On the Nature and Laws of Friction. 7 
Ill. Of the Friction of Bodies when the Motion is uniformly 
accelerated. 
In this case the general proportion (6) remains the same as 
Hey Oretes : 1 
when the motion is uniform, that is I: cra 
But by the laws of accelerated motion the space abraded will 
be as the square of the velocity; the body being moved from 
rest. Therefore 7 ONS toe : 
And F :1IxA, becomes F: 1, (10). 
Consequently in this case friction is an uniformly retarding force, 
as Professor Vince has shown by his ingenious experiments. 
In the case of bodies moved from rest, the theory above stated 
fully explains the phenomena observed by Coulomb: it removes 
all the seeming anomalies respecting the friction of heterogeneous 
bodies, and enables us to determine the quantity of friction from 
the properties of bodies which have been investigated. The 
most convenient method of doing this is to change the general 
proportions into equations ; the constant members of which may 
be easily got from experiments. Let these constants be a, J,. 
and c¢, for the three cases then, 
In bodies moved from rest F=PXExCxa, 
Fa PXEXx€xs 
Vv 
In uniform motions 
And in uniformly accelerated motions, F=P x Ex C xc. 
Consequently when a, L, and ¢ are determined for one body, the’ 
friction of any other body may be found, its extensibility and co- 
hesive force being known, or the weight of its modulus of elas- 
ticity and cohesive force being known ; 
cohesive force * 
For weight of modulus = — 
extensibility 
The bodies should be free from any intermixture of hard par- 
ticles, otherwise these laws will not obtain: and it may be further 
observed, that friction is increased by introducing the fragments 
of hard bodies between the rubbing surfaces ; as these fragments 
become indented into the surfaces in proportion to their hard- 
ness, and consequently cause a greater degree of abrasion. On 
this principle the art of stone-sawing, &c. depends. On the 
contrary, the introduction of soft substances prevents the sur- 
faces acting upon one another, thus lessens the abrasion, and 
consequently the friction ; but in order that these substances may 
produce the desired effect, it is necessary that they should be of 
a sufficient degree of consistence to keep the bodies from in- 
denting into one another: hence it is that tallow answers better 
* An extensive set of tables of the cohesive force of bodies may be found 
in Phil. Mag. vol. L. p. 421, and the extensibility or modulus of elasticity 
may be got from Dr. T. Young's Nat. Phil. vol. ii. p. 509. 
A 4 than 
