C?5 
MECHANIC S. 
Mr. Gottlieb, the conftraftor of a new crane, has re¬ 
ceived a patent for what he calls an anti-attrition axle- 
tree, the beneficial effefts of'which he has afcertained by 
a variety of trials. It confilts of a fteel roller R, fig. 109, 
about four or fix inches long, which turns within a groove 
cut in the inferior part of the axle-tree C, which runs in 
the nave AB of the wheel. When the carriage wheels 
are at reft, Mr. Gottlieb has given the friction-wheel its 
proper pofition ; but it is evident that the point of greateft 
preffure will change when they are put in motion, and will 
be nearer the front of the carriage. This point, however, 
will vary with the weight of the load ; but it is fufficiently 
obvious that the friction.roller fhould be at a little dis¬ 
tance from the lowelt point of the axle-tree. 
Mr. Garnett, of Briltol, has applied fridtion-rollers in a 
different manner, which does not, like the preceding me¬ 
thod, weaken the axle-tree. Inftead of fixing them in 
k the iron part of the axle, he leaves a fpace between the 
nave and the axis to be filled with equal rollers almoft 
touching each other. A feftion of this apparatus is re- 
prefented in fig. no. where A B C D is the metallic ring 
inferted in the nave of the wheel. The axle-tree is repre- 
fented at E, placed between the friftion-rollers I, I, I, 
made of metal, and having their axes inferted into a circle 
of brafs which paffes through their centres. The circles 
are rivetted together by means of bolts palling between 
the rollers, in order to keep them feparate and parallel. 
As it appears from the experiments of M. Coulumb, that 
the lealt friction is generated when poliftied iron moves 
upon brafs, the gudgeons and pivots of wheels, and the 
axles of friction-rollers, fhould all be made of poliftied 
iron; and the bullies in which thefe gudgeons move, and 
the friCtion-wheels, ftiould be formed of poliftied brafs. 
When every mechanical contrivance has been adopted 
for diminifhing the obltruCtion which arifes from the at¬ 
trition of the communicating parts, it may be ftill farther 
removed by the judicious application of unguents. The 
moft proper for this purpofe are fwine’s greafe and tallow 
■when the furfaces are matTe of wood, and oil when they 
are of metal. When the force with which the furfaces 
are prefted together is very great, tallow will diminilh the 
friCtion more than fwine’s greafe. When the wooden 
furfaces are very fmall, unguents will lefien their fridion 
a little, but it will be greatly diminiftied if wood moves 
upon metal greafed with tallow. If the velocities, how¬ 
ever, are increafed, or the unguent not often enough re¬ 
newed, in both thefe cafes, but particularly in the laft, the 
xmguent will be more injurious than ufeful. The bell 
mode of applying it, is to cover the rubbing-furfaces with 
as thin a ftratum as pollible, for the fridion will then be' 
a conltant quantity, and will not be increafed by an aug¬ 
mentation of velocity. 
In fmall works of wood, the interpofition of the powder 
of black lead has been found very ufeful in relieving the 
motion. The ropes of pulleys fhould be rubbed with 
tallow; and, whenever the (crew is ufed, the fquare threads 
fhould be preferred. Appendix to Fergujon's Lettures. 
II. When ropes pais over cylinders or pulleys, a confi- 
derable force is necelfary to bend them into the form of 
the circumference round which they are coiled. The force 
■which is necelfary to overcome this refinance is called the 
Jliffnefs or rigidity of the ropes . This important fubjeCt was 
firft examined by Amontons, (Mem. Acad. 1699.) who 
contrived an ingenious apparatus for alcertaining the ri¬ 
gidity of ropes. His experiments were repeated and con¬ 
firmed in part by fubftquent philofophers, but particu¬ 
larly by M. Coulomb, who has inveltigated the fubjeft 
with more care and fuccefs than any ot his predeceflors. 
His experiments were made both with the apparatus of 
Amontons, and with one of his own invention ; and, as 
there was no great Jifcrepancy in the refults, he was au- 
ihorifed to place more confidence in his experiments. The 
limits of this article will not permit us ro give an account 
®f the manner in which the experiments were condu&edj 
or even to give a detailed view of the various conclufions 
which were obtained. We can only' prefent the reader 
with fome of tliofe leading refults which may be ufeful 
in the conftruction of machinery. 
1. The rigidity of ropes increafes, the more that the 
fibres of which they are compofed are twilled. 
2. The rigidity of ropes increafes in the duplicate ratio 
of their diameters. According to Amontons and Defa- 
guliers, the rigidity increafes in the fimple ratio of the 
diameters of the ropes; but this probably arofe from the 
flexibility of the ropes which they employed ; for Defa- 
guliers remarks, that, when he ufed a rope whofe diame¬ 
ter was half an inch, its rigidity was increafed in a greater 
proportion ; fo that it is probable that, if they had em¬ 
ployed ropes from two to four inches in diameter, like 
thole ufed by Coulomb, they would have obtained limi- 
lar refults. (SeeN°9.) 
3. The rigidity of ropes is in the fimple and direct 
ratio of their tenfion. 
4. The rigidity of ropes is in the inverfe ratio of the 
diameters of the cylinders round which they are coiled. 
5. In general, the rigidity of ropes is direftly as their 
tenfions and the fquares of their diameters, and inverfely 
as the diameters of the cylinders round which they are 
wound. 
6. The rigidity of ropes increafes fo little with the ve¬ 
locity of the machine, that it need not be taken into the 
account when computing the effects of machines. 
7. The rigidity of fmall ropes is diminifhed when pene¬ 
trated with moilture ; but, when the ropes are thick, their 
rigidity is increafed. 
8. The rigidity of ropes is increafed, and their ftrength 
diminifhed, when they are covered with pitch; but, when 
ropes of this kind are alternately immerfed in the lea 
and expofed to the air, they laft longer than when they 
are not pitched. This increafe of rigidity, however, is 
not lo perceptible in fmall ropes as in tliofe which are 
pretty thick. 
9. The rigidity of ropes covered with pitch is a fixth 
part greater during froft than in the middle of fummer; 
but this increafe of rigidity does not follow the ratio of 
their tenfions. 
10. The refiltance to be overcome in bending a rope 
over a pulley or cylinder may be reprefented by a for¬ 
mula compofed of two terms. The firft term is a 
r 
conltant quantity independent of the tenfion ; a beino- a 
conltant quantity determined by experiment, D" a power 
oj the diameter D of the rope, and r the radius of the 
pulley or cylinder round which the rope is coiled. The 
IT) 
fecond term of the formula is Tx-5 where T is the 
r 
tenfion of the rope, b a conftant quantity, and D” and 
r the famAas before. Hence the complete formula is 
aD" bT) n D" 
-|-TX-= Xrt+T<$. The exponent n of the 
r t ' 
quantity D diminifhes with the flexibility of the rope, but 
is generally equal to 1*7 or i - 8 ; or, as in N° 2, the rigi¬ 
dity is nearly in the duplicate ratio of the diameter of the 
rope. When the cord is much ufed, its flexibility is in- 
creafed, and n becomes equal to 1*5 or 1*4. 
Of WHEEL-CARRIAGES. 
When a wheel furmounts an obftacle, it a<fls as a lever 
of the firft kind, and its power to overcome fuch refin¬ 
ances increafes with its diameter. The power of the force 
P, Plate VIII. fig 1. to raife the wheel NB over the emi¬ 
nence C, is proportional to the vertical lever F C, which 
increafes with the diameter of the wheel, while the lever 
ot refiltance FA, by which the weight W of the wheel 
n<fts, remains unchanged; hence we fee the advantages of 
large wheels for overcoming fuch obltacles as generally 
relilt the motion of wheel-carriages. There are fome cir- 
2 cumftancesj 
