WHEEL 
posed by some of the best authors that the 
epicycloidal tooth has also the advantage of 
completely avoiding friction ; this is how- 
ever by no means true> and it is even im- 
pi acticable to invent any form for the teeth 
of a wheel, which will enable them to act 
on other teeth without friction. In order 
to diminish it as much as possible, the teeth 
must be as small and as numerous as is con- 
sistent with strength and durability ; for the 
effect of friction always increases, with the 
distance of the point of contact from the 
•line joining the centres of the wheels. In 
calculating the quantity of the friction, the 
velocity with which the parts slide over 
each other has generally been taken for 
its measure ; this is a sliclit inaecuracy 
of conception fir it is certain that, the 
actual resistance is not at all increased by 
increasing the relative velocity ; but the 
effect of that resistance, in retarding the 
motion of the wheels, mayvbe shown, from 
the general laws of mechanics, to be propor- 
tional to the relative velocity thus ascer- 
tained. When it is possible to make one 
wheel act on teeth fixed in the concave sur- 
face of another, the friction may be thus di- 
minished in the proportion of the dif- 
ference of the diameters to their sum. It 
the face of the teeth, where they are in con- 
tact, is too much inclined to the radius, 
their mutual friction is not much affecteel, 
but a great pressure on their axis is pro- 
duced ; and this occasions a strain on the 
machinery, as well as an increase of the 
friction on the axis. If it is desired to pro- 
duce a great angular velocity witli the 
smallest possible quantity of wheel-work, 
the diameter of each wheel must be be- 
tween three and four times as great as that 
of the pinion on which it acts. Where the 
pinion impels the wheel, it is sometimes 
made with three or four teeth only ; but it 
is much better in general to have at least 
six or eight ; and considering the addi- 
tional labour of increasing the number of 
wheels, it may be advisable to allot more 
teeth to each of them than the number re- 
sulting from the calculation ; so that we 
may allow thirty or forty teeth to a wheel 
acting on a pinion of six or eight. In 
works which do not require a great degree 
of strength, the wheels have sometimes a 
much greater number of teeth than this ; 
and on the other hand, an endless screw or a 
spiral acts as a pinion of one tooth, since it 
propels the wheel through the breadth of 
one tooth only in each revolution. For a 
pinion of six teeth, it would be better to 
have a wheel of thirty-five or thirty-seven 
WORK. 
than thirty-six ; for each tooth of the wlieel 
would thus act in turn upon each tootli of 
the pinion, and the work would be more 
equally worn than if the same teeth conti- 
nued to meet in each revolution. The teeth 
of the pinion should also be somewhat 
stronger than those of the wheel, in order to 
support the more frequent recurrence of 
friction. It has been proposed, for the 
coarser kinds of wheel-work, to divide the 
distance between the middle points of two 
adjoining teeth into thirty parts, and to 
allot sixteen to the tooth of the pinion, and 
thirteen to that of the wheel, allowing one, 
for freedom of motion. 
The wheel and pinion may either he si- 
tuated in the same plane, both being com- 
monly of the kind denominated spur- 
wheels, or their planes may form an angle ; 
in this case one of them may be a crown or 
contrate wheel ; or both of them may be 
bevelled, the teeth being cut obliquely. 
According to the relative magnitude of the 
wheels, the angle of the bevel must be dif- 
ferent, so that the velocities of the wheels 
may be in the same proportion at botli ends 
of their oblique faces ; for this purpose, the 
faces of all the teeth must be directed to the 
point where the axes would meet. In 
cases where a motion not quite equable is 
required, as it sometimes happens in the 
construction of clocks, hut more frequently 
in orreries, the wheels may either be di- ^ 
vided a little unequally, or the axis may be 
placed a little out of the centre ; and these 
eccentric wheels may either act on other 
eccentric wheels, or if they are made as 
' contrate wheels, upon a lengthened pinion. 
An arrangement is sometimes made for se- 
parating wheels which are intended to turn 
each other, and for replacing them at plea- 
sure ; tlie wheels are said to be thrown by 
these operations out of gear and into gear 
again. When a wheel revolves round 
another, and is so fixed as to remain nearly 
in a parallel direction, and to cause the 
central wheel to turn round its axis, the ap- 
paratus is called a snn and planet wheel. In 
this case, the circumference of the central 
wheel moves as fast as that of the revolving 
wheel, each point of which describes a 
circle equal in diameter to the distance of 
the centres of the two wheels; conse- 
quently, when the wheels are equal, the 
central wheel makes two revolutions, every 
time that the exterior wheel travels round 
it. If the central wheel be fixed, and the 
exterior wheel be caused to turn on its own 
centre during its revolution, by the effect of 
the contact, of the teeth, it will make in 
