674 , MEC Hl'N I C S. 
force of prefllon ; and, when a lefs furface and other weights 
were ufed, the fridion was—-—, -, -- Similar 
a'30 2‘42 2'40 
refults u’ere obtained in all Coulomb’s experiments, even 
when metallic furfaces were employed. 
The fecond part of the proportion has alfo been efta- 
blidied by Coulomb. He found that the greateft: fridion 
is engendered when oak moves upon pine, and that it 
amounts to-- of the force of predion ; on the contrary, 
1 ' 7 ® 
when iron moves upon brafs, the leaf! fridion is produced, 
and it amounts to i of the force of predion. 
Prop. LXXX. Fridion is in general not increafed by aug¬ 
menting the rubbing furfaces .■—When a fuperficies of three 
feet fquare was employed, the fridion, with different 
freights, was 
at a medium ; but when a fmall furface 
Was ufed, the fridion inftead of being greater, as might 
1 
have been expeded, was only * 
Prop. LXXXI. Fridion for the mojl part is not augmented 
by an increafe of velocity. In fome cafes, it is diminifhed by 
an augmentation of celerity.— M. Coulomb found, that, 
when wood moved upon wood in the diredion of the 
fibres, the fridion was a conftant quantity, however much 
the velocity was varied ; but that, when the furfaces were 
very fmall in refped to the force with which they were 
prefied, the fridion was diminifhed by augmenting the rapidity; 
the fridion, on the contrary, was increaled when the 
furfaces were very large as compared with the force of 
prelfure. When the wood was moved contrary to the di- 
redion of its fibres, the fridion in every cafe remained th« 
fame. If wood be moved upon metals, the fridion is 
greatly increafed by an increafe of velocity; and, when 
metals move upon wood befmeared with tallow, the fric¬ 
tion is dill augmented by adding to the velocity. When 
metals move upon metals, the fridion is always a conftant 
quantity; but, when heterogeneous fubftances are em¬ 
ployed which are not bedaubed with tallow, the fridion 
is fo increafed with the velocity, as to form an arithmetical 
progrefiion when the velocities form a geometrical one. 
Prop. LXXXII. The fridion of loaded cylinders rolling 
upon a horizontal plane, is in the dired ratio of their weights, 
and the inverfe ratio of their diameters. —In Coulomb’s ex¬ 
periments, the fridion of cylinders of guaiacum w'ood, 
which were two inches in diameter, and were loaded with 
3000 pounds, was 18 pounds, or 3*5 of the force of predion. 
In cylinders of elm, the fridion was greater by and was 
fcarcely diminifhed by the interpofuion of tallow. 
From a variety of experiments on the fridion of the 
axes of pulleys, M. Coulomb obtained the following re- 
fults.—When an iron axle moved in a brafs bufii, the fric¬ 
tion was £ of the preffure ; but, when the bufh was be- 
fmeared with very clean tallow, the fridion was only fj-, 
when fwine’s greafe was interpofed, the fridion amounted 
to— ; and, when olive-oil was employed as an unguent, 
8-5 
the fridion was never lefs than § or — • When the axis 
TS . 
was of green oak, and the bufh of guaiacum-wood, the 
fridion was when tallow was interpofed ; but, when 
the tallow was removed, fo that a fmall quantity only co¬ 
vered the furface, the fridion was increafed to f?. Wiien 
the bufh was made of elm, the fridion was in iimilar cir- 
cumftances and which is the leaft of all. If the 
axis be made of box, and the bufh of guaiacum-wood, 
the fridion will be and circumfvances being the 
fame as before. If the axle be of box, and the bufh of 
elm, the fridion will be fy and ^ ; and, if the axle be 
©f iron and the bufh of elm, the fridion will be of the 
force of preffion. 
Having thus confidered the nature and effeds of fridion, 
we (hall now attend to the method of lefleningthe refift- 
ance which it oppofes to the motion of machines. The 
mod efficacious mode of accomplifhing this is to convert 
that fpecies of fridion which arifes from one body being 
dragged over another, into that which is occafioned by 
one body rolling upon another. As this will always 
diminifh the refiftance, it may be eafily effeded by ap¬ 
plying wheels or rollers to the fockets or bullies which 
fuftain the gudgeons of large wheels, and the axles of 
wheel-carriages. Cafatus feems to have been the firft who 
recommended this apparatus. It was afterwards men¬ 
tioned by Sturmius and Wollius ; but was not ufed in 
pradice till Sully applied it to clocks in the year 1716, 
and Mondran to cranes in 1725. Notvvithftanding thefe 
folitary attempts to introduce fridion-wheels, they feem to 
have attraded little notice till the celebrated Euler exa¬ 
mined and explained, with his ufual accuracy, their na¬ 
ture and advantages. The diameter of the gudgeons and 
pivots fhould be made as fmall as the weight of the wheel 
and the impelling force will permit. The gudgeons fhould 
reft upon wheels as large as circumftances will allow, hav¬ 
ing their axes as near each other as poflible, but no thicker 
than what is abfolutely necefTary to fuftain the fuperin- 
cumbent weight. When thefe precautions are properly 
attended to, the rtefiftance which arifes from the fridion 
of the gudgeons, See. will he extremely trifling. 
The effeds of fridion may likewife in fome meafure b» 
removed by a judicious application of the impelling power, 
and by proportioning the fize of the fridion-wheels to the 
preffure which they feverally fuftain. If we fuppofe, for 
example, that the weight of a wheel, whofe iron gud¬ 
geons move in bufhes of brafs, is ioo pounds; then the 
fridion arifing from both its gudgeons will be equivalent 
to 25 pounds. If we fuppofe alfo that a force equal to 
40 pounds is employed to impel the wheel, and ads in the 
diredion of gravity, as in the cafes of overfliot-wheels, 
the preffure of the gudgeons upon their fupports will then 
be 140 pounds, and the fridion 35 pounds. But, if the 
force of 40 pounds could be applied in fuch a manner as 
to ad in dired oppofition to the wheel’s weight, the pref- 
fure of the gudgeons upon their fupports would be 100—40, 
or 60 pounds, and the fridion only 15 pounds. It is im- 
poffible indeed to make the moving force ad in dired op¬ 
pofition to the gravity of the wheel, in the cafe of water¬ 
mills ; and it is often impradicable for the engineer to 
apply the impelling power but in a given way ; but there 
are many cafes in which the moving force may be fo 
exerted, as at leaft not tojncreafe the fridion which arifes 
from the wheel’s weight. 
When the moving force is not exerted in a perpendi¬ 
cular diredion, but obliqueiy, as in underfhot-wheels, 
the gudgeon will prefs with greater force oil one part of 
the locket than on any other part. This point will evi¬ 
dently be on the fide of the bufh oppofite to that where 
the power is applied ; and, its diftance from the lowefl: 
point of the focket, which is fuppofed circular and con¬ 
centric with the gudgeon, being called x, we (hall have 
pj 
tang. i that is, the tangent of the arch contained 
between the point of greateft preffure and the loweft point 
of the bufh is equal to the fum of all the horizontal forces 
divided by the lum of all the vertical forces and the weight 
of the wheel, H reprefenting the former and V the latter 
quantities. The point of greateft preffure being thus de¬ 
termined, the gudgeon mutt be fupported at that part of 
the largeft tridion-wheel, in order to equalize the fridion 
upon their axles. 
The application of thefe general principles to particular 
cafes is lo Ample as not to require any illustration. To 
aid the conceptions, however, of the pradical mechanic, 
we may mention two cafes in which fridion-wheels have 
been fuccefsfully employed, 
Mr 0j 
