182
VI
ON HARDNESS
this value we can make this assertion, that all contacts with a
circular surface of pressure for which
2 / 3p (P11 +P₁₂+ P21 + Pag)² < H,
(F₂+ F₂)²
3p
Z₂
=
=-
2παλ
or for which
22
P(P11 +P12+ P21 +29)² <
(D1 + D2)²
can be borne, and only these.
TSH3
24
The force which is just sufficient to drive a point with
spherical end into the plane surface of a softer body, is pro-
portional to the cube of the hardness of this latter body, to
the square of the radius of curvature of the end of the point,
and also to the square of the mean of the coefficients 9 for the
two bodies. To bring this assertion into better accord with
the usual determinations of hardness we might be tempted
to measure the latter not by the normal pressure itself, but
rather by its cube. Apart from the fact that the analogy
thus produced would be fictitious (for the force necessary to
drive one and the same point into different bodies would not
even then be proportionate to the hardness of the bodies), this
proceeding would be irrational, since it would remove hardness
from its place in the series of strengths of material.
Though our deductions rest on results which are satis-
factorily verified by experience, still they themselves stand much
in need of experimental verification. For it might be that
actual bodies correspond very slightly with the assumptions of
homogeneity which we have made our basis. Indeed, it is
sufficiently well known that the conditions as to strength near
the surface, with which we are here concerned, are quite different
from those inside the bodies. I have made only a few experi-
ments on glass. In glass and all similar bodies the first trans-
gression beyond the elastic limit shows itself as a circular crack
which arises in the surface at the edge of the compressed surface,
and is propagated inwards along a surface conical outwards when
the pressure increases. When the pressure increases still
further, a second crack encircles the first and similarly pro-
pagates itself inwards; then a third appears, and so on, the
phenomenon naturally becoming more and more irregular.