VI
181
ON HARDNESS
one.
surface of pressure in different materials, and that the positions
of the points of hardness in the surface of strength may be
very dissimilar.
We have to remark that the second body
which was used to determine the hardness of A might have
been of the same material A; we therefore do not require a
second material at all to determine the hardness of a given
This circumstance justifies us in designating the above
as an absolute measurement. To prove the second point,
suppose two bodies of different materials pressed together; let
the surface of pressure be circular; let the hardness, defined as
above, be for one body H, for the second softer one h.
If now
we increase the pressure between them until the normal
pressure at the origin just exceeds h, the body of hardness h
will experience a permanent indentation, whilst the other one
is nowhere strained beyond its elastic limit; by moving one
body over the other with a suitable pressure we can in the
former produce a series of permanent indentations, whilst the
latter remains intact. If the latter body have a sharp point
we can describe the process as a scratching of the softer by
the harder body, and thus our scale of hardness agrees with
the mineralogical one. It is true that our theory does not
say whether the same holds good for all contacts, for which
the compressed surface is elliptical; but this silence is justifi-
able. It is easy to see that just as hardness has been defined
by reference to a circular surface of pressure, so it could have
been defined by assuming for it any definite ellipticity. The
hardnesses thus diversely defined will show slight numerical
variations. Now the order of the bodies in the different
scales of hardness is either the same, or it is not. In the first
case, our definition agrees generally with the mineralogical one.
In the second case, the fault lies with the mineralogical
definition, since it cannot then give a definite scale of hardness
at all. It is indeed probable that the deviations from one
another of the variously defined hardnesses would be found
only very small; so that with a slight sacrifice of accuracy we
might omit the limitation to a circular surface of pressure
both in the above and in what follows. Experiments alone
can decide with certainty.
Now let H be the hardness of a body which is in contact
with another of hardness greater than H. Then by help of