On the Nature and Laws of Friction. 5 
Assuming, then, that the surfaces are actually abraded in the 
case of motion, and that the magnitude of the base of each in- 
dented part is proportional to the depth of indentation; also 
let F be the friction; I the depth of indentation; and A the 
force necessary to abrade or tear the surfaces indented together: 
then FTA.’ (1) 
That is, the friction is directly as the depth of indentation and 
the resistance to abrasion. 
I. Of the Friction of Bodies moved from Rest. 
When the surfaces of bodies are pressed together, whether it 
be from the weight uf one of the bodies or any other force, a cer- 
tain time must elapse before the indentation is a maximum ; 
which, when the modulus of elasticity of the body is known, may 
be easily determined from the principles of dynamics. But in the 
case now under consideration the body is supposed to be moved 
from rest, and consequently that the indentation is a maximum 
and proportional to the pressure: call this pressure P. And as the 
extension and compression of hodies are equal when the forces 
are equal, Jet the extension corresponding to the weight that would 
produce fracture be denoted by E; also make L=the length, and 
B = the breadth of the surfaces in contact. 
Now the indentation will be directly as the pressure and the 
extensibility, and inversely as the length and breadth ; that is, 
Px 
1: aa ned : 
The resistance to abrasion will be directly as the surface and as 
the cohesive force of the body; and let C be the cohesive force, 
then A: LxBxC.. (3) 
But by the general proportion (L}E. Doe A, 
therefore, by Prop. (2) and (30 Fiebxc Beaei€ (4) 
Hence it appears that when bodies of the same kind are moved 
from rest, the friction is as the pressure, as has been shown by 
experiments. It also appears that the friction is directly as the 
extensibility and cohesion ; or that body which bends the most, 
and sustains the greatest weight at the time of fracture, will have 
the greatest degree of friction, and vice versd *, 
Hitherto the rubbing surfaces have been considered to be of 
the same material: but when the materials are of different kinds, 
that which has the least cohesive force will be abraded ; and as 
1t 
* There are several qualities of bodies which depend on the cohesion 
and extensibility ; but their names convey a very imperfect idea of their na- 
ture. The following definitions are submitted for the consideration of the 
reader. 
When the extensibility and cohesion are at the least, I would call the body 
brittle. When they are a maximum, f would eall it tough. When the co- 
A3 hesion 
