178
VI
ON HARDNESS
so as not to exceed the elastic limits. All these causes together
preclude our obtaining any but very imperfect curves of pressure,
and in measuring these there is room for discretion. I obtained
values which were always of the order of magnitude of those
calculated, but were too uncertain to be of use in accurately
testing the theory. However, the numbers given show con-
clusively that our formulæ are in no sense speculations, and
so will justify the application now to be made of them. The
object of this is to gain a clearer notion and an exact measure
of that property of bodies which we call hardness.
The hardness of a body is usually defined as the resist-
ance it opposes to the penetration of points and edges into it.
Mineralogists are satisfied in recognising in it a merely com-
parative property; they call one body harder than another
when it scratches the other. The condition that a series of
bodies may be arranged in order of hardness according to this
definition is that, if A scratches B and B scratches C, then A
should scratch C and not vice versa; further, if a point of A
scratches a plane plate of B, then a point of B should not
penetrate into a plane of A. The necessity of the concurrence
of these presuppositions is not directly manifest. Although
experience has justified them, the method cannot give a
quantitative determination of hardness of any value. Several
attempts have been made to find one. Muschenbroek measured
hardness by the number of blows on a chisel which were
necessary to cut through a small bar of given dimensions of
the material to be examined. About the year 1850 Crace-
Calvert and Johnson measured hardness by the weight which
was necessary to drive a blunt steel cone with a plane end
1.25 mm. in diameter to a depth of 3.5 mm. into the given
material in half an hour. According to a book published in
1865,¹ Hugueny measured the same property by the weight
necessary to drive a perfectly determinate point 0.1 mm. deep
into the material. More recent attempts at a definition I
have not met with. To all these attempts we may urge the
following objections: (1) The measure obtained is not only not
absolute, since a harder body is essential for the determination,
but it is also entirely dependent on a point selected at random.
From the results obtained we can draw no conclusions at all
1 F. Hugueny, Recherches expérimentales sur la dureté des corps.