must be 
half that of the opposite wheel ; and in 
this case it is demonstrable that the plane 
surface of each tooth will act on the curved 
surface of the opposite tooth so as to pro- 
duce an equable angular motion in both 
wheels ; the other method is, to form all the 
surfaces into portions of the involutes of cir- 
cles, or the curves described by a point of a 
thread which has been wound round the 
wheel, while it is uncoiled ; and this method 
appears to answer the purpose in an easier 
and simpler manner than the former. It 
may be experimentally demonstrated, that 
an equable motion is produced by the 
action of these curves on each other ; if 
we cut two boards into forms terminated 
by them, divide the surfaces by lines into 
equal or proportional angular portions, and 
fix them on any two centres, we shall find 
that as they revolve, whatever parts of the 
surfaces may be in contact, the correspond- 
ing lines will always meet each other. 
Both these methods may be derived 
from the general principle, that the teeth of 
the one wheel must be of such a form, that ^ 
their outline may bd desciibed by the re- 
volution of a curve upon a given circle, 
while the outline of the teeth of the other 
wheel is described by the same curve re- 
volving within the circle. It has been sup- , 
O 0 2 
