6 On the Nature and Laws of Friction. 
it can only be torn away to the depth which the more coherent 
body indents into it, in the general proportion 
. F:PXExC, (4) 
E must be the extensibility of the more coherent body, and C 
the cohesion of the other body. 
Consequently,—adhering to the definitions of hardness, &c. 
given in a preceding note,—a hard body moving on a soft one 
will have less friction than a hard body rubbing against a hard 
body, or a soft body moving on a soft one. But a tough body 
‘moving on a brittle one, will have more friction than brittle mov- 
ing on brittle, or tough on tough bodies, These are important de- 
ductions in a practical point of view, particularly when it is re- 
collected that Coulomb obtained results which agree with them, 
in his experiments on friction. 
II. Of the Friction of Bodies in Motion when the Motion is 
uniform. 
In the preceding investigation the indentation was supposed to 
have reached its maximum. This, however, cannot be the case 
when the body is in motion, unless this motion be very slow. 
But when the indentation does not attain its maximum, it will 
vary directly as the extensibility, the force, and square of the 
time, and inversely as the area of the surface; or, because the 
other quantities are constant in the same body, putting T for the 
time, we have 
but, ds 
But the time is inversely as the velocity of the body; and sub- 
stituting this value of T, we have 
i 
I : ve 3 (6). 
Also, the surface abraded, in a given time, will be as the area of 
the body, and the space passed over: therefore 
A:V.L. B.C, or because L. B.C is a constant quantity for 
the same body, > piglets Miyep: Cai is 
1 
By Prop. (1) F:1xA, therefore F: vy? (8). 
In uniform motions, then, the friction is inversely as the velocity. 
hesion is a maximum, and the extensibility a minimum, the body may be 
called hard : and when the cohesion is a minimum, and the extensibility a 
maximum, the body may be.called soft. Consequently the hardness would 
C F : ? Jf RS 
be as rer if M be the weight of the modulus of elasticity = ==: 
: } F 
then, we have hardness : M ; softness : re toughness : CE; and brittle- 
1 
ness: 7, And the friction of tough bodies would be the greatest, and 
that of brittle bodies the least. ; 
Ill. Of 
