198 On Friction ix Machinery ; 
is at present much in yogue, is not less remarkable for possessing 
‘the fault alluded to in the highest perfection. A person whois at 
all acquainted with the principles on which such teeth are formed, 
will readily perceive that wheels of this construction can only 
work smoothly, when their centres are exactly at a certain di 
stance from each other; and, that if this distance be any how 
altered, although in a small degree, they must act with great dis- 
advantage. Now there are many causes which may conspire to 
change this distance ; such as the bending of the several parts of 
the machine—the expansion and contraction.of metals by change 
of temperature. But the grand and fertile source of this mis- 
fortune, J presume, is contained in the sudden tapering figure of 
the teeth themselves, by which an almost irresistible repulsion is 
introduced between the wheels, in consequence of their mutual 
action being in a great measure directed to their centres. It is 
likewise plain, that if the distance of their centres is a very little 
augmented, the repulsion will be prodigiously increased, and have 
a tendency to go on increasing sine limite, especially when the 
wheels contain a small number of teeth. It may no doubt be 
alleged that all wheels have a tendency to repel each other; but 
certainly the more this is avoided, so much the better; and of 
course wheels are the nearer to perfection, according as the di- 
rection of their mutual action approaches to a coincidence with 
the perpendicular to a straight line joining their centres, pro- 
vided the teeth are fermed on strict mathematical principles : for 
it might easily be shown, that such wheels are not so prone to 
change their distance ; nor yet is the smoothness of their motion 
so soon disturbed, on the event of such achange taking place, as 
those of the tapering form are. 
In fine machinery, this unfortunate repulsion is seldom want- 
ing; for, though often in clock-work the teeth are quite of a 
superfluous length, yet as two wheels commonly little more than 
touch with the rounded ends of their teeth, we may rest assured 
they have their own share of repulsion. 
It is a common notion, (though only with the vulgar), that fric- 
tion is lessened by diminishing the rubbing surface ; but the sur- 
face may often be augmented with manifest advantage: because 
ordinarily where the pressure is confined to a small space, it soon 
‘creates heat sufficiently intense both to increase friction and also 
to dry up any unctuous application. 
Another vulgar notion js, that a machine moves easier after the 
wearing parts become heated ;—for immediately after the machine 
has been stopped, it is more easily set in uiotion than if it had re- 
mained at rest for a considerable time. But this seems only to 
be in conformity with the well known fact, that friction requires 
time aé rest to attain its maximum. ? 
t 
Was >. 
